Search

Lower tropospheric thermal structure greatly affects atmospheric boundary-layer (ABL) stability and mixing processes with the free troposphere. In particular, in polluted urban zones, ABL stratification becomes a key variable in air quality research. This study focuses on generating a climatology (1990–2017) of the seasonal variability of ABL thermal structure in Mexico City by way of radiosonde analysis. Thermal inversion intensity and frequency are shown to be greater during winter and spring, a behaviour which coincides with greater pollutant concentrations. Higher concentrations are found during the dry season (November to May) than during the rainy months. In addition, significantly higher than normal surface pollutant concentrations are found on days with simple thermal inversion layers as well as during multilayer inversion days. Furthermore, stable layers, determined by potential temperature, are found throughout the year but more frequently during winter, whereas stable layers based on the virtual potential temperature prevail all year. In regions of complex terrain, such multiple stable layers have also been identified by previous authors. Additionally, the most unstable surface layers (in which the bulk Richardson number ( $${Ri}_{\mathrm {B}}$$ ) is small) develop during the rainy season, whereas during winter there are more levels in the vertical column with higher $${Ri}_{\mathrm {B}}$$ values. Although the Mexico City ABL and pollution episodes have been widely studied, this represents the first long-term investigation to consider the thermal stability of the ABL. Therefore, the present study provides a baseline for further research employing different observational techniques and high-resolution numerical models.

We evaluated the performance of the Weather Research and Forecasting Model in simulating the boundary-layer structure at an urban site in Seoul on two clear summer days against observations made using a ceilometer, a Doppler wind lidar, and a microwave radiometer. The planetary boundary-layer height (PBLH) was estimated from two different methods using observations: the ceilometer-based method (CBM) and bulk Richardson number method (BRM). The maximum PBLH was well captured by the model but PBLH was underestimated in the late afternoon and evening. To examine the cause for underestimation of PBLH in the evening, we compared the wind and virtual potential temperature structure between the simulation and observations. The model captured the timing of the sea breeze well, but it considerably overestimated the intensity of the simulated sea breeze, resulting in an overestimated cold advection by a sea breeze. The effect of the overestimated cold advection on evening PBLH was greater when the sea breeze arrived in the late afternoon and hence the vertical extent of the sea breeze was shallow. This study underscores the importance of accurately simulating the sea breeze for PBLH prediction in the evening, over the inland urban areas under sea breeze penetration.

Entrainment of density flows is a key parameter in constructing predictive models of global climate, ocean flows, and turbidity currents. Our numerical experiment, which included 10 subaqueous dilu...

An internal wave is a propagating disturbance within a stable density-stratified fluid. The internal seiche amplitude is often estimated through theories that describe the amplitude growth based on the Bulk Richardson number (Ri). However, most theoretical formulations neglect secondary effects that may influence the evolution of internal seiches. Since these waves have been pointed out as the most important process of vertical mixing, influencing the biogeochemical fluxes in stratified basins, the wrong estimation may have several impacts on the prediction of the system dynamics. This research paid particular attention to the importance of secondary effects that may play a major role on the basin-scale internal wave amplitude, especially related to the interaction between internal waves and lake boundaries, internal wave depth, and mixing processes due to turbulence. Based on a set of methods, which include auto- and cross-correlations, spectral analysis, and mathematical models, we analyzed the effect of total water depth, wind-resonance, and higher vertical modes on the amplitude growth. We based our analysis on underwater temperature measurements and meteorological data obtained from two small thermally-stratified basins, complemented with numerical simulations. We introduce here a new parametrization which takes into account the total water depth (H), lake length (L), epilimnion thickness ( $$h_e$$ ), as well as the resonance effect. We observed that the rate of amplitude growth decreases compared to linear theory when $$Ri~h_e/L\le 1$$ . In these cases, we suggests that previous theories overestimate the internal seiche amplitude, neglecting the instabilities generated near the wave crest due to weak stability and wave interactions. However, under shallow thermocline conditions, due to extra pressure in the upper layer, the vertical displacement may be higher than that predicted by the linear theory.

Climate models still have deficits in reproducing the surface energy and momentum budgets in Arctic regions. One of the reasons is that currently used transfer coefficients occurring in parameterizations of the turbulent fluxes are based on stability functions derived from measurements over land and not over sea ice. An improved parameterization is developed using the Monin–Obukhov similarity theory (MOST) and corresponding stability functions that reproduce measurements over sea ice obtained during the Surface Heat Budget of the Arctic Ocean (SHEBA) campaign. The new stability functions for the stable surface layer represent a modification of earlier ones also based on SHEBA measurements. It is shown that the new functions are superior to the former ones with respect to the representation of the measured relationship between the MOST stability parameter and the bulk Richardson number. Nevertheless, the functions fulfill the same criteria of applicability as the earlier functions and contain, as an extension, a dependence on the neutral-limit turbulent Prandtl number. Applying the new functions we develop an efficient noniterative parameterization of the near-surface turbulent fluxes of momentum and heat with transfer coefficients as a function of the bulk Richardson number (Rib) and roughness parameters. A hierarchy of transfer coefficients is recommended for weather and climate models. They agree better with SHEBA data for strong stability (Rib > 0.1) than previous parameterizations and they agree well with those based on the Businger–Dyer functions in the range Rib ≤ 0.1.

Thunderstorm overshooting is rare but not an unusual phenomenon in a metropolitan of India, Kolkata (22.57° N; 88.36° E) during the pre-monsoon months (April–May). An attempt is made in this study to identify the important parameters differentiating the thunderstorms in overshooting and non-overshooting categories through data analytics from 2000 to 2015. The present investigation on parametric classification would facilitate in estimating the predictability of thunderstorms with overshooting which subsequently might assist in operational forecast of thunderstorm severity over Kolkata. The altitudes of lifting condensation level (LCL), wind shear, bulk Richardson number (BRN), gust speed, boundary layer characteristics and their correlation with thunderstorm cloud top height (CTH) and also their variation and distribution during overshooting (OTS) and non-overshooting (TS) thunderstorms are analyzed in this study. The result depicts that over Kolkata the intensity of storms during OTS is higher than during TS though the frequency of OTS is less than that of TS. The results further show that the potential temperature (θ), equivalent potential temperature (θe), mixing ratio (es) in the boundary layer, convective available potential energy, convective inhibition energy, BRN and gust speed play significant roles in regulating the CTH during OTS and TS thunderstorms over Kolkata.

Four cases of an overlying inversion imposed on a stable boundary layer are investigated, extending the earlier work of Hancock and Hayden (Boundary-Layer Meteorol 168:29–57, 2018), where no inversion was imposed. The inversion is imposed to one or other of two depths within the layer: midway or deep. Four cases of changed surface condition are also investigated, and it is seen that the surface and imposed conditions behave independently. A change of imposed inversion condition leaves the bottom 1/3 of the layer almost completely unaffected; a change of the surface condition leaves the top 2/3 unaffected. Comparisons are made against two sets of local-scaling systems over the full height of the boundary layer. Both show some influence of the inversion condition. The surface heat flux and the reduction in surface shear stress, and hence the ratio of the boundary-layer height to surface Obukhov length, are determined by the temperature difference across the surface layer (not the whole layer), bringing all cases together in single correlations as functions of a surface-layer bulk Richardson number.

Diurnal variations in the planetary boundary layer height (PBLH) at different latitudes over different surface characteristics are described, based on 45 years (1973−2017) of radiosonde observations. The PBLH is determined from the radiosonde data by the bulk Richardson number (BRN) method and verified by the parcel method and the potential temperature gradient method. In general, the BRN method is able to represent the height of the convective boundary layer (BL) and neutral residual layer cases but has relatively large uncertainty in the stable BL cases. The diurnal cycle of the PBLH over land is quite different from the cycle over ocean, as are their seasonal variations. For stations over land, the PBLH shows an apparent diurnal cycle, with a distinct maximum around 15:00 LT, and seasonal variation, with higher values in summer. Compared with the PBLH over land, over oceans the PBLH diurnal cycles are quite mild, the PBLHs are much lower, and the seasonal changes are less pronounced. The seasonal variations in the median PBLH diurnal cycle are positively correlated with the near-surface temperature and negatively correlated with the near-surface relative humidity. Finally, although at most latitudes the daytime PBLH exhibits, over these 45 years, a statistically significant increasing trend at most hours between 12:00 LT and 18:00 LT over both land and ocean, there is no significant trend over either land or ocean in the nighttime PBLH for almost all the studied latitudes.

Atmospheric stability has a significant effect on wind shear and turbulence intensity, and these variables, in turn, have a direct impact on wind power production and loads on wind turbines. It is therefore important to know how to characterise atmospheric stability in order to make better energy yield estimation in a wind farm. Based on the research-grade meteorological mast at Alaiz (CENER's test site in Navarre, Spain) named MP5, this work compares and evaluates different instrument set-ups and methodologies for stability characterisation, namely the Obukhov parameter, measured with a sonic anemometer, and the bulk Richardson number based on two temperature and one wind speed measurement. The methods are examined considering their theoretical background, implementation complexity, instrumentation requirements, and practical use in connection to wind energy applications. The sonic method provides a more precise local measurement of stability while the bulk Richardson is a simpler, robust and cost-effective technique to implement in wind assessment campaigns. Using the sonic method as a benchmark, it is shown that to obtain reliable bulk Richardson measurements in onshore sites it is necessary to install one of the temperature sensors close to the ground where the temperature gradient is stronger.

Ceilometer measurements of aerosol backscatter profiles have been widely used to provide continuous PBLHT estimations. To investigate the robustness of ceilometer-estimated PBLHT under different atmospheric conditions, we compared ceilometer- and radiosonde-estimated PBLHTs using long term U.S. Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) ceilometer and balloon-borne sounding data at three ARM fixed-location atmospheric observatories and from three ARM mobile observatories deployed around the world for various field campaigns, which cover from Tropics to Polar regions and over both ocean and land surfaces. Statistical comparisons of ceilometer-estimated PBLHTs from the Vaisala CL31 ceilometer data with radiosonde-estimated PBLHTs from the ARM PBLHT-SONDE Value-added Product (VAP) are performed under different atmospheric conditions including stable and unstable atmospheric boundary layer, low-level cloud-free, and cloudy conditions at these ARM observatories. Under unstable atmospheric boundary layer conditions, good comparisons are found between ceilometer- and radiosonde-estimated PBLHTs at ARM low- and mid-latitude land observatories. However, it is still challenging to obtain reliable PBLHT estimations over ocean surfaces even using radiosonde data. Under stable atmospheric boundary layer conditions, ceilometer- and radiosonde-estimated PBLHTs have weak correlations. Among different PBLHT estimations utilizing the Heffter, the Liu-Liang, and the bulk Richardson number methods in the ARM PBLHT-SONDE VAP, ceilometer-estimated PBLHTs have better comparisons with the Liu-Liang method under unstable and with the bulk Richardson number method under stable atmospheric boundary layer conditions.

Publisher Copyright: © Copyright © 2021 Huo, Wang, Paasonen, Liu, Tang, Ma, Petaja, Kerminen and Kulmala. Boundary layer height (BLH) is an important parameter in climatology and air pollution research, especially in urban city. We calculated the BLH with a bulk Richardson number (Ri) method over urban cities of China during 1980–2018 using European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-interim data after carefully validation with sounding data obtained from two meteorology stations in eastern China during 2010–2018. The values of BLH between these two types of data have correlation coefficients in the range of 0.65–0.87, which indicates that it is reasonable to analyze long-term trends of the BLH from ERA data sets. Using ERA-interim calculated BLH, we found that there is an increasing trend in the daytime BLH in most cities of eastern China, particularly during the spring season. A correlation analysis between the BLH and temperature, wind speed, relative humidity and visibility revealed that the variability in meteorological parameters, as well as in aerosol concentrations over highly polluted eastern China, play important roles in the development of the BLH.

An inflow generation method for large-eddy simulations of wall-bounded turbulent flows is presented. The method builds upon the work of Munoz-Esparza et al. (“A Stochastic Perturbation Method to Ge...

The calculation of the near-surface turbulent fluxes of energy and momentum in climate and weather prediction models requires transfer coefficients. Currently used parametrizations of these coefficients are based on stability functions derived from measurements over land and not over sea ice. However, recently, a non-iterative parametrization has been proposed by Gryanik and Lüpkes (2018), which can be applied to climate and weather prediction models as well but uses stability functions of Grachev et al. (2007). These functions had been obtained from measurements during the Surface Heat Budget over the Arctic Ocean campaign (SHEBA) and thus from measurements over sea ice. A drawback of the scheme of Gryanik and Lüpkes (2018) is that there is still some complexity due to the complexity of the SHEBA based functions.Thus new stability functions are proposed for the stable boundary layer, which are also based on the SHEBA measurements but avoid the complexity. It is shown that the new functions are superior to the former ones with respect to the representation of the measured relationship between the Obukhov length and the bulk Richardson number. Moreover, the resulting transfer coefficients agree slightly better with the SHEBA observations in the very stable range. Nevertheless, the functions fulfill the same criteria of applicability as the earlier functions and contain furthermore as an extension a dependence on the neutral Prandtl number. Applying the new functions, an efficient non-iterative parametrization of the near-surface turbulent fluxes of momentum and heat is developed where transfer coefficients result as a function of the bulk Richardson number (Rib) and roughness parameters. The new transfer coefficients, which are recommended for weather and climate models, agree well with the SHEBA data in a large range of stability (0< Ribb ReferencesGrachev A.A., Andreas E.L, Fairall C.W., Guest P.S., Persson POG (2007) Boundary-Layer Meteorol., 124, 315–333.Gryanik, V.M. and Lüpkes C. (2018) An Efficient Non-iterative Bulk Parametrization of Surface Fluxes for Stable Atmospheric Conditions Over Polar Sea-Ice,Boundary-Layer Meteorol 166:301-325

s The release of airborne hazardous substances in the urban roughness sublayer (RSL) is a risk to human health. The atmospheric dispersion of these materials should be contained to mitigate their adverse consequences. This study investigates the effects of atmospheric stability on the air, heat, and pollutant transport within RSL by a validated 3-D RANS code. A building morphology with height variance is proposed for better representing the real urban environment and characterizing the complex interactions between the roughness elements and the flow regimes. The thermal stratification stability test subject to the ground-inflow temperature difference is extended to span from strongly unstable to moderately stable. The quantitative indicators, including air exchange rate, heat removal rate, pollutant removal rate, heat transfer coefficient, and pollutant transfer coefficient, are introduced and analyzed. The correlations between indicators and thermal stabilities are established, which provides explicit expressions to describe the influence of the changing bulk Richardson number (Rb). Results show that the design of height-variance elements enables a stronger lateral momentum towards the target street canyon, which suppresses the spanwise dispersion of pollutants. The discussions upon heat and pollutant transport based on stability categories show a high Rb-dependence of heat/mass transfer efficiency. The stability threshold is demonstrated to be Rb ≈ 0.7, where the flow speed near the ground approaches zero. As a result, the high temperature gradient is formed and acts as positive feedback to facilitate a more stratified condition. The accurate and rational correlations obtained in this study will save the computational cost considerably for further research. Also, the available results will be a reference for environmentally friendly designs.

The objective of this chapter is to perform laboratory and direct numerical modeling of turbulent wind over water surface under stable stratification conditions. Laboratory and numerical experiments are performed under the same bulk Reynolds and Richardson numbers which allow a direct comparison between the measurements and calculations. The laboratory experiments are performed in a wind-wave flume on the basis of a thermostratified tank facility at IAP RAS. A sufficiently strong stable stratification (with the air–water temperature difference of up to 18 K) and a comparatively large bulk Richardson number (up to Ri ≈ 0.04) in the experiment are created by heating the incoming air flow while maintaining a relatively low wind speed (up to 3 m/s) and the corresponding bulk Reynolds number up to Re ≈ 60000. The air velocity field is retrieved by employing both contact (Pitot tube) and PIV methods, and the air temperature profile is measured simultaneously by a set of contact probes. The same bulk Ri and Re are prescribed in direct numerical simulation where turbulent Couette flow is considered as a model of the near water constant stress atmospheric boundary layer. The mean velocity and temperature profiles obtained in our laboratory and numerical experiments agree well and also are well predicted by the Monin–Obukhov similarity theory. The results show that sufficiently strong stratification, although allowing a statistically stationary turbulent regime, leads to a drastic reduction of both turbulent momentum and heat fluxes. Under this regime, the flow turbulent Reynolds number (based on the Obukhov length scale and friction velocity) is found to be in agreement with known criteria characterizing stationary strongly stratified turbulence.

Atmospheric flow and temperature dynamics in the urban roughness sublayer exhibit numerous complexities that cannot all be investigated using models or scaled-down experiments, thus these complexities necessitate careful field observations. Such dynamics were studied under a comprehensive set of wind directions, wind speeds, and thermal stability conditions in a field campaign held in Guelph, Ontario, Canada, from 13th to 25th of August 2017. The urban site was a quasi-two-dimensional canyon with unit canyon aspect ratio. Beside characterizing thermal stability, inertial effects, urban heat island intensity, and mean properties of the atmosphere, the turbulence statistics were studied carefully as functions of roof-level wind angle, diurnal time, the building Reynolds number, or the bulk Richardson number. Turbulence statistics in the vertical direction were observed to be influenced by local conditions, such as flow properties and nearby surface temperatures. These statistics also indicated presence of small integral lengthscales and short integral timescales. On the other hand, turbulence statistics in the horizontal directions were influenced by non-local conditions, such as horizontal heterogeneity in heating or urban morphology. These statistics indicated presence of large integral lengthscales and long integral timescales. In addition, a rigorous scaling analysis was performed to seek significant correlations between turbulence statistics and other known flow variables both locally or as measured at a nearby non-urban rural station. Variances scaled more successfully to mean quantities than covariances (Reynolds stresses and turbulence kinematic heat fluxes). In addition, the statistics in the vertical direction scaled more successfully compared to horizontal directions. Statistics in the horizontal directions, particularly in the along-canyon axis direction, were poorly scaled, suggesting presence of unorganized and irregular turbulence structures influenced by non-local conditions. Temperature difference between the atmosphere and nearby surfaces as well as measured velocity scales showed to scale vertical heat fluxes successfully.

We analyze Uruguyan measurements, focusing on gusts at turbine hub height. Large gusts, exceeding 15 m/s, are observed to occur when the surface layer (as assessed by the bulk Richardson number R i ) is neutral, and are uncommon when the layer is stable or even unstable. Gust factors (the ratio of the gusts to the mean winds) are inversely related to the mean winds but increase as the atmosphere becomes more unstable. Numerical simulations using different planetary boundary layer (PBL) schemes and mesoscale grid resolutions are employed in the development of a gust parameterization (GP) utilizing forecasts of surface layer R i and winds above hub height. The GP, which provides gust factors to be applied to predicted turbine-level winds, provides higher skill at relatively coarser resolution than a simpler algorithm based solely on surface layer information, although its success is strongly dependent on the PBL and surface layer schemes selected.

Stratified flow in nocturnal boundary layers is studied using direct numerical simulation (DNS) of the Ekman layer, a model problem that is useful to understand atmospheric boundary-layer (ABL) turbulence. A stabilizing buoyancy flux is applied for a finite time to a neutral Ekman layer. Based on previous studies and the simulations conducted here, the choice of $L_{\mathit{cri}}^{+}=Lu_{\ast }/\unicode[STIX]{x1D708}\approx 700$ ($L$ is the Obukhov length scale and $u_{\ast }$ is the friction velocity) provides a cooling flux that is sufficiently strong to cause the initial collapse of turbulence. The turbulent kinetic energy decays over a time scale of $4.06L/u_{\ast }$ during the collapse. The simulations suggest that imposing $L_{\mathit{cri}}^{+}\approx 700$ on the neutral Ekman layer results in turbulence collapse during the initial transient, independent of Reynolds number, $Re_{\ast }$. However, the long-time state of the flow, i.e. turbulent with spatial intermittency or non-turbulent, is found to depend on the initial value of $Re_{\ast }$ since the cooling flux and resultant stratification increase with $Re_{\ast }$ for a given $L^{+}$. The lower-$Re_{\ast }$ cases have sustained turbulence with shear and stratification profiles that evolve in a manner such that the gradient Richardson number, $Ri_{g}$, in the near-surface layer, including the low-level jet, remains subcritical. The highest $Re_{\ast }$ case has supercritical $Ri_{g}$ in the low-level jet and turbulence does not recover. A theoretical discussion is performed to infer that the bulk Richardson number, $Ri_{b}$, is more suitable than $L^{+}$ to determine the fate of stratified Ekman layers at late time. DNS results support the implications of $Ri_{b}$ for the effect of initial $Re_{\ast }$ and $L^{+}$ on the flow.

For the moderate-to-strong anisotropic turbulence, the previously derived turbulence refractive-index fluctuations spectral models assumed the circular symmetric distribution of turbulence cells in the plane orthogonal to the direction of propagation. For the real anisotropic turbulence, this kind of distribution is very special and not always fit the real turbulence. In this work, to describe the general distribution of turbulence cells in the moderate-to-strong anisotropic turbulence, new turbulence refractive-index fluctuations spectral model is derived with the extended Rytov approximation theory. Then, it is applied to investigate the irradiance scintillation index for optical plane and spherical waves propagating through moderate-to-strong anisotropic turbulence. Two anisotropic factors are introduced to describe the asymmetric distribution of turbulence cells. Compared with the Kolmogorov turbulence, the general spectral power law in the range of 3–4 is also considered. The derived irradiance scintillation index models of optical waves are applicable in a wide range of turbulence strength. In the special case of weak anisotropic turbulence, they have good consistency with those derived in weak anisotropic turbulence.

This study conducted meteorological simulations in northern Colombia by analyzing different planetary boundary layer (PBL) schemes available in the numerical Weather Research and Forecasting (WRF) model. The study area included three nested domains with horizontal resolutions of 18 km, 6 km, and 2 km, with 38 vertical levels. The evolution and structure of the PBL were analyzed during the driest months (March, April, and May 2016) and in regions with the highest particulate matter concentrations. Sensitivity analysis of the WRF model was performed with two local and two non-local PBL schemes. The results were validated using observations of the surface air temperature, relative humidity, and surface wind speed collected from three meteorological stations in the area. The PBL heights were experimentally determined using radiosonde data provided by a station located in the center of the study area. Variations in PBL heights were estimated using linear regression methods and minimization of statistical errors for the bulk Richardson number, as well as analysis of vertical temperature and wind profiles. The WRF model reliably reproduced the daily values and diurnal cycles of temperature, relative humidity, and wind speed within the PBL and accounted for the influence of topography and sea breezes. Horizontal heat advection dominates the upwelling of air masses when sea breezes are active. The onshore wind direction starts to change from east to northwest, implying a decay in the land breeze regime. All schemes overestimate the mixing height and tend to underestimate surface air temperature values at night. All show wetter conditions and underestimate wind speed. Although the non-local Yonsei University (YSU) scheme shows the best performance, it also shows the largest sources of errors when determining the behavior of the surface layer during stable conditions. Relative humidity and wind speed estimates provided by the local Mellor‐Yamada‐Nakanishi‐Niino (MYNN) scheme were closer to those recorded at the meteorological stations.

The availability of 5-year time series of velocity and temperature data from two sonic anemometers installed at Jang Bogo Station, Antarctica, allowed a systematic investigation of the turbulence features in a stable layer affected by submeso motions and characterized by the vertical divergence of some second-order moments for a large fraction of time (quite a non-ideal surface layer). The investigation of the effect of the averaging time interval on the statistics of the second-order moments showed that this is greater for the variances of the velocity components with respect to that for the vertical fluxes. This corresponds to a greater contribution from low-frequency motions. The turbulence statistics were investigated and compared with current literature results in terms of vertical structure, share of energy between horizontal and vertical components, skewness of the vertical velocity and turbulent velocities. As a general result, all the normalized second-order moments show a clear change passing from neutral to stable conditions, passing through the range of bulk Richardson number equal to 0.1–1.

The seasonal thermocline in shallow shelf seas acts as a natural barrier for boundary-generated turbulence, damping scalar transport to the upper regions of the water column, and controlling primary production to a certain extent. To better understand turbulence and mixing conditions within the thermocline, two unique 12- and 17-day datasets with continuous measurements of the dissipation rate of turbulent kinetic energy (e) collected by autonomous underwater gliders under stratified to well-mixed conditions are presented. A highly intermittent e signal was observed in the stratified thermocline region, which was mainly characterized by quiescent flow (turbulent activity index below 7). The rate of diapycnal mixing remained relatively constant for the majority of the time with peaks of higher fluxes that were responsible for much of the increase in bottom mixed layer temperature. The water column stayed predominantly strongly stratified, with a bulk Richardson number across the thermocline well above 2. A positive relationship between the intensity of turbulence, shear and stratification was found. The trend between turbulence levels and the bulk Richardson number was relatively weak, but suggests that e increases as the bulk Richardson number approaches 1. The results also highlight the interpretation difficulties in both quantifying turbulent thermocline fluxes, as well as the responsible mechanisms.

The paper investigates buoyancy impact on the vertical flow over a backward-facing step at low Prandtl number by Direct Numerical Simulation. In particular, the very low Prandtl number of liquid sodium, 0.0088, is considered in the regime of mixed convection, i.e. for Richardson numbers below unity. The effects of buoyancy on mean flow, heat transfer and turbulence are assessed. Buoyancy is found to attenuate recirculation and, consequently, increase heat transfer. Turbulence is decreased in the attached boundary layer for moderate buoyancy impact but surpasses the levels found in forced convection at the largest Richardson number investigated. Beyond the mean flow and second moments, the budgets of turbulent kinetic energy, Reynolds shear stress, temperature variance, and turbulent heat flux components are studied and related to the alterations in the mean field quantities. Due to scale separation, production and dissipation nearly balance for temperature variance while this is not the case for turbulent kinetic energy. Similar findings for the turbulent heat fluxes show that the correlation between temperature and pressure gradient is the most important contribution to the budget aside from production and dissipation. In addition to the physical insight into this flow, the data presented may be used for the validation and improvement of turbulence models for liquid metal flows.

In climate and weather prediction models the near-surface turbulent fluxes of heat and momentum and related transfer coefficients are usually parametrized on the basis of Monin–Obukhov similarity theory (MOST). To avoid iteration, required for the numerical solution of the MOST equations, many models apply parametrizations of the transfer coefficients based on an approach relating these coefficients to the bulk Richardson number $$Ri_{b}$$ . However, the parametrizations that are presently used in most climate models are valid only for weaker stability and larger surface roughnesses than those documented during the Surface Heat Budget of the Arctic Ocean campaign (SHEBA). The latter delivered a well-accepted set of turbulence data in the stable surface layer over polar sea-ice. Using stability functions based on the SHEBA data, we solve the MOST equations applying a new semi-analytic approach that results in transfer coefficients as a function of $$Ri_{b}$$ and roughness lengths for momentum and heat. It is shown that the new coefficients reproduce the coefficients obtained by the numerical iterative method with a good accuracy in the most relevant range of stability and roughness lengths. For small $$Ri_{b}$$ , the new bulk transfer coefficients are similar to the traditional coefficients, but for large $$Ri_{b}$$ they are much smaller than currently used coefficients. Finally, a possible adjustment of the latter and the implementation of the new proposed parametrizations in models are discussed.

Separating “shear induced turbulence” and “bubble induced turbulence” contributions in gas-liquid bubbly flows is still experimentally difficult to characterize. Numerical simulations were investigated in order to isolate the turbulence produced by the mean velocity gradient of the continuous phase which comprises the turbulence generated in bubbles wakes, from the pseudo-turbulence induced by the bubbles’ displacements. Simulations of the uniformly sheared flow over an isolated sphere are carried out to superimpose the homogeneous turbulence with constant shear at equilibrium conditions with the turbulence produced in the bubble wake. The analyses of the turbulence statistics computed on a control volume whose size is set based on void fractions, for different shear rates, are carried out in order to assess the modelling of the transport equation of the “shear induced turbulence”. Simulation results show that for low void fractions, the hypothesis of turbulence equilibrium in the bubble wake is verified in a wide range of shear rate. Numerical results are in satisfactory agreement with the formulations resulting from the reduction of second order turbulence closures in bubbly flow. These formulations are based on a dimensionless number expressed in terms of two time scales which characterizes the bubbles’ effects on turbulence structure in sheared flow.

The Miles–Howard theorem states that a necessary condition for normal-mode instability in parallel, inviscid, steady stratified shear flows is that the minimum gradient Richardson number, $Ri_{g,min}$, is less than $1/4$ somewhere in the flow. However, the non-normality of the Navier–Stokes and buoyancy equations may allow for substantial perturbation energy growth at finite times. We calculate numerically the linear optimal perturbations which maximize the perturbation energy gain for a stably stratified shear layer consisting of a hyperbolic tangent velocity distribution with characteristic velocity $U_{0}^{\ast }$ and a uniform stratification with constant buoyancy frequency $N_{0}^{\ast }$. We vary the bulk Richardson number $Ri_{b}=N_{0}^{\ast 2}h^{\ast 2}/U_{0}^{\ast 2}$ (corresponding to $Ri_{g,min}$) between 0.20 and 0.50 and the Reynolds numbers $\mathit{Re}=U_{0}^{\ast }h^{\ast }/\unicode[STIX]{x1D708}^{\ast }$ between 1000 and 8000, with the Prandtl number held fixed at $\mathit{Pr}=1$. We find the transient growth of non-normal perturbations may be sufficient to trigger strongly nonlinear effects and breakdown into small-scale structures, thereby leading to enhanced dissipation and non-trivial modification of the background flow even in flows where $Ri_{g,min}>1/4$. We show that the effects of nonlinearity are more significant for flows with higher $\mathit{Re}$, lower $Ri_{b}$ and higher initial perturbation amplitude $E_{0}$. Enhanced kinetic energy dissipation is observed for higher-$Re$ and lower-$Ri_{b}$ flows, and the mixing efficiency, quantified here by $\unicode[STIX]{x1D700}_{p}/(\unicode[STIX]{x1D700}_{p}+\unicode[STIX]{x1D700}_{k})$ where $\unicode[STIX]{x1D700}_{p}$ is the dissipation rate of density variance and $\unicode[STIX]{x1D700}_{k}$ is the dissipation rate of kinetic energy, is found to be approximately 0.35 for the most strongly nonlinear cases.

A non-iterative analytical scheme is developed for unstable stratification that parametrizes the Monin–Obukhov stability parameter $$\zeta $$ ( $${=}z{/}L$$ , where z is the height above the ground and L is the Obukhov length) in terms of bulk Richardson number ( $$Ri_B$$ ) within the framework of Businger–Dyer type similarity functions. The proposed scheme is valid for a wide range of roughness lengths of heat and momentum. The absolute relative error in the transfer coefficients of heat and momentum is found to be less than 1.5% as compared to those obtained from an iterative scheme for Businger–Dyer type similarity functions. An attempt has been made to extend this scheme to incorporate the similarity functions having a theoretically consistent free convection limit. Further, the performance of the scheme is evaluated using observational data from two different sites. The proposed scheme is simple, non-iterative and relatively more accurate compared to the schemes reported in the literature and can be used as a potential alternative to iterative schemes used in numerical models of the atmosphere.

The mixing properties of statically stable density interfaces subject to imposed vertical shear are studied using direct numerical simulations of stratified plane Couette flow. The simulations are designed to investigate possible self-maintaining mechanisms of sharp density interfaces motivated by Phillips’ argument (Deep-Sea Res., vol. 19, 1972, pp. 79–81) by which layers and interfaces can spontaneously form due to vertical variations of diapycnal flux. At the start of each simulation, a sharp density interface with the same initial thickness is introduced at the midplane between two flat, horizontal walls counter-moving at velocities$\pm U_{w}$. Particular attention is paid to the effects of varying Prandtl number$\mathit{Pr}\equiv \unicode[STIX]{x1D708}/\unicode[STIX]{x1D705}$, where$\unicode[STIX]{x1D708}$and$\unicode[STIX]{x1D705}$are the molecular kinematic viscosity and diffusivity respectively, over two orders of magnitude from 0.7, 7 and 70. Varying$\mathit{Pr}$enables the system to access a considerable range of characteristic turbulent Péclet numbers$\mathit{Pe}_{\ast }\equiv {\mathcal{U}}_{\ast }{\mathcal{L}}_{\ast }/\unicode[STIX]{x1D705}$, where${\mathcal{U}}_{\ast }$and${\mathcal{L}}_{\ast }$are characteristic velocity and length scales, respectively, of the motion which acts to ‘scour’ the density interface. The dynamics of the interface varies with the stability of the interface which is characterised by a bulk Richardson number$\mathit{Ri}\,\equiv \,b_{0}h/U_{w}^{2}$, where$b_{0}$is half the initial buoyancy difference across the interface and$h$is the half-height of the channel. Shear-induced turbulence occurs at small$\mathit{Ri}$, whereas internal waves propagating on the interface dominate at large$\mathit{Ri}$. For a highly stable (i.e. large$\mathit{Ri}$) interface at sufficiently large$\mathit{Pe}_{\ast }$, the complex interfacial dynamics allows the interface to remain sharp. This ‘self-sharpening’ is due to the combined effects of the ‘scouring’ induced by the turbulence external to the interface and comparatively weak molecular diffusion across the core region of the interface. The effective diapycnal diffusivity and irreversible buoyancy flux are quantified in the tracer-based reference coordinate proposed by Winters & D’Asaro (J. Fluid Mech., vol. 317, 1996, pp. 179–193) and Nakamura (J. Atmos. Sci., vol. 53, 1996, pp. 1524–1537), which enables a detailed investigation of the self-sharpening process by analysing the local budget of buoyancy gradient in the reference coordinate. We further discuss the dependence of the effective diffusivity and overall mixing efficiency on the characteristic parameters of the flow, such as the buoyancy Reynolds number and the local gradient Richardson number, and highlight the possible role of the molecular properties of fluids on diapycnal mixing.

This study explores the behavior of the exchange coefficients for wind stress (CD), sensible heat flux (CH), and water vapor flux (CE) as functions of surface wind speed (U10) and atmospheric stability using direct turbulent flux measurements obtained from a platform equipped with fast-response turbulence sensors in a low-to-moderate wind region. Turbulent fluxes are calculated using the eddy-correlation method with extensive observations. The total numbers of quality-controlled 30 min flux runs are 12,240, 5813, and 5637 for estimation of CD, CH, and CE, respectively. When adjusted to neutral stability using the Monin-Obukhov similarity theory (MOST), we found that CDN, CHN, and CEN decrease with neutral-adjusted wind speed when wind speed is less than 5 m/s. CDN is constant over the range 5 m/s 12 m/s. In contrast, CHN and CEN exhibit no clear dependence on wind speed and are generally constant, with mean values of 0.96 × 10−3 and 1.2 × 10−3, respectively. This behavior of neutral exchange coefficients is consistent with the findings of previous studies. We also found that CDN under offshore winds is generally greater than that under onshore wind conditions, which is ascribed to the younger wind waves present due to the shorter fetch in the former case. However, this behavior is not exhibited by CHN or CEN. The original CD, CH, and CE values without MOST adjustment are also investigated to develop a new parameterization based on wind speed and stability. Three stability parameters are tested, including the bulk Richardson number, stability as defined in COARE 3.0, and a simplified Richardson number using the Charnock parameter. This new parameterization is free of MOST and the associated self-correlation. Compared with previous studies and COARE 3.0 results, the new parameterization using the simplified Richardson number performs well, with an increased correlation coefficient and reduction of root-mean-square error and bias.

Observations of the heat flux over the open sea and in the coastal zone are analyzed to reexamine the relation of the heat flux to the air–sea temperature difference and wind speed. The study begins by examining problems with different methods for estimating the air–sea temperature difference. The difference between the air and within-water temperature is found to be most suitable for one dataset, while the difference between the air and the radiometrically measured sea surface temperature must be used for the second dataset. On average, the heat flux is linearly proportional to the product of the air–sea temperature difference and wind speed corresponding to approximately constant transfer coefficient for heat CH. Deviations of the heat flux from this simple relationship were generally weakly related or unrelated to the surface bulk Richardson number Rb, even for the coastal zone site. Similar results are also found for the moisture flux. In contrast to the general success of constant transfer coefficient for heat, CH plotted directly as a function of Rb is systematically related to the square root of Rb. The role of the wind speed as a shared variable between CH and Rb also predicts such a square root dependence, suggesting that the relationship could be largely due to self-correlation, which is also supported by a nominal study of self-correlation. However, confident isolation of the influences of stability, self-correlation, uncertainties in the air–sea temperature difference, and other physics requires more extensive data.

We present the linear stability properties and nonlinear evolution of two-dimensional plane Couette flow for a statically stable Boussinesq three-layer fluid of total depth$2h$between two horizontal plates driven at constant velocity$\pm \unicode[STIX]{x0394}U$. Initially the three layers have equal depth$2h/3$and densities$\unicode[STIX]{x1D70C}_{0}+\unicode[STIX]{x0394}\unicode[STIX]{x1D70C}$,$\unicode[STIX]{x1D70C}_{0}$and$\unicode[STIX]{x1D70C}_{0}-\unicode[STIX]{x0394}\unicode[STIX]{x1D70C}$, such that$\unicode[STIX]{x1D70C}_{0}\gg \unicode[STIX]{x0394}\unicode[STIX]{x1D70C}$. At finite Reynolds and Prandtl number, we demonstrate that this flow is susceptible to two distinct primary linear instabilities for sufficiently large bulk Richardson number$Ri_{B}=g\unicode[STIX]{x0394}\unicode[STIX]{x1D70C}h/(\unicode[STIX]{x1D70C}_{0}\unicode[STIX]{x0394}U^{2})$. For a given bulk Richardson number$Ri_{B}$, the zero phase speed ‘Taylor’ instability is always predicted to have the largest growth rate and to be an inherently two-dimensional instability. An inherently viscous instability, reminiscent of the ‘Holmboe’ instability, is also predicted to have a non-zero growth rate. For flows with Prandtl number$Pr=\unicode[STIX]{x1D708}/\unicode[STIX]{x1D705}=1$, where$\unicode[STIX]{x1D708}$is the kinematic viscosity, and$\unicode[STIX]{x1D705}$is the diffusivity of the density distribution, we find that the most unstable Taylor instability, maximized across wavenumber and$Ri_{B}$, has a (linear) growth rate which is a non-monotonic function of Reynolds number$Re=\unicode[STIX]{x0394}Uh/\unicode[STIX]{x1D708}$, with a global maximum at$Re=700$over 50 % larger than the growth rate as$Re\rightarrow \infty$. In a fully nonlinear evolution of the flows with$Re=700$and$Pr=1$, the two interfaces between the three density layers diffuse more rapidly than the underlying instabilities can grow from small amplitude. Therefore, we investigate numerically the nonlinear evolution of the flow at$Re=600$and$Pr=300$, and at$Re=5000$and$Pr=70$in two-dimensional domains with streamwise extent equal to two wavelengths of the Taylor instability with the largest growth rate. At both sets of parameter values, the primary Taylor instability undergoes a period of identifiable exponential ‘linear’ growth. However, we demonstrate that, unlike the so-called ‘Kelvin–Helmholtz’ instability that it superficially resembles, the Taylor instability’s finite-amplitude state of an elliptical vortex in the middle layer appears not to saturate into a quasiequilibrium state, but is rapidly destroyed by the background shear. The decay process reveals$Re$-dependent secondary processes. For the$Re=600$simulation, this decay allows the development to finite amplitude of the co-existing primary ‘viscous Holmboe wave instability’, which has a substantially smaller linear growth rate. For the$Re=5000$simulation, the Taylor instability decay induces a non-trivial modification of the mean velocity and density distributions, which nonlinearly develops into more classical finite-amplitude Holmboe waves. In both cases, the saturated nonlinear Holmboe waves are robust and long-lived in two-dimensional flow.

As an important parameter that characterizes the structure of Atmospheric boundary layer (ABL), the boundary layer height (BLH) determines the degree of turbulent diffusion and exchange of heat and momentum within ABL. In this paper, synchronized observations of ground-based microwave radiometer (MWR) and radiosonde in Beijing Southern Meteorological Observatory from April 2017 to March 2018 are obtained to estimate BLH, based on the multiple linear regression algorithm and bulk Richardson number method, respectively. The BLHs derived from the two observations are compared and the temporal variation of BLH in Beijing are finally analyzed. Main conclusions are as follows: 1) the BLH retrieved by MWR is higher than that obtained by radiosonde by 157 m on average. The average deviation of BLH between MWR and radiosonde is smaller at 08 Beijing time (BJT) and 20 BJT than at 14 BJT, and the deviation is relatively smaller in spring and summer than other seasons. 2) BLH at 08 BJT is generally lower than that at 14 BJT and 20 BJT from both MWR and radiosonde observations. 3) radiosonde-obtained BLH peaks in the May while MWR-retrieved BLH reaches maximum in January and February. 4) BLH in Beijing at night is relatively low, which reaches the minimum $(\sim 622\mathrm {m}$ on average) around 05 BJT or 06 BJT. BLH gradually increases after 08 BJT and reaches the maximum $( \sim 908\mathrm {m}$ on average) around 15 BJT.

A new parameterization for the estuarine turbulent eddy viscosity coefficient is developed considering the influence of wind forcing and feedback between stratification and shear. The emerging tidally averaged eddy viscosity profile A v T is parameterized as parabolic under well-mixed conditions, and is composed of a skewed-Gaussian-like form for the upper layer, and a parabolic form for the bottom layer under stratified conditions. The precise shape of the profiles depends parametrically on the bottom boundary layer thickness, the bulk Richardson number, and the Wedderburn number. The parameterized A v T profiles show excellent agreement with profiles obtained from numerical models. To explore the importance of vertically varying A v T with regard to exchange processes, an analytical model is designed. This one-dimensional model is based on a balance between frictional forces and pressure gradient. The resulting exchange flow is analyzed over the relevant parameter space that is associated with horizontal and vertical stratification through the bulk Richardson number, and the bi-directional wind stress via the Wedderburn number. Down-estuary wind enhances the up-estuary flow near the bottom and down-estuary flow near the surface driving an exchange flow pattern typically associated with gravitational circulation. Up-estuary wind results in either a two-layer inverted circulation opposing the gravitational circulation, or a three-layer flow that is up-estuarine at the surface with classical two-layer circulation underneath. Three-layer flow emerges with a weak wind. With increasing runoff velocity, three-layer flow transitions to a single layer flow under weak stratification conditions.

International audience; An experimental study conducted in a wind tunnel on the mixing of moist air by a scaled wind turbine is presented. The experimental setupallows us to generate stable stratification conditions with respect to relative humidity and temperature in a closed-loop wind tunnel. The flowand its thermodynamic properties were characterized using a Cobra probe (a multi-hole pitot tube) and a sensor of local temperature and rel-ative humidity, both used simultaneously to obtain vertical profiles. The flow and its stratification were measured downstream of a scaledrotor at two different streamwise distances (1 and 10 rotor diameters) and two Reynolds numbers based on the diameter of the wind turbinerotor (22000 and 44000, respectively). This was then compared to the inflow conditions. The wake mean structure and the humidity andtemperature stratifications of the flow are found to be affected by the presence of the rotor. In particular, the stratification was always smallerone diameter downstream from the model (when compared to the empty test section case), and then was mostly recovered in the far wake(10 diameters downstream). This effect depended not only on the streamwise distance, but also on the Reynolds number of the flow. Finally,the bulk Richardson number R b was found to be an appropriate parameter to quantify this effect.

This research study investigated the three-dimensional nature and characteristics of buoyant thermals in the mixed convection turbulent boundary layer. Thermals were visualized using a multi-plane flow visualization technique. Experiments were performed in a variety of conditions where the bulk Richardson number was varied to cover a range describing both inertia dominant flow ( R i L = 0.05 ) and buoyancy dominant flow ( R i L = 2.0 ). Qualitative results define key interactions between thermals and the adjacent turbulent boundary layer flow. A robust algorithm for automatic thermal detection was developed and validated. This algorithm was then applied to experimental images to detect thermals and facilitate a quantitative analysis on the size and spatial distribution of buoyant thermals. Based on these findings an overall flow structure is proposed featuring convective cell like patterns at high Richardson numbers. A first approximation on the shape of thermals and velocity of key thermofluid interactions between thermals and turbulent boundary layer is made. Results indicate these thermal interactions can exhibit motion substantially different from the surrounding turbulent boundary layer flow.

Air quality forecast systems need reliable and accurate representations of the planetary boundary layer (PBL) to perform well. An important question is how accurately numerical weather prediction models can reproduce conditions in diverse synoptic flow types. Here, observations from the summer 2014 HygrA-CD (Hygroscopic Aerosols to Cloud Droplets) experimental campaign are used to validate simulations from the Weather Research and Forecasting (WRF) model over the complex, urban terrain of the Greater Athens Area. Three typical atmospheric flow types were identified during the 39-day campaign based on 2-day backward trajectories: Continental, Etesians, and Saharan. It is shown that the numerical model simulations differ dramatically depending on the PBL scheme, atmospheric dynamics, and meteorological parameter (e.g., 2-m air temperature). Eight PBL schemes from WRF version 3.4 are tested with daily simulations on an inner domain at 1-km grid spacing. Near-surface observations of 2-m air temperature and relative humidity and 10-m wind speed are collected from multiple meteorological stations. Estimates of the PBL height come from measurements using a multiwavelength Raman lidar, with an adaptive extended Kalman filter technique. Vertical profiles of atmospheric variables are obtained from radiosonde launches, along with PBL heights calculated using bulk Richardson number. Daytime maximum PBL heights ranged from 2.57 km during Etesian flows, to as low as 0.37 km during Saharan flows. The largest differences between model and observations are found with simulated PBL height during Saharan synoptic flows. During the daytime, campaign-averaged near-surface variables show WRF tended to have a cool, moist bias with higher simulated wind speeds than the observations, especially near the coast. It is determined that non-local PBL schemes give the most agreeable solutions when compared with observations.

A simple relation to diagnose the existence of a thermally driven down-valley wind in a shallow (100 m deep) and narrow (1–2 km wide) valley based on routine weather measurements has been determined. The relation is based on a method that has been derived from a forecast verification principle. It consists of optimizing a threshold of permanently measured quantities to nowcast the thermally driven Cadarache (southeastern France) down-valley wind. Three parameters permanently observed at a 110-m-high tower have been examined: the potential temperature difference between the heights of 110 and 2 m, the wind speed at 110 m, and a bulk Richardson number. The thresholds are optimized using the wind observations obtained within the valley during the Katabatic Winds and Stability over Cadarache for the Dispersion of Effluents (KASCADE) field experiment, which was conducted in the winter of 2013. The highest predictability of the down-valley wind at the height of 10 m (correct nowcasting ratio of 0.90) was found for the potential temperature difference at a threshold value of 2.6 K. The applicability of the method to other heights of the down-valley wind (2 and 30 m) and to summer conditions is also demonstrated. This allowed a reconstruction of the climatology of the thermally driven down-valley wind that demonstrates that the wind exists throughout the year and is strongly linked to nighttime duration. This threshold technique will make it possible to forecast the subgrid-scale down-valley wind from operational numerical weather coarse-grid simulations by means of statistical downscaling.

High-resolution observations of velocity, salinity, and turbulence quantities were collected in a salt wedge estuary to quantify the efficiency of stratified mixing in a high-energy environment. During the ebb tide, a midwater column layer of strong shear and stratification developed, exhibiting near-critical gradient Richardson numbers and turbulent kinetic energy (TKE) dissipation rates greater than 10−4 m2 s−3, based on inertial subrange spectra. Collocated estimates of scalar variance dissipation from microconductivity sensors were used to estimate buoyancy flux and the flux Richardson number Rif. The majority of the samples were outside the boundary layer, based on the ratio of Ozmidov and boundary length scales, and had a mean Rif = 0.23 ± 0.01 (dissipation flux coefficient Γ = 0.30 ± 0.02) and a median gradient Richardson number Rig = 0.25. The boundary-influenced subset of the data had decreased efficiency, with Rif = 0.17 ± 0.02 (Γ = 0.20 ± 0.03) and median Rig = 0.16. The relationship between Rif and Rig was consistent with a turbulent Prandtl number of 1. Acoustic backscatter imagery revealed coherent braids in the mixing layer during the early ebb and a transition to more homogeneous turbulence in the midebb. A temporal trend in efficiency was also visible, with higher efficiency in the early ebb and lower efficiency in the late ebb when the bottom boundary layer had greater influence on the flow. These findings show that mixing efficiency of turbulence in a continuously forced, energetic, free shear layer can be significantly greater than the broadly cited upper bound from Osborn of 0.15–0.17.

In this work, the coupled momentum and energy equations have been solved to elucidate the effect of aiding-buoyancy on the laminar mixed-convection from a spheroidal particle in power-law media over wide ranges of the pertinent parameters: Richardson number, 0≤Ri≤5; Reynolds number, 1≤Re≤100; Prandtl number, 1≤Pr≤100; power-law index, 0.3≤n≤1.8, and aspect ratio, 0.2≤e≤5 for the case of constant thermo-physical properties. New results for the velocity and temperature fields are discussed in terms of the streamline and isotherm contours, surface pressure and vorticity contours, drag coefficient, local and surface averaged Nusselt number. The effect of particle shape on the flow is seen to be more pronounced in the case of oblates (e 1). The propensity for wake formation reduces with the rising values of power-law index, Richardson number and slenderness of the body shape (e > 1). Also, the drag coefficient is seen to increase with the Richardson number and power-law index. All else being equal, the Nusselt number shows a positive dependence on the Richardson number and Reynolds number and an inverse dependence on the power-law index and aspect ratio of the spheroid. Limited results were also obtained by considering the exponential temperature dependence of the power-law consistency index. This factor can increase the values of the average Nusselt number by up to ~10-12% with reference to the corresponding values for the case of the constant thermo-physical properties under otherwise identical conditions. Finally, the present values of the Nusselt number have been consolidated in the form of Colburn j-factor as a function of the modified Reynolds and Prandtl numbers for each value of the aspect ratio (e). The effect of the temperature dependent viscosity is included in this correlation in terms of a multiplication factor.

Planetary boundary layer (PBL) processes are important for the estimation of surface-atmosphere exchanges that impact global climate. One way of characterizing the strength of these processes is the PBL depth. In the Goddard Earth Observing System (GEOS-5) atmospheric general circulation model, the PBL depth is also used in calculating the turbulent length scale, which, in turn, is used in estimating the turbulence and vertical mixing within the model. Therefore, changing the PBL depth definition directly affects the model climate. This study evaluates the climatological model response of two long-term simulations using different PBL depth definitions. The first definition is based on a bulk Richardson number; the second uses a combination of the same bulk Richardson number definition over land plus a definition based on the turbulent eddy diffusion coefficient over water. The two simulations produce different spatiotemporal patterns of temperature, specific humidity, and wind speed related to the differences in turbulence. The largest differences, as expected, are present over water. Due to differences in atmospheric stability, the relationship between the two PBL depth estimates differ among the majority of the oceans and off the west coasts of continents, affecting the climatic response. Due to its optimization of the climatic response while maintaining a realistic diurnal cycle of PBL depth, the mixed PBL depth configuration is preferred.

The Stokes drift of surface waves significantly modifies the upper-ocean turbulence because of the Craik–Leibovich vortex force (Langmuir turbulence). Under tropical cyclones the contribution of the surface waves varies significantly depending on complex wind and wave conditions. Therefore, turbulence closure models used in ocean models need to explicitly include the sea state–dependent impacts of the Langmuir turbulence. In this study, the K-profile parameterization (KPP) first-moment turbulence closure model is modified to include the explicit Langmuir turbulence effect, and its performance is tested against equivalent large-eddy simulation (LES) experiments under tropical cyclone conditions. First, the KPP model is retuned to reproduce LES results without Langmuir turbulence to eliminate implicit Langmuir turbulence effects included in the standard KPP model. Next, the Lagrangian currents are used in place of the Eulerian currents in the KPP equations that calculate the bulk Richardson number and the vertical turbulent momentum flux. Finally, an enhancement to the turbulent mixing is introduced as a function of the nondimensional turbulent Langmuir number. The retuned KPP, with the Lagrangian currents replacing the Eulerian currents and the turbulent mixing enhanced, significantly improves prediction of upper-ocean temperature and currents compared to the standard (unmodified) KPP model under tropical cyclones and shows improvements over the standard KPP at constant moderate winds (10 m s−1).

The stability of stratified shear flows with multilayered density distributions and monotonic velocity profiles without inflection points is studied using a class of flows of an ideal incompressible three–layer medium as a model. The flow velocity Vx=U(z) is assumed to be increasing from zero at the bottom (z=0) to its maximum value U0 (when z→∞), with d2U/dz2

Planetary boundary layer (PBL) height plays a significant role in climate modeling, weather forecasting, air quality prediction, and pollution transport processes. This study examined the climatology of PBL-associated meteorological parameters over the Korean peninsula and surrounding sea using data from the ERA5 dataset produced by the European Centre for Medium-range Weather Forecasts (ECMWF). The data covered the period from 2008 to 2017. The bulk Richardson number methodology was used to determine the PBL height (PBLH). The PBLH obtained from the ERA5 data agreed well with that derived from sounding and Global Positioning System Radio Occultation datasets. Significant diurnal and seasonal variability in PBLH was observed. The PBLH increases from morning to late afternoon, decreases in the evening, and is lowest at night. It is high in the summer, lower in spring and autumn, and lowest in winter. The variability of the PBLH with respect to temperature, relative humidity, surface pressure, wind speed, lower tropospheric stability, soil moisture, and surface fluxes was also examined. The growth of the PBLH was high in the spring and in southern regions due to the low soil moisture content of the surface. A high PBLH pattern is evident in high-elevation regions. Increasing trends of the surface temperature and accordingly PBLH were observed from 2008 to 2017.

Amplitude modulation is assumed to be a major annoyance factor of wind turbine sound. However, studies on the generation of amplitude modulation and the impact of atmospheric conditions on amplitude modulation are limited, especially in cold climates. Long-term acoustic and meteorological measurements in the vicinity of a wind farm in northern Sweden show a dependence of the occurrence of amplitude modulation on wind direction and atmospheric stability. The occurrence of amplitude modulation is highest for crosswinds from southwest, compared with the other wind directions. Moreover, the occurrence of amplitude modulation is clearly linked to atmospheric stability and highest for very stable conditions. The impact of atmospheric stability is supported by analyses of wind shear, the wind speed gradient close to the surface and the bulk Richardson number. Amplitude modulation is more likely during winter than during summer and more likely during night and early morning than during noon and early afternoon.

The role of thermally-driven local downslope or katabatic flows in the dynamics and turbulent features of the stable boundary layer (SBL) is investigated using observations. Measurements are carried out in a relatively flat area 2-km away from the steep slopes of the Guadarrama Mountain Range (Spain). Forty katabatic events are selected from an observational database spanning the 2017-summer period, by using an objective and systematic algorithm that is able to account for local and synoptic forcings. We subsequently classify the katabatic events into weak, moderate and intense according to the observed maximum wind speed. This classification enables us to contrast the main differences in dynamics and thermal structure. We find that the stronger katabatic events are associated with an earlier onset time of these flows. We relate it to very low soil-moisture values ( 3 m −3 , i.e. smaller than the median during the analysed period) and a weak synoptic wind ( V 850 −1 ) having the same direction as the katabatic. The relative flatness of the area favours the formation of very stable boundary layers characterized by a longwave radiative cooling of around 60–70 W m −2 and very weak turbulence (friction velocity ( u * ) −1 ). They occur when katabatics are weak, and are occasionally associated with the formation of skin flows, that are manifested as weak jets ( U −1 ) at 3 m. Intense katabatics, instead, are characterised by a strong and increasing bulk shear (the maximum u * is close to 1 m s −1 ) that avoids the development of the surface-based thermal inversion, giving rise to the so-called weakly stable boundary layer. We identify the transition between the two regimes for a threshold katabatic wind speed of around 1.5 m s −1 , in agreement with the hockey-stick transition hypothesis. Our analysis is extended by calculating non-dimensional numbers to characterize the transition: the shear capacity, the bulk Richardson number and z/L . On the other hand, by inspecting individual weak and intense events, we further explore the interaction between katabatic flows and turbulence, and the impact on CO 2 concentration. By relating the dynamics of the two regimes with the CO 2 budget, we are able to estimate the contribution of the different terms. For the intense event, indeed, we infer a horizontal transport of 67 ppm in 3 h driven by the katabatic advection.

Since the 1960s the Holzworth method has remained a primary tool for operational mixed-layer height determination. The air volume through which ground-based pollutants vertically disperse defines the mixed layer. The appeal of this method rests on the simple mechanics of making a forecast where knowledge of the surface air temperature in concert with the background vertical structure is sufficient. The National Weather Service routinely issues forecasts using this method for air-quality and wildland fire activities. Methods of this type that are based principally on the static stability structure of the atmosphere and exclude vapor content or dynamical processes (e.g., advection and wind shear) can misrepresent the mixing height calculation. Systematic errors, such as the height being too low or high, can complicate wildland fire activities (e.g., go/no-go burn decisions). Motivation for the present study emerges from this premise, and thus examines the mixing height computed from four methods. Mixing height methods employed in this study include Holzworth, Stull, bulk Richardson number, and turbulent kinetic energy—where the latter two include dynamical processes. Mixing height also was derived from satellite-based lidar data to provide an observed proxy and validation. Results from a method intercomparison show that turbulent kinetic energy is the most robust and well suited as a national standard method for operational use—having both thermodynamic and dynamic processes incorporated. The bulk Richardson number and Stull methods are other possibilities because their calculations are not model dependent and heights are consistent with those from turbulent kinetic energy.

A series of flume experiments has been conducted to investigate sediment transport of sand–silt mixtures in both wave-only and wave-with-current conditions. Two types of sediments collected from a typical silty tidal flat were used: a silt-sized mixture with median grain size of 46 μm, and a very fine sand-sized mixture with median grain size of 88 μm. A high concentration layer (HCL) was observed near the bottom together with ripples under wave-only conditions. Sediment concentrations inside the HCL are quasi-stationary with the bulk Richardson number approaching a constant value. The thickness of the HCL can be scaled with approximately two times the damped wave boundary layer thickness. For the concentration profiles, we find that the vertical profile of the silt concentration appears different from the profile of the sand concentration, since the silt concentration decreases logarithmically within HCL, while homogeneously distributes outside the HCL. Finally, the reference concentration formulation of van Rijn (2007b) was recalibrated for the silt classes and applied in a multi-fraction model to predict the vertical concentration profile for silt and sand classes. The results show a promising agreement with the measurements, for both wave-only and wave-with-current conditions.

High resolution 3-dimensional simulations are presented of the interactions between turbulent shear flows moving with mean relative velocity ∆U below a stably stratified region with buoyancy frequency (N+). An artificial forcing in the simulation, with a similar effect as a small negative eddy viscosity, leads to a steady state flow which models thin interfaces. Characteristic eddies of the turbulence have length scale L. If the bulk Richardson number Rib=(LN+/∆U)2 lies between lower and upper critical values denoted as Ri*( R˜i, vertical propagating waves are generated, with shear stresses carrying significant momentum flux, and progressively less as Rib increases. Simulations for a jet and a turbulent mixing layer show similar results. A perturbation analysis, using inhomogeneous Rapid Distortion Theory (RDT), models the transition zone between shear eddies below the interface and the fluctuations in the stratified region, consistent with the simulations. It demonstrates how the wave-momentum-flux has a maximum when Rib~2, and then decreases as Rib increases. This coupling mechanism between eddies and waves which is neglected in eddy viscosity models for shear layers, can drive flows in the stratosphere and the deeper ocean, with significant consequences for short and long term flow phenomena. The ’detached layer’ is a mechanism that contributes to the formation of stratus clouds and polluted layers above the atmospheric boundary layer.

We study stratified turbulence in plane Couette flow using direct numerical simulations. Two external dimensionless parameters control the dynamics, the Reynolds number $\mathit{Re}=Uh/{\it\nu}$ and the bulk Richardson number $\mathit{Ri}=g{\it\alpha}_{V}Th/U^{2}$, where $U$ and $T$ are half the velocity and temperature difference between the two walls respectively, $h$ is the half channel depth, ${\it\nu}$ is the kinematic viscosity and $g{\it\alpha}_{V}$ is the buoyancy parameter. We focus on spatio-temporal intermittency due to stratification and we explore the boundary between fully developed turbulence and intermittent flow in the $\mathit{Re}{-}\mathit{Ri}$ plane. The structures populating the intermittent flow regime show coexistence between laminar and turbulent patches, and we demonstrate that there are qualitative differences between the previously studied low-$\mathit{Re}$ low-$\mathit{Ri}$ intermittent regime and the high-$\mathit{Re}$ high-$\mathit{Ri}$ intermittent regime. At low-$\mathit{Re}$ low-$\mathit{Ri}$, turbulent regions span the entire gap, whereas at high-$\mathit{Re}$ high-$\mathit{Ri}$, turbulence is confined vertically with complex dynamics arising from interacting turbulent layers. Consistent with a previous investigation of Flores & Riley (Boundary-Layer Meteorol., vol. 129 (2), 2010, pp. 241–259), we present evidence suggesting that intermittency in the asymptotic regime of high-$\mathit{Re}$ Couette flows appears for $L^{+}, where $L^{+}=Lu_{{\it\tau}}/{\it\nu}$, with $L$ being the Monin–Obukhov length scale, $L=u_{{\it\tau}}^{3}/C_{{\it\kappa}}q_{w}$, $q_{w}$ the wall heat flux, $C_{{\it\kappa}}$ the von Kármán constant and $u_{{\it\tau}}=\sqrt{{\it\tau}_{w}/{\it\rho}_{0}}$ the friction velocity determined from the wall shear stress ${\it\tau}_{w}$, where ${\it\rho}_{0}$ is the constant background density. We also consider the mixing as quantified by various versions of the flux Richardson number $\mathit{Ri}_{f}$, defined as the ratio of the conversion rate from kinetic to potential energy to the turbulent kinetic energy injection rate due to shear. We investigate how laminar and turbulent regions separately contribute to the overall mixing. Remarkably, we find that although fluctuations are greatly suppressed in the laminar regions, $\mathit{Ri}_{f}$ does not change significantly compared with its value in turbulent regions. As we observe a tight coupling between the mean temperature and velocity fields, we demonstrate that both Monin–Obukhov self-similarity theory (Monin & Obukhov, Contrib. Geophys. Inst. Acad. Sci. USSR, vol. 151, 1954, pp. 163–187) and the explicit algebraic model of Lazeroms et al. (J. Fluid Mech., vol. 723, 2013, pp. 91–125) predict the mean profiles well. We thus use these models to trace out the boundary between fully developed turbulence and intermittency in the $\mathit{Re}{-}\mathit{Ri}$ plane.

In this study, a newly developed direct numerical simulation (DNS) solver is utilized for the simulations of numerous stably stratified open-channel flows with bulk Reynolds number (Re b ) spanning 3400–16,900. Overall, the simulated bulk Richardson number ( $$Ri_b$$ ) ranges from 0.08 (weakly stable) to 0.49 (very stable). Thus, both continuously turbulent and (globally) intermittently turbulent cases are represented in the DNS database. Using this comprehensive database, various flux-based and gradient-based similarity relationships for energy dissipation rate (e) and temperature structure parameter ( $$C_T^2$$ ) are developed. Interestingly, these relationships exhibit only minor dependency on Re b . In order to further probe into this Re b -effect, similarity relationships are also estimated from a large-eddy simulation (LES) run of an idealized atmospheric boundary layer (very high Re b ) case study. Despite the fundamental differences in the estimation of e and $$C_T^2$$ from the DNS- and the LES-generated data, the resulting similarity relationships, especially the gradient-based ones, from these numerical approaches are found to be remarkably similar. More importantly, these simulated relationships are also comparable, at least qualitatively, to the traditional observational data-based ones. Since these simulated similarity relationships do not require Taylor’s hypothesis and do not suffer from mesoscale disturbances and/or measurement noise, they have the potential to complement the existing similarity relationships.