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Convective dissolution is an important mechanism for long-term CO $_2$ sequestration in deep saline aquifers. The presence of an unstable geothermal gradient can affect the process of dissolution. In this paper, we present direct numerical simulations in a three-dimensional porous medium at three different concentration Rayleigh numbers $Ra_S$ with a set of thermal Rayleigh numbers $Ra_T$ . Simulations reveal that the flow structures alter when ${\textit {Ra}}_T$ increases for a fixed ${\textit {Ra}}_S$ . Strong thermal gradient can yield large-scale convection rolls which change the horizontal distribution and motions of concentration fingers. The time evolution of fluxes also has different responses to different ${\textit {Ra}}_T$ . A theoretical model is developed and successfully describes the evolution of concentration flux and volume averaged concentration during the final shutdown stage. We further calculate the dissolved CO $_2$ into the interior over time, which shows non-monotonic variations as ${\textit {Ra}}_T$ increases. At the end of our simulations, the maximum increment of dissolved CO $_2$ occurs when density ratio is around unity for all three concentration Rayleigh numbers we have explored. We apply our results to a typical geological reservoir and discuss their implications.

In this work we investigate the thermal convection driven by heat-releasing point particles. Three-dimensional direct numerical simulations are conducted for $1\times 10^7\le {\textit {Ra}} \le 1\times 10^{10}$ and $0.01\le {\textit {St}} \le 10$ , where the Rayleigh number ${\textit {Ra}}$ and Stokes number ${\textit {St}}$ measure the strengths of the heat releasing rate and the Stokes drag, respectively. A regime at intermediate Stokes numbers is identified with most particles accumulating into the top boundary layer region, while for other cases particles are constantly advected over the entire domain. For the latter state, the flow motions are stronger at the upper part of the domain. The thicknesses of both momentum and thermal boundary layers at the top plate follow the same scaling law with ${\textit {Ra}}$ and show minor dependences on ${\textit {St}}$ . The volume-averaged temperature and convective flux exhibit non-monotonic variations as ${\textit {St}}$ increases and reach their minimums at intermediate ${\textit {St}}$ . The fraction coefficient of heat flux, i.e. the ratio between the heat flux through the bottom plate and the total flux through both plates, shares the similar dependence on ${\textit {St}}$ as the convective flux. The relation between these scaling laws can be explained by using the global balance between the dissipation and convective flux. The scaling laws for the transition between different flow regimes are also proposed and agree with the numerical results. The preferential concentration of particles is observed for all cases and is strongest at intermediate Stokes numbers, for which multiscale clustering emerges with small clusters forming larger ones.

We conduct direct numerical simulations and study the evolution of a pair of counter-rotating vortices in a stratified and turbulent environment beyond the first vortex linking (which is due to the Crow instability). The initial position of the two vortices is perpendicular to the direction of thermal stratification. We vary the Froude number, the background turbulence intensity and the Reynolds number, covering strong, weak and neutral stratification; low, moderate and high background turbulence; and low and moderate Reynolds numbers. We observe a second vortex linking in a weakly stratified environment for the first time. The second vortex linking is followed by turbulence bursts that lead to the rapid decay of the residual vortices after the first vortex linking, leading to a short-living vortex pair. This challenges the conventional view that residual vortices have a long life span, which is true only in an unstratified environment. In addition to the second vortex linking, we observe the following. First, strong background turbulence quickly breaks the two vortices. Second, the two vortices induce secondary and tertiary vortices and lose energy to gravitational waves in a strongly stratified ( $Fr\leqslant 0.7$ ) environment.

In this work, we numerically study the impact of a water droplet onto a deep oil pool. Two fluids are immiscible and the viscosity of the pool liquid is changed systematically. We focus on the cavity dynamics during the impact and especially the effects of the pool liquid viscosity and the impacting velocity. For the parameter range explored, we identify the regime where splashing occurs with corolla breaking into droplets, and the regime where no splashing is observed. Similarity is found for the time evolution of cavity depth for fixed impact velocity and different viscosity, if the cavity depth and time are nondimensionalized by the maximal depth and the time when the maximal depth is reached. Effective power-law scalings are also proposed to describe the dependence of the maximal cavity depth and the corresponding time on the impact velocity and pool liquid viscosity, in the term of Froude and Reynolds numbers.

In this study the effects of the actuation waveforms on the droplet generation in a drop-on-demand inkjet printing are studied systematically by numerical simulations. Two different types of waveforms, namely the unipolar and bipolar actuations, are investigated for three fluids with different physical properties. We focus on two key parameters, which are the dwell time and the velocity amplitude. For the unipolar driving, the ejection velocity and the ejected liquid volume are both increased as the velocity amplitude becomes larger. The dwell time only has minor effects on both the ejection velocity and the ejected liquid volume. The ejection velocity decreases significantly for large liquid viscosity, while the influences of viscosity on the ejected liquid volume are much weaker. Four different droplet morphologies and the corresponding parameter ranges are identified. The droplet radius can be successfully reduced to about 40% of the nozzle exit radius. For the bipolar waveforms, same droplet morphologies are observed but with shifted boundaries in the phase space. The minimal radius of stable droplet produced by the bipolar waveforms is even smaller compared to the unipolar ones.

In this work fingering double diffusive convection, i.e. the buoyancy-driven flow with fluid density being affected by two different scalar components, is investigated numerically with special efforts on the influences of the physical properties of two scalar components. We show that different scalar properties can affect the global transport behaviors. The concentration flux exhibits different exponents in their power-law scalings for different combinations of scalar components. The scaling exponents of heat flux, however, depend mainly on the ratio of the diffusivities of two scalars. If one uses the local parameters of the finger layer in the bulk, the behaviors are very similar to those found in the fully periodic simulations. The horizontal width of the fingers is consistent with the wavelength of the fast growing mode. For one case we observe evidences of the thermohaline staircase, namely, the typical width of the flow structures changes significantly in different layers within the flow domain.

In this work we study the convection flow driven by a heat-releasing concentration field which itself is stably stratified. The heat-releasing rate is linearly proportional to concentration. Linear stability analysis is conducted to determine the critical heat-releasing rate for given fluid properties and concentration differences. The most unstable mode associated with the critical heat-releasing rate can be oscillatory for a large concentration Rayleigh number, i.e. the non-dimensionalized concentration difference and large Schmidt number, i.e. the ratio of viscosity to diffusivity of the concentration component. Fully developed flows are then investigated by direct numerical simulations. Flow structures near the bottom plate have larger horizontal scales than those near the top plate. The concentration in the bulk is almost constant and takes a similar value for all the explored parameters, which results in the convective flux increasing linearly with height. To explain the dependences of the global transport properties, we extend the unifying theory of the Rayleigh–Bénard convection to the current system and develop scaling laws for the global fluxes. The numerical results can be described accurately by the theoretical model.

The droplet formation dynamics of a Newtonian liquid in a drop-on-demand (DOD) inkjet process is numerically investigated by using a volume-of-fluid (VOF) method. We focus on the nozzle geometry, wettability of the interior surface, and the fluid properties to achieve the stable droplet formation with higher velocity. It is found that a nozzle with contracting angle of 45° generates the most stable and fastest single droplet, which is beneficial for the enhanced printing quality and high-throughput printing rate. For this nozzle with the optimal geometry, we systematically change the wettability of the interior surface, i.e., different contact angles. As the contact angle increases, pinch-off time increases and the droplet speed reduces. Finally, fluids with different properties are investigated to identify the printability range.

Turbulent convection plays a crucial role in many natural environments and engineering applications. One of the most fundamental questions is how the heat flux depends on the thermal driving and fluid property. It has been proposed that when the fluid layer experiences extremely strong thermal driving, the boundary layers will become fully turbulent and the so-called ultimate regime will emerge. In this work we proposed a numerical experiment in which the thermal boundary layer can be spatially decoupled with the viscous one. We demonstrate that, once the thermal boundary layer is fully decoupled from the viscous boundary layer and locates entirely inside the turbulent bulk, the scaling laws corresponding to the ultimate regime can be obtained, namely the Prandtl number, respectively. Therefore, our results support the physical conjecture of the ultimate regime for the turbulent convection.

A neural network (NN) is a powerful tool for approximating bounded continuous functions in machine learning. The NN provides a framework for numerically solving ordinary differential equations (ODEs) and partial differential equations (PDEs) combined with the automatic differentiation (AD) technique. In this work, we explore the use of NN for the function approximation and propose a universal solver for ODEs and PDEs. The solver is tested for initial value problems and boundary value problems of ODEs, and the results exhibit high accuracy for not only the unknown functions but also their derivatives. The same strategy can be used to construct a PDE solver based on collocation points instead of a mesh, which is tested with the Burgers equation and the heat equation (i.e., the Laplace equation).

We conduct direct numerical simulations for turbulent Rayleigh-B\'{e}nard (RB) convection, driven simultaneously by two scalar components (say, temperature and salt concentration) with different molecular diffusivities, and measure the respective fluxes and the Reynolds number. To account for the results, we generalize the Grossmann-Lohse theory for traditional RB convections~(Grossmann and Lohse, J. Fluid Mech., 407, 27-56; Phys. Rev. Lett., 86, 3316-3319; Stevens et al., J. Fluid Mech., 730, 295-308) to this two-scalar turbulent convection. Our numerical results suggest that the generalized theory can successfully predict the overall trends for the fluxes of two scalars and the Reynolds number. In fact, for most of the parameters explored here, the theory can even predict the absolute values of the fluxes and the Reynolds number with good accuracy. The current study extends the generality of the Grossmann-Lohse theory in the area of the buoyancy-driven convection flows., Comment: 13 pages, 3 figures, and 1 table

In this paper the macroscopic damping model for dynamical behavior of the structures with random polycrystalline configurations at micro–nano scales is established. First, the global motion equation of a crystal is decomposed into a set of motion equations with independent single degree of freedom (SDOF) along normal discrete modes, and then damping behavior is introduced into each SDOF motion. Through the interpolation of discrete modes, the continuous representation of damping effects for the crystal is obtained. Second, from energy conservation law the expression of the damping coefficient is derived, and the approximate formula of damping coefficient is given. Next, the continuous damping coefficient for polycrystalline cluster is expressed, the continuous dynamical equation with damping term is obtained, and then the concrete damping coefficients for a polycrystalline Cu sample are shown. Finally, by using statistical two-scale homogenization method, the macroscopic homogenized dynamical equation containing damping term for the structures with random polycrystalline configurations at micro–nano scales is set up.

We present systematic investigations examining the shock responses of nanoporous aluminum (np-Al) by nonequilibrium molecular dynamics simulations. The dislocation nucleation sites are observed to be concentrated in the low latitude region near the equator of the spherical void surfaces. We propose a continuum wave reflection theory and a resolved shear stress model to explain the distribution of dislocation nucleation sites. The simulations reveals two mechanisms of void collapse: the plasticity mechanism and the internal jetting mechanism. The plasticity mechanism, which leads to transverse collapse of voids, prevails under relatively weaker shocks; the internal jetting mechanism, which leads to longitudinal filling of the void vacuum, plays a more significant role as the shock intensity increases. In addition, we observed that the temperature rises while the pressure drops for tens of picoseconds in the shocked np-Al. This thermodynamic phenomenon is different from that observed in single-crystal Al, where the temperature and pressure immediately reach the Hugoniot constants. The influences of void collapse on spall fracture of np-Al are studied. Under the same loading velocity, the spall strength of np-Al is observed to be lower than that of single-crystal Al; however, the spall resistance is higher in np-Al than in single-crystal Al. This resistance is explained by the combined influences of thermal dissipation and stress attenuation during shock wave propagation in np-Al.

Purpose Using Shanghai as an example, the purpose of this paper is to perform grade evaluation and zoning for different land use spaces by GIS by identifying the major restrictive factors in current socio-economic development. Design/methodology/approach Based on short plate theory, 11 major restrictive indicators that will restrict socio-economic development in Shanghai are identified, and urban land is divided into four subspaces and the restrictive grade evaluation of urban land subspace is achieved with GIS spatial analysis; then, land development zoning is processed according to the results of the evaluation. Findings In all, 11 major restrictive indicators that will restrict socio-economic development in Shanghai are identified. The restrictive grades of the agricultural production, urban construction and ecological protection subspaces are mainly common, weak and weaker, and the relatively strong restrictive grade of industrial development subspace is mainly concentrated in the more developed industrial districts (counties). The areas of the common and good regions of constructive development and ecological development zones account for 87.4 and 98.3 per cent of each total area, respectively, and urban land still has significant development potential in Shanghai. Originality/value This paper proposes various urban land space evaluations and zoning strategies based on restrictive indicators and perspectives, enriching the ideas and methods of urban land use evaluation.

This study analysed the sustainability of fuel-ethyl levulinate (EL) production along with furfural, as a by-product, from cornstalk in China. A life cycle assessment (LCA) was conducted using the SimaPro software to evaluate the energy consumption (EC), greenhouse gas (GHG) and criteria emissions, from cornstalk growth to EL utilisation. The total life cycle EC was found to be 4.54 MJ/MJ EL, of which 94.7% was biomass energy. EC in the EL production stage was the highest, accounting for 96.8% of total EC. Fossil EC in this stage was estimated to be 0.095 MJ/MJ, which also represents the highest fossil EC throughout the life cycle (39.5% of the total). The ratio of biomass to fossil EC over the life cycle was 17.9, indicating good utilisation of renewable energy in cornstalk-based EL production. The net life cycle GHG emissions were 96.6 g CO 2 -eq/MJ. The EL production stage demonstrated the highest GHG emissions, representing 53.4% of the total positive amount. Criteria emissions of carbon monoxide (CO) and particulates ⩽10 μm (PM10) showed negative values, of −3.15 and −0.72 g/MJ, respectively. Nitrogen oxides (NO x ) and sulphur dioxide (SO 2 ) emissions showed positive values of 0.33 and 0.28 g/MJ, respectively, mainly arising from the EL production stage. According to the sensitivity analysis, increasing or removing the cornstalk revenue in the LCA leads to an increase or decrease in the EC and environmental emissions while burning cornstalk directly in the field results in large increases in emissions of NMVOC, CO, NO x and PM10 but decreases in fossil EC, and SO 2 and GHG emissions.

Atomic-Continuum Coupled Model (ACCM) is a multiscale computation model proposed by Xiang et al. (in IOP conference series materials science and engineering, 2010), which is used to study and simulate dynamics and thermal---mechanical coupling behavior of crystal materials, especially metallic crystals. In this paper, we construct a set of interpolation basis functions for the common BCC and FCC lattices, respectively, implementing the computation of ACCM. Based on this interpolation approximation, we give a rigorous mathematical analysis of the error of momentum conservation equation introduced by ACCM, and derive a sequence of inequalities that bound the error. Numerical experiment is carried out to verify our result.

In this paper, we review some recent studies on compressible turbulence conducted by the authors’ group, which include fundamental studies on compressible isotropic turbulence (CIT) and applied studies on developing a constrained large eddy simulation (CLES) for wall-bounded turbulence. In the first part, we begin with a newly proposed hybrid compact–weighted essentially nonoscillatory (WENO) scheme for a CIT simulation that has been used to construct a systematic database of CIT. Using this database various fundamental properties of compressible turbulence have been examined, including the statistics and scaling of compressible modes, the shocklet–turbulence interaction, the effect of local compressibility on small scales, the kinetic energy cascade, and some preliminary results from a Lagrangian point of view. In the second part, the idea and formulas of the CLES are reviewed, followed by the validations of CLES and some applications in compressible engineering problems.

A slip boundary has been shown to have a significant impact on flow past bluff bodies. In this work and using a circular cylinder as a model system, the effects of various slip configurations on the passing flow are investigated. A theoretical analysis using matched-asymptotic expansion is first performed in the small-Reynolds number regime following Stokes and Oseen. A slip boundary condition is shown to lead to only higher-order effects (similar to 1/ln(Re)) on the resulting drag coefficient. For higher Reynolds numbers (100-500), the effects of five types of symmetric slip boundary conditions, namely, no slip, fore-side slip, aft-side slip, flank slip, and all slip on the flow field and pertinent parameters are investigated with numerical simulations. Detailed results on the flow structure and force distribution are presented. Flank slip is found to have the best effect for drag reduction with comparable coverage of slip area. For asymmetric slip distributions, torque and lift are found to generally occur. (C) 2014 Elsevier Ltd. All rights reserved.

Direct numerical simulations are conducted for double diffusive convection (DDC) bounded by two parallel plates. The Prandtl numbers, i.e. the ratios between the viscosity and the molecular diffusivities of scalars, are similar to the values of seawater. The DDC flow is driven by an unstable salinity difference (here across the two plates) and stabilized at the same time by a temperature difference. For these conditions the flow can be in the finger regime. We develop scaling laws for three key response parameters of the system: the non-dimensional salinity flux $\mathit{Nu}_{S}$ mainly depends on the salinity Rayleigh number $\mathit{Ra}_{S}$, which measures the strength of the salinity difference and exhibits a very weak dependence on the density ratio $\unicode[STIX]{x1D6EC}$, which is the ratio of the buoyancy forces induced by two scalar differences. The non-dimensional flow velocity $Re$ and the non-dimensional heat flux $\mathit{Nu}_{T}$ are dependent on both $\mathit{Ra}_{S}$ and $\unicode[STIX]{x1D6EC}$. However, the rescaled Reynolds number $Re\unicode[STIX]{x1D6EC}^{\unicode[STIX]{x1D6FC}_{u}^{eff}}$ and the rescaled convective heat flux $(\mathit{Nu}_{T}-1)\unicode[STIX]{x1D6EC}^{\unicode[STIX]{x1D6FC}_{T}^{eff}}$ depend only on $\mathit{Ra}_{S}$. The two exponents are dependent on the fluid properties and are determined from the numerical results as $\unicode[STIX]{x1D6FC}_{u}^{eff}=0.25\pm 0.02$ and $\unicode[STIX]{x1D6FC}_{T}^{eff}=0.75\pm 0.03$. Moreover, the behaviours of $\mathit{Nu}_{S}$ and $Re\unicode[STIX]{x1D6EC}^{\unicode[STIX]{x1D6FC}_{u}^{eff}}$ agree with the predictions of the Grossmann–Lohse theory which was originally developed for the Rayleigh–Bénard flow. The non-dimensional salt-finger width and the thickness of the velocity boundary layers, after being rescaled by $\unicode[STIX]{x1D6EC}^{\unicode[STIX]{x1D6FC}_{u}^{eff}/2}$, collapse and obey a similar power-law scaling relation with $\mathit{Ra}_{S}$. When $\mathit{Ra}_{S}$ is large enough, salt fingers do not extend from one plate to the other and horizontal zonal flows emerge in the bulk region. We then show that the current scaling strategy can be successfully applied to the experimental results of a heat–copper–ion system (Hage & Tilgner, Phys. Fluids, vol. 22, 2010, 076603). The fluid has different properties and the exponent $\unicode[STIX]{x1D6FC}_{u}^{eff}$ takes a different value $0.54\pm 0.10$.

In the traditional hybrid RANS/LES approaches for the simulation of wall-bounded fluid turbulence, such as detached-eddy simulation (DES), the whole flow domain is divided into an inner layer and an outer layer. Typically the Reynolds-averaged Navier–Stokes (RANS) equations are used for the inner layer, while large-eddy simulation (LES) is used for the outer layer. The transition from the inner-layer solution to the outer-layer solution is often problematic due to the lack of small-scale dynamics in the RANS region. In this paper, we propose to simulate the whole flow domain by large-eddy simulation while enforcing a Reynolds-stress constraint on the subgrid-scale (SGS) stress model in the inner layer. Both the algebraic eddy-viscosity model and the one-equation Spalart–Allmaras (SA) model have been used to constrain the Reynolds stress in the inner layer. In this way, we improve the LES methodology by allowing the mean flow of the inner layer to satisfy the RANS solution while small-scale dynamics is included. We validate the Reynolds-stress-constrained large-eddy simulation (RSC-LES) model by simulating three-dimensional turbulent channel flow and flow past a circular cylinder. Our model is able to predict mean velocity, turbulent stress and skin-friction coefficients more accurately in turbulent channel flow and to estimate the pressure coefficient after separation more precisely in flow past a circular cylinder compared with the pure dynamic Smagorinsky model (DSM) and DES using the same grid resolution. Furthermore, the computational cost of the RSC-LES is almost the same as that of DES.

Turbulent channel flow with spanwise rotation is studied by direct numerical simulation (DNS) and the so-called helical wave decomposition (HWD). For a wall-bounded channel domain, HWD decomposes the flow fields into helical modes with different scales and opposite polarities, which allows us to investigate the energy distribution and nonlinear transfer among various scales. Our numerical results reveal that for slow rotation, the fluctuating energy concentrates into large-scale modes. The flow visualizations show that the fine vortices at the unstable side of the channel form long columns, which are basically along the streamwise direction and may be related to the roll cells reported in previous studies. As the rotation rate increases, the concentration of the fluctuating energy shifts towards smaller scales. For strong rotation, an inverse energy cascade occurs due to the nonlinear interaction of the fluctuating modes. A possible mechanism for this inverse cascade is then proposed and attributed to the Coriolis effect. That is, under strong rotation the fluctuating Coriolis force tends to be parallel to the fluctuating vorticity in the region where the streamwise mean velocity has linear profile. Thus the force can induce strong axial stretching/shrinking of the vortices and change the scales of the vortical structures significantly.

Using helical-wave decomposition (HWD), a solenoidal vector field can be decomposed into helical modes with different wavenumbers and polarities. Here, we first review the general formulation of HWD in an arbitrary single-connected domain, along with some new development. We then apply the theory to a viscous incompressible turbulent channel flow with system rotation, including a derivation of helical bases for a channel domain. By these helical bases, we construct the inviscid inertial-wave (IW) solutions in a rotating channel and derive their existing condition. The condition determines the specific wavenumber and polarity of the IW. For a set of channel turbulent flows rotating about a streamwise axis, this channel-domain HWD is used to decompose the flow data obtained by direct numerical simulation. The numerical results indicate that the streamwise rotation induces a polarity-asymmetry and concentrates the fluctuating energy to particular helical modes. At large rotation rates, the energy spectra of opposite polarities exhibit different scaling laws. The nonlinear energy transfer between different helical modes is also discussed. Further investigation reveals that the IWs do exist when the streamwise rotation is strong enough, for which the theoretical predictions and numerical results are in perfect agreement in the core region. The wavenumber and polarity of the IW coincide with that of the most energetic helical modes in the energy spectra. The flow visualizations show that away from the channel walls, the small vortical structures are clustered to form very long columns, which move in the wall-parallel plane and serve as the carrier of the IW. These discoveries also help clarify certain puzzling problems raised in previous studies of streamwise-rotating channel turbulence.

Shear flow past a deep cavity can generate self-sustained oscillations, including locked-on flow tones, due to coupling between the inherent instability of the separated shear layer and an acoustic mode of the cavity resonator. This investigation focuses on the dimensionless pressure amplitude response within a deep cavity, as a function of the streamwise length of the cavity opening; for each length, the pressure response is characterized over a wide range of dimensionless inflow velocity. Criteria for locked-on flow tones are assessed. They include a measure of the strength of lock-on, SoL and the quality factor Q. All self-excited oscillations are assessed using both of these criteria, in order to interpret dimensionless forms of the fluctuation pressure amplitude. The dimensionless pressure amplitude response of the cavity involves several successive regimes, due to variations of streamwise length L of the cavity opening. These regimes are defined in relation to L/θ, where θ is the momentum thickness of the inflow boundary layer. Below a minimum value of L/θ, flow tones cannot be generated. Furthermore, these regimes are defined in terms of the possible hydrodynamic modes (stages) of the unsteady shear layer and the acoustic modes of the deep cavity.

The concept vortex force in aerodynamics is systematically examined based on a new steady vortex-force theory (Wu et al., Vorticity and vortex dynamics, Springer, 2006) which expresses the aerodynamic force (and moment) by the volume and boundary integrals of the Lamb vector. In this paper, the underlying physics of this theory is explored, including the general role of the Lamb vector in nonlinear aerodynamics, its initial formation, and its relevance to the total-pressure non-uniformity. As a typical example, the theory is applied to the flow over a slender delta wing at a large angle of attack. The highly localized flow structures with high Lamb-vector peaks are identified in terms of their net contribution to various constituents of the total aerodynamic force. This vortex-force diagnosis sheds new light on the flow control and configuration optimization.

We investigate how compressibility affects the turbulent statistics from a Lagrangian point of view, particularly in the parameter range where the flow transits from the incompressible type to a state dominated by shocklets. A series of three-dimensional simulations were conducted for different types of driving and several Mach numbers. For purely solenoidal driving, as the Mach number increases a new self-similar region first emerges in the Lagrangian structure functions at sub-Kolmogorov time scale and gradually extends to larger time scale. In this region the relative scaling exponent saturates and the saturated value decreases as the compressibility becomes stronger, which can be attributed to the shocklets. The scaling exponent for the inertial range is still very close to that of incompressible turbulence for small Mach number, and discrepancy becomes visible when the Mach number is high enough. When the driving force is dominated by the compressive component the shocklet-induced self-similar region occupies a much wider range of time scales than that in the purely solenoidal driving case. Regardless of the type of driving force, the probability density functions of the velocity increment collapse onto one another for the time scales in the new self-similar region after proper normalization.

Interaction of a deep-water wave with a vertical cylinder is characterized using techniques of high-image-density particle image velocimetry, in conjunction with measurement of the transverse and in-line loading coefficients. Phase-locked patterns of locally two-dimensional vortex formation are attainable only for sufficiently high values of the Keulegan–Carpenter number KC, e.g. along the span.Taken together, the patterns of locally two-dimensional (sectional) structure and the three-dimensional structure along the span indicate a criterion for locally phase-locked quasi-two-dimensional vortex formation: it occurs when the pattern of transverse velocity is of the same sign over a significant spanwise distance along the span of the cylinder.

The double diffusive convection between two parallel plates is numerically studied for a series of parameters. The flow is driven by the salinity difference and stabilised by the thermal field. Our simulations are directly compared with experiments by Hage & Tilgner (Phys. Fluids, vol. 22, 2010, 076603) for several sets of parameters and reasonable agreement is found. This, in particular, holds for the salinity flux and its dependence on the salinity Rayleigh number. Salt fingers are present in all simulations and extend through the entire height. The thermal Rayleigh number seems to have a minor influence on the salinity flux but affects the Reynolds number and the morphology of the flow. In addition to the numerical calculation, we apply the Grossmann–Lohse theory for Rayleigh–Bénard flow to the present problem without introducing any new coefficients. The theory successfully predicts the salinity flux both with respect to the scaling and even with respect to the absolute value for the numerical and experimental results.

A technique of high-image-density particle image velocimetry is employed to characterize the instantaneous and averaged patterns of velocity, vorticity and Reynolds stress due to flow past two cylinders in tandem. These features of the flow patterns are characterized in the gap region as a function of the distance between the cylinders. In turn, they are related to the patterns in the near-wake of the two-cylinder system. Along the gap between the cylinders, small-scale concentrations of vorticity are formed in the separated shear layers. These concentrations buffet the surface boundary layer on the downstream cylinder, and thereby influence the eventual shedding of large-scale vortices. Within the gap, the instantaneous structure of the recirculation zones can exhibit both symmetrical and asymmetrical patterns. In the near-wake of the downstream cylinder, the form of the vortex shedding, as well as the averaged patterns of the flow structure, are substantially altered, relative to the case of a single cylinder. The width of the near-wake, as represented by averaged patterns of vorticity, is substantially narrower and the magnitudes of the peak Reynolds stress are significantly attenuated. On the other hand, if the gap region is sufficiently large such that Karman-like vortices form between the cylinders, the near-wake of the downstream cylinder shows distinctive patterns, and both the wake width and the magnitude of the Reynolds stresses become larger, relative to those at smaller gap width.

A vertical cylinder is located in a free-surface wave, and a two-camera version of high-image-density particle image velocimetry is employed to characterize the spanwise modes of the flow structure in terms of instantaneous velocity and vorticity. These modes are classified according to organized patterns of velocity in the near wake, and are further interpreted in terms of distinctive arrangements of streamwise vorticity concentrations.At low Keulegan–Carpenter number, which corresponds to small wave height, locally two-dimensional vortices having small scale and circulation tend to form as a symmetrical pair and remain attached, or in close proximity, to the surface of the cylinder. Along the span of the cylinder, the near wake shows either a sinuous S or a unidirectional U mode. The spanwise wavelength λ of the S modes, relative to the cylinder diameter D, lies in the range 1 [lsim ] λ/D [lsim ] 4:5. These values of λ/D represent the spacing between extrema of patterns of cross flow velocity, as well as between clusters of streamwise vorticity of like sign. As the free surface is approached, the value of λ/D scales with the ratio of the minor to major axes of the elliptical particle trajectory of the wave.At moderate values of the Keulegan–Carpenter number, locally two-dimensional vortices having large scale and circulation are shed from the cylinder in an asymmetric arrangement. The corresponding spanwise mode represents the phase variation of this shedding along the span of the cylinder. These sinuous S modes involve large-scale distortions of patterns of both cross flow velocity and streamwise vorticity, which have wavelengths in the range 10 [lsim ] λ/D [lsim ] 110, in contrast to the spacing between individual concentrations of vorticity, which is 1:5D to 4D. Remarkably, it is possible to attain a unidirectional U mode, whereby the phase of the locally two-dimensional vortex shedding is preserved along the entire extent of the cylinder. Signatures of the moments due to the transverse and in-line forces on the cylinder were acquired simultaneously with the patterns of instantaneous velocity and vorticity. Severe modulations of the moment due to the transverse force are associated with spontaneous transformations between basic forms of the sinuous S and unidirectional U modes. The overall form of the signature of the moment due to the in-line force is, however, not generally affected by the spontaneous transformation between modes, but distortion of its peaks is evident.

The technique of high-image-density particle image velocimetry (PIV) can lead to instantaneous, global representations of the wake of a cylinder in a steady current and free-surface waves. Approaches to characterizing the complex patterns of the wake are described for several classes of experimental systems. Emphasis is on imaging in different planes, with the aim of providing insight into the quasi-two- and three-dimensional features of the near-wake.

Numerical simulations are conducted to investigate the dynamics of inertial particles being passively convected in a compressible homogeneous turbulence. Heavy and light particles exhibit very different types of non-uniform distributions due to their different behaviors near shocklets. Because of the relaxation nature of the Stokes drag, the heavy particles are decelerated mainly at downstream adjacent to the shocklets and form high-number-density clouds. The light particles are strongly decelerated by the added-mass effect and stay in the compression region for a relatively long time period. They cluster into thin filament structures near shocklets.

It is well recognized that vorticity and vortical structures appear inevitably in viscous compressor flows and have strong influence on the compressor performance. However, conventional analysis and design procedure cannot pinpoint the quantitative contribution of each individual vortical structure to the integrated performance of a compressor, such as the stagnation-pressure ratio and efficiency. We fill this gap by using the so-called derivative-moment transformation, which has been successfully applied to external aerodynamics. We show that the compressor performance is mainly controlled by the radial distribution of azimuthal vorticity, of which an optimization in the through-flow design stage leads to a simple Abel equation of the second kind. The satisfaction of the equation yields desired circulation distribution that optimizes the blade geometry. The advantage of this new procedure is demonstrated by numerical examples, including the posterior performance check by 3D Navier–Stokes simulation.

An expression for the rate-of-strain tensor on a rigid surface due to Caswell is generalized to an arbitrarily moving and continuously deforming surface or interface between two immiscible fluids. Corresponding expressions for the velocity gradient and vorticity tensors are derived in an inertial frame of reference. A noteworthy feature of the expression for the rate-of-strain tensor is the presence of a tangent-tangent component, which is absent in the case of a rigid surface. Kinematic applications based on numerical solutions of the Navier-Stokes equation for laminar and turbulent flow demonstrate the significance and implications of the derived expressions.

Four existing invariant criteria for defining a vortex are diagnosed analytically and demonstrated by the Burgers and Sullivan vortices. Two of the criteria are found disqualified as generally applicable, and one underestimates the core radius. The diagnosis leads to a general requirement for any possible criterion: it should be able to identify the vortex axis and allow for arbitrary axial strain.

This paper presents Reynolds stress constrained large eddy simulation (RSC-LES) method applied to a U-duct flow. Different from traditional Reynolds-averaged Navier-Stokes/detached eddy simulation (RANS/DES) hybrid method (including DES method), the RSC-LES method solves the LES equations in the whole computation domain with the near-wall regions being constrained by a prescribed Reynolds stress. By doing so it is possible to overcome the log-law mismatch (LLM) problem in hybrid method. The RSC-LES results show better agreement with experiment result. Compared with RANS and DES, RSC-LES gives more accurate pressure coefficients and friction coefficients on the wall, because the RSC-LES method captures the separation point and reattachment point on the inner wall. The computation results show that the RSC-LES method has the potential to solve the log-law mismatch problem of RANS/DES hybrid method and predict complex phenomena of internal flow field.