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Abstract: We investigate mixing processes under stratified conditions on the Northwest European Continental shelf using a numerical model (POLCOMS). Our results indicate that convection induced by vertical shearing of horizontal density gradients (‘shear-induced convection’) is a regularly occurring feature in the bottom and surface boundary layers in this open shelf-sea situation. Two types of turbulence models are investigated to study their capability for reproducing the observed location of tidal mixing fronts, and the physical processes occurring in seasonally stratified waters. The first model is a one-equation variant of the Mellor–Yamada model, whereas the second model combines a more recent second-momentum closure with a two-equation model. It is found that generally mean frontal positions (as estimated from ICES data) are predicted more accurately by the two-equation model. The one-equation model reproduces the mean frontal locations to 18.1km (<3 grid spacings) and the two-equation model to 17.1km; although in the Celtic Sea the accuracy is ∼33 and ∼12km, respectively. Comparison with historical tide gauges, current metres, CTD stations, and thermistor chain data from the North Sea Project all show an improvement in accuracy when the two-equation model is used. This is particularly apparent in the model''s ability to reproduce the spring–neap variability during stratification. We find that in the presence of shear-induced convection the routinely applied clipping of the turbulent length-scale, previously thought to be a minor ingredient in a turbulence model, has a dramatic effect on the results: if the length-scale clipping is not applied, substantial over-mixing is observed to occur. The causes and possible remedies of this effect are investigated. Overall our results demonstrate a sensitivity to the details of the turbulence model that is significantly greater than previously thought. [Copyright &y& Elsevier]

Abstract: Recent contributions to second-order turbulence modelling are reviewed with an emphasis on models of the coastal ocean. Classical and recent turbulence models are reformulated using a unifying notation, making differences in model structure and model parameters more transparent. The essential characteristics of a number of models are compared. It is further demonstrated that the mathematical stability and realisability of the models is crucial for practical applications. The parameter constraints to insure stable computations are discussed. Model performance is evaluated for a number of idealised entrainment scenarios that are typical for shelf seas: entrainment in linearly stratified and two-layer fluids caused by (a) surface wind stress (b) bottom stress due to water motion driven by a barotropic pressure gradient (c) bottom stress due to water motion in a bottom jet. It is shown that the predicted entrainment velocities are in good agreement with available laboratory data, provided the models have been calibrated according to a theoretical constraint. In addition, model behaviour in free convection is re-analysed with the help of recent data from large eddy simulations (LES). It is shown that even the most simple models, which do not solve a differential equation for the turbulent kinetic energy (TKE), can approximately reproduce the entrainment depth, however, they fail completely in reproducing the correct budget of the TKE-balance. In contrast, second-order models solving transport equations for the TKE and a length scale determining variable are in reasonable agreement with the TKE-budgets from LES. [Copyright &y& Elsevier]

Abstract: Direct numerical simulations (DNS) and model results from a number of one-point turbulence models are compared for homogeneous, stably stratified flows. Because of their wide spread use in numerical ocean modelling, only explicit algebraic second-moment models are investigated. Considered are two types of shear flows with either purely vertical or purely horizontal shear. The dissipation rate is evaluated from the observation that the shear-number becomes independent of stratification for low to moderate Richardson numbers as soon as the flow approaches self-similarity. For the cases with vertical shear, it is found that all statistical models essentially reproduced the DNS results, though with different accuracy. In contrast, only the most recent model was able to predict the salient features of horizontally sheared flows, i.e. a steady-state Richardson number that is about an order of magnitude larger and a vertical mixing efficiency that is about twice as large compared to the case with vertical shear. This model also reproduced other key parameters like the turbulent Froude number and the turbulent Prandtl number with good accuracy, but it failed to predict quantitatively the reduction of the shear anisotropy with increasing stratification. For strong stratification, none of the models was able to describe the rapid decrease of the mixing efficiency associated with the collapse and fossilisation of turbulence. [Copyright &y& Elsevier]

Abstract: We have developed a Lagrangian model to investigate a potential mechanism based on phototaxis behavior of phytoplankton cells for the formation of thin layers. We assume that all cells follow a time-regulated diurnal vertical migration during which they experience photo-acclimation based on the Denman and Marra (1986) model. When a cell experiences stress due to strong light that exceeds a threshold level, the cell swims downward, away from the light. We applied the Lagrangian model to a one dimensional second order turbulence closure model that generates a realistic surface mixing condition for a given set of physical parameters, such as wind and optical water type. For the chosen swimming velocities and prescribed behavior, we found that, in coastal water type and Jerlov III type, thin layer formation takes place up to 5ms−1 winds, while 10ms−1 winds cause sufficiently strong mixing to prevent the formation of thin layer. We have also investigated the effects of changing the irradiance threshold for the onset of the photoinhibition, the initial density profile and random walk swimming. In conclusion, thin layer formation due to photoinhibition may be possible for a low value of photoinhibition threshold that may occur either due to upwelling or strong light exposure. [Copyright &y& Elsevier]

The Knudsen theorem for estuarine exchange flow, based on mass conservation of water and salt, and its generalization with resolution in salinity coordinates, the Total Exchange Flow (TEF) analysis framework, are reviewed here. The former had been developed, and applied to quantify exchange flow between the North Sea and the Baltic Sea, more than a century ago. In this paper, the underlying short research paper published in 1900 by Martin Knudsen, originally written in German, is translated into English. Reaching far beyond the Knudsen relation in particular, the extensive scientific achievements of Martin Knudsen on the salinity of seawater are reviewed. Using the Knudsen theorem and the TEF analysis framework, validated multi-decadal (years 1949–2013) model simulations are analyzed in terms of exchange flow through straits of the Western Baltic Sea. When comparing the model results to the original findings of Martin Knudsen, it is impressive to see how relevant his analysis of ratios of averaged inflowing and outflowing water masses still is today, given that they were based on just a few salinity observations. The model-based long-term Knudsen and TEF analyses of exchange flow in the Western Baltic Sea reproduces the Major Baltic Inflows (MBIs) that have occurred since the 1950s. For the complex inflow years 2002/2003, with two baroclinic summer inflows and one barotropic winter inflow in between, the strong underestimation of the exchange flow by Eulerian analysis as compared to TEF analysis is demonstrated. [ABSTRACT FROM AUTHOR]

A high resolution k – ω two-equation turbulence closure model, including surface wave forcing was employed to fully resolve turbulence dissipation rate profiles close to the ocean surface. Model results were compared with observations from Surface Wave Instrument Floats with Tracking (SWIFTs) in the nearshore region at New River Inlet, North Carolina USA, in June 2012. A sensitivity analysis for different physical parameters and wave and turbulence formulations was performed. The flux of turbulent kinetic energy (TKE) prescribed by wave dissipation from a numerical wave model was compared with the conventional prescription using the wind friction velocity. A surface roughness length of 0.6 times the significant wave height was proposed, and the flux of TKE was applied at a distance below the mean sea surface that is half of this roughness length. The wave enhanced layer had a total depth that is almost three times the significant wave height. In this layer the non-dimensionalized Terray scaling with power of − 1.8 (instead of − 2 ) was applicable. [ABSTRACT FROM AUTHOR]

Straining of a horizontal density gradient by tidal currents acts to periodically produce and destroy near-bottom stratification, which has been shown to modulate turbulence in the bottom boundary layer (BBL). Previous observations of such periodic variations have been limited to the coastal ocean and estuaries, where horizontal density gradients are maintained by river runoff or differential heating. In the present study, we show evidence for the existence of tidal straining over the continental shelf, outside any regions of freshwater influence, where horizontal density gradients are likely to result from the projection of the interior vertical stratification onto sloping topography. Based on microstructure data obtained in the East China Sea, we demonstrate that the tidal current shear interacting with the cross-isobath density gradient results in semidiurnal switching between unstable and stable stratification in the lower part of the BBL. The cycle of turbulent dissipation is quarter-diurnal, corresponding to the semidiurnal variation of tidal current shear. In addition, a noticeable diurnal modulation in stratification as well as a significant diurnal cycle of turbulent dissipation are observed in the upper part of the BBL, where the time evolution of stratification is dominated by tidal advection, rather than tidal straining. [ABSTRACT FROM AUTHOR]

Abstract: In the transition area between the North Sea and the Baltic Sea entrainment processes dominate the vertical mixing in the inflowing saline bottom water. The hot spots of these processes are located at the Darss Sill and the Bornholm Channel in the western Baltic Sea. In the central Baltic Sea the horizontal advection of saline water in deep layers below the permanent halocline dominate the temporal changes and associated transports. This is accompanied by the turbulent vertical transport through the halocline into the surface layers. The related vertical salt transport into the entire surface mixed layer estimated by various methods is slightly above 30kg/(m2 a). During stagnation periods, the residence time of the deep water in the Eastern Gotland Basin increases roughly by a factor of five. Vertical mixing through the halocline is drastically reduced when inflows are lacking, the potential processes of diapycnal mixing are discussed to the present knowledge. The turbulent motion resulting from breaking internal waves is capable of turbulent transports through the halocline corresponding to the estimates of the salt transport into the surface mixed layer. The actual knowledge about boundary mixing due to internal waves in the Baltic Sea is poor. Mesoscale eddies may contribute to the vertical mixing, but it is not known whether they really do and which of the possible direct and indirect mixing mechanisms is most effective. Near-bottom currents induced by inflow events likely enhance vertical mixing. Coastal upwelling certainly contributes to the vertical transport, but the depth of its origin and the volume transport are hard to determine for large-scale quantifications. The short spatiotemporal scale of turbulent transports through the halocline resulting in a weakening of the halocline during summer together with the mixing of the entire surface layer down to the halocline in winter form a consistent description of the vertical salt transport. It is hypothesised that the longer residence time of the deep water during stagnation periods results from the lack of energy imported by the inflows and directly or indirectly feeding the diapycnal mixing processes. The vertical transport of nutrients such as the phosphate is quantitatively not sufficiently understood and needs further interdisciplinary research activities. [Copyright &y& Elsevier]

Abstract: Only recently, medium intensity inflow events into the Baltic Sea have gained more awareness because of their potential to ventilate intermediate layers in the Southern Baltic Sea basins. With the present high-resolution model study of the Western Baltic Sea a first attempt is made to obtain model based realistic estimates of turbulent mixing in this area where dense bottom currents resulting from medium intensity inflow events are weakened by turbulent entrainment. The numerical model simulation which is carried out using the General Estuarine Transport Model (GETM) during nine months in 2003 and 2004 is first validated by means of three automatic stations at the Drogden and Darss Sills and in the Arkona Sea. In order to obtain good agreement between observations and model results, the nautical mile bathymetry had to be adjusted in order to account for the fact that even at that scale many relevant topographic features are not resolved. Current velocity, salinity and turbulence observations during a medium intensity inflow event through the Øresund are then compared to the model results. Given the general problems of point to point comparisons between observations and model simulations, the agreement is fairly good with the characteristic features of the inflow event well represented by the model simulations. Two different bulk measures for mixing activity are then introduced, the vertically integrated decay of salinity variance, which is equal to the production of micro-scale salinity variance, and the vertically integrated turbulent salt flux, which is related to an increase of potential energy due to vertical mixing of stably stratified flow. Both measures give qualitatively similar results and identify the Drogden and Darss Sills as well as the Bornholm Channel as mixing hot spots. Further regions of strong mixing are the dense bottom current pathways from these sills into the Arkona Sea, areas around Kriegers Flak (a shoal in the western Arkona Sea) and north–west of the island of Rügen. [Copyright &y& Elsevier]

Abstract: In January/February 2004 a ship cruise into the Arkona Sea (Western Baltic) happened to start just prior to a medium-size inflow event and to last until a few days after the inflow. The bottom layer of saline inflow water in the southern Sound has a current speed of up to 1m/s. The current bifurcates at Kriegers Shoal, where only the smaller branch follows the contour lines of the bathymetry at the western rim of the basin, while the main flow proceeds on the steepest path north of Kriegers Shoal. The pycnocline tilt due to geostrophy matches with current observations in both branches. Old bottom water in the basin is lifted up by the denser inflow and pushed forward to Bornholm Gate. Inflow from the Darss Sill at first consists of low-salinity Baltic surface water and a small amount of higher salinity water at the bottom. After a few days the water over the sill is mixed and moves east, establishing a strong subsurface current at the southern rim of the Arkona Basin. Neither the inflow through the Sound nor the water masses from the Darss Sill reached the Bornholm Gate in the east of the Arkona Sea before the end of the survey. The saline outflow observed there consists of bottom water that had been present in the Arkona Sea prior to the new inflow. Overflow water spreading on the sea bottom is modified by entrainment from the low salinity water body above. Best guesses of the entrainment rate, somewhat tentative due to salinity variations at the entrance, are in line with formulae from the literature. [Copyright &y& Elsevier]