Stochastic modelling of unresolved eddy fluxes

A subgrid-scale parameterization scheme motivated by statistical closure theory, but employing statistics obtained from high-resolution direct numerical simulations, is applied to large eddy simulations of two-level quasigeostrophic turbulence on the sphere. It is shown that these parameterizations are consistent with the phenomenology of quasigeostrophic turbulence. The parameterizations consist of 2 × 2 dissipation and stochastic forcing covariance matrices at each wavenumber, with the off-diagonal elements of the matrices representing vertical mixing. Two flow regimes, characterized by their deformation scales, are considered, namely atmospheric and oceanic. In the former, the deformation scale is fully resolved, and the truncation scale is within the enstrophy cascading interial range. In the latter, the deformation scale is not fully resolved, and the truncation scale is within the energy cascading inertial range. It is demonstrated through numerical experiments that both stochastic and deterministic variants of the scheme give comparable results for the energy spectra in the atmospheric regime. In the oceanic regime, the stochastic variant again gives excellent results, but the deterministic variant is found to be numerically unstable.     

Simulation of airflow around rain gauges: Comparison of LES with RANS models

Wind is responsible for systematic errors that affect rain gauge measurements. The authors investigate the use of computational fluid dynamics (CFD) to calculate airflow around rain gauges by applying a high-resolution large eddy simulation (LES) model to determine the flow fields around a measuring system of two rain gauges. The simulated air flow field is characterized by the presence of massive separation which induces the formation and shedding of highly unsteady eddies in the detached shear layers and wakes. Parts of these detached structures occur over the orifice of the rain gauges and may substantially affect the dynamics of the raindrops in this critical region. Non-dissipative LES methods used with fine enough meshes can successfully predict these eddies and their associated fluctuations. The authors compare statistics from LES with steady-state Reynolds averaged Navier–Stokes (RANS) simulations using the k–ε and shear stress transport k–ω turbulence models. They find that both RANS and LES models predict similar mean velocity distributions around the rain gauges. However, they determine the distribution of the resolved turbulent kinetic energy (TKE) to be strongly dependent on the RANS model used. Neither RANS model predictions of TKE are close to those of LES. The authors conclude that the failure of RANS to predict TKE is an important limitation, as TKE is needed to scale the local velocity fluctuations in stochastic models used to calculate the motion of raindrops in the flow field.     

Sand settling through bedform-generated turbulence in rivers

Fluvial bedforms generate a turbulent wake that can impact suspended-sediment settling in the passing flow. This impact has implications for local suspended-sediment transport, bedform stability, and channel evolution; however, it is typically not well-considered in geomorphologic models. Our study uses a three-dimensional OpenFOAM hydrodynamic and particle-tracking model to investigate how turbulence generated from bedforms and the channel bed influences medium sand-sized particle settling, in terms of the distribution of suspended particles within the flow field and particle-settling velocities. The model resolved the effect of an engineered bedform, which altered the flow field in a manner similar to a natural dune. The modelling scenarios alternated bed morphology and the simulation of turbulence, using detached eddy simulation (DES), to differentiate the influence of bedform-generated turbulence relative to that of turbulence generated from the channel bed. The bedform generated a turbulent wake that was composed of eddies with significant anisotropic properties. The eddies and, to a lesser degree, turbulence arising from velocity shear at the bed substantially reduced settling velocities relative to the settling velocities predicted in the absence of turbulence. The eddies tended to advect sediment particles in their primary direction, diffuse particles throughout the flow column, and reduced settling likely due to production of a positively skewed vertical-velocity fluctuation distribution. Study results suggest that the bedform wake has a significant impact on particle-settling behaviour (up to a 50% reduction in settling velocity) at a scale capable of modulating local suspended transport rates and bedform dynamics. © 2020 John Wiley & Sons, Ltd.     

Dynamic Model of Mesoscale Eddies

Oceanic mesoscale eddies which are analogs of well known synoptic eddies (cyclones and anticyclones), are studied on the basis of the turbulence model originated by Dubovikov (Dubovikov, M.S., "Dynamical model of turbulent eddies", Int. J. Mod. Phys. B7, 4631-4645 (1993).) and further developed by Canuto and Dubovikov (Canuto, V.M. and Dubovikov, M.S., "A dynamical model for turbulence: I. General formalism", Phys. Fluids 8, 571-586 (1996a) (CD96a); Canuto, V.M. and Dubovikov, M.S., "A dynamical model for turbulence: II. Sheardriven flows", Phys. Fluids 8, 587-598 (1996b) (CD96b); Canuto, V.M., Dubovikov, M.S., Cheng, Y. and Dienstfrey, A., "A dynamical model for turbulence: III. Numerical results", Phys. Fluids 8, 599-613 (1996c)(CD96c); Canuto, V.M., Dubovikov, M.S. and Dienstfrey, A., "A dynamical model for turbulence: IV. Buoyancy-driven flows", Phys. Fluids 9, 2118-2131 (1997a) (CD97a); Canuto, V.M. and Dubovikov, M.S., "A dynamical model for turbulence: V. The effect of rotation", Phys. Fluids 9, 2132-2140 (1997b) (CD97b); Canuto, V.M., Dubovikov, M.S. and Wielaard, D.J., "A dynamical model for turbulence: VI. Two dimensional turbulence", Phys. Fluids 9, 2141-2147 (1997c) (CD97c); Canuto, V.M. and Dubovikov, M.S., "Physical regimes and dimensional structure of rotating turbulence", Phys. Rev. Lett. 78, 666-669 (1997d) (CD97d); Canuto, V.M., Dubovikov, M.S. and Dienstfrey, A., "Turbulent convection in a spectral model", Phys. Rev. Lett. 78, 662-665 (1997e) (CD97e); Canuto, V.M. and Dubovikov, M.S., "A new approach to turbulence", Int. J. Mod. Phys. 12, 3121-3152 (1997f) (CD97f); Canuto, V.M. and Dubovikov, M.S., "Two scaling regimes for rotating Raleigh-Benard convection", Phys. Rev. Letters 78, 281-284, (1998) (CD98); Canuto, V.M. and Dubovikov, M.S., "A dynamical model for turbulence: VII. The five invariants for shear driven flows", Phys. Fluids 11, 659-664 (1999a) (CD99a); Canuto, V.M., Dubovikov, M.S. and Yu, G., "A dynamical model for turbulence: VIII. IR and UV Reynolds stress spectra for shear driven flows", Phys. Fluids 11, 656-677 (1999b) (CD99b); Canuto, V.M., Dubovikov, M.S. and Yu, G., "A dynamical model for turbulence: IX. The Reynolds stress for shear driven flows", Phys. Fluids 11, 678-694 (1999c) (CD99c).). The CD model derives from general principles and does not resort to any free parameters. Yet, it successfully describes a wide variety of quite different turbulent flows. In the present work we apply CD model to the compressible ocean. The model yields mesoscale eddies generated by the baroclinic instability. The latter, in turn, arises from the nonhorizontal orientation of the surfaces of the constant potential density (isopycnals). The obtained dynamic equations for eddy fields reduce to a vertical eigen value problem, an eigen value real part yielding an eddy radius, while an imaginary part - an eddy drift velocity. The size of the eddy is about 3r_d (where r_d is the Rossby deformation radius). The eddy dynamics has the following distinctive features: (1) the large scale potential energy feeds the eddy potential energy (EPE) at scales ～ r_d , (2) from r_d EPE cascades to the smaller scales down to ～ l ₁ determined from the condition that the spectral Rossby number Ro(q) ≡ qU'(q)f^?1 becomes ～ 1 (q is two-dimensional wave number within an isopycnal surface), (3) at scales ～ l ₁ EPE transforms into eddy kinetic energy (EKE) which cascades backwards to the larger scales up to ～ r_d , where it transforms back into EPE, thereby closing the energy flux circulation in a wavenumber space, (4) dissipation of the eddy energy (EE) occurs at scales ～ l ₁ since at those scales the fluctuating component of the vertical shear is maximal and equals to the Brunt-Vaisala frequency. The latter equality is the well known condition for generating the vertical turbulence which dissipates EE. The model enables to determine all turbulence characteristics, including the horizontal (isopycnal) diffusivity κ _h in terms of the large scale mean fields. From the typical values of the latter follow estimates for the parameters of an eddy which agree well with the observational and simulational data: k_h ～ 10³m²s^?1, EKE K ～ 10³m²s^?1, r_d ～ 3 × 10⁴m, l_I ～ 10. In what concerns the bolus velocity, it contains additional terms (as compared to the model of Gent and McWilliams (Gent, P.R. and McWilliams, J.C., "Isopycnal mixing in ocean circulation models", J. Phys. Oceanogr. 20, 150-155 (1990)) which result from the eddy fields advection by a mean velocity ū. Since the latter varies with depth, it is inevitable to differ from the eddy drift velocity that produces a shearing force eroding the eddy coherent structures and, therefore, contributing negatively to EE production. This is in contrast with the positive contribution from the GM term (which is due to the baroclinic instability). In those regions where the disruptive action is stronger, there is no eddy generation.     

Three-dimensional structure of mesoscale eddies in the western tropical Pacific as revealed by a high-resolution ocean simulation

The three-dimensional structure of mesoscale eddies in the western tropical Pacific(6°S–20°N, 120°E–150°E)is investigated using a high-resolution ocean model simulation. Eddy detection and eddy tracking algorithms are applied to simulated horizontal velocity vectors, and the anticyclonic and cyclonic eddies identified are composited to obtain their three-dimensional structures. The mean lifetime of all long-lived eddies is about 52 days, and their mean diameter is 147 km. Two typical characteristics of mesoscale eddies are revealed and possible dynamic explanations are analyzed. One typical characteristic is that surface eddies are generally separated from subthermocline eddies along the bifurcation latitude(~13°N) of the North Equatorial Current in the western tropical Pacific, which may be associated with different eddy energy sources and vertical eddy energy fluxes in subtropical and tropical gyres. Surface eddies have maximum swirl velocities of 8–9 cm s~(-1) and can extend to about 1500 m depth. Subthermocline eddies occur below 200 m, with their cores at about 400–600 m depth, and their maximum swirl velocities can reach 10 cm s~(-1). The other typical characteristic is that the meridional velocity component of the eddy is much larger than the zonal component. This characteristic might be due to more zonal eddy pairs(two eddies at the same latitude),which is also supported by the zonal wavelength(about 200 km) in the high-frequency meridional velocity component of the horizontal velocity.     

A three-dimensional numerical shelf-sea front model with variable eddy viscosity and diffusivity

A three-dimensional numerical model of circulation and eddy development in shelf-sea fronts is applied to three frontal structures, with two parameterization schemes for vertical eddy viscosity and diffusivity. The three fronts resemble those in the German Bight (a front between relatively fresh coastal water and saltier water offshore, with an interface extending from surface to bottom), the Norwegian Coastal Current (also formed by fresh coastal water but with a thermocline on one side), and the Celtic Sea (a front between water which is stratified in summer and water which is well mixed throughout the year). The two mixing assumptions, modelling the reduction of turbulence in stratified zones, are based on the Munk-Anderson scheme and the turbulent energy equation. Many features of frontal dynamics are common to all the results: strong surface currents along the front, cross-frontal circulation cells, a considerable enhancement of vertical velocities when eddies are formed, and development of eddies into cyclonic-anticyclonic vortex pairs. Cross-frontal circulation and frontal sharpening are the variables most sensitive to the different mixing assumptions. The German Bight front is the one most affected by changing these assumptions. The comparisons suggest that realistic results may be obtained from models despite the present uncertainty about vertical mixing in stratified shelf seas.     

间歇湍流的分形特征——分数维及分数阶导数的应用

分数维由Mandelbrot创立已有30年,分数阶导数在1695年由L’Hospital提出已有400年的历史.本文用物理学中的间歇湍流问题说明分数维及分数阶导数的物理意义.由于间歇湍流涡旋不完全充满空间,所以其维数为2相似文献   

Analysis of bedload transport in laminar flows

Bedload transport generally depends on the bed shear stress and Reynolds number. Many studies conducted for the condition of turbulent flows have revealed the dependence of the transport rate on the bed shear stress, while knowledge of the Reynolds number effect on the transport rate is very limited. As an extreme case to reflect the viscous effect on sediment transport, sediment transport in laminar flows is considered in this paper. A stochastic approach is adopted to explore how the transport rate can be associated with characteristics of laminar flows. First, the probability of erosion in the absence of turbulence is assumed to depend only on the randomness of bed particles. The probability is then applied to formulate the sediment transport rate, of which the derivation is made largely based on Einstein’s bedload theory. The theoretical result indicates that the dimensionless transport rate for laminar flows is dependent on the dimensionless shear stress and dimensionless particle diameter or the shear Reynolds number. Comparisons are finally made between the derived formula and an empirical correlation available in the literature.     

Turbulence flux measurement above the overstory of a subtropical Pinus plantation over the hilly region in southeastern China

Continuous turbulence flux measurement using the eddy covariance (EC) technique was made from January 1 to December 31 in 2003 at two and three canopy heights of a subtropical Pinus plantation on the red earth hilly region in southeastern China. To be able to make sure that the measured turbulence flux will equal the net ecosystem/atmosphere exchange, the quality of the data has to be assessed. Three criteria were investigated here, including the power spectra and cospectra analyses, flux variance similarity (integral turbulence test) and energy balance closure. The spectral analyses suggested that above-canopy power spectral slopes for all velocity components and scalars such as CO2, H2O and air temperature followed the expected -2/3 power law in the inertial subrange, and their cospectral slopes were close to -4/3 power law in the inertial subrange. The important contribution of large-scale motions to energy and mass transfer above the canopy at higher measurement level was also confirmed by the spectral analyses. The eddy covariance systems have the ability to resolve fluctuations associated with small-scale eddies and did not induce an obvious underestimation of the measured turbulence flux. The Monin-Obukhov similarity functions for the normalized standard deviation of vertical wind speed and air temperature were well-defined functions of atmospheric stability at two heights above the forest canopy, which indicated that turbulence flux measurements made at two heights were within the surface layer. Nocturnal flux underestimation and departures of this normalized standard deviation of vertical wind speed similarity function from that expected from Monin-Obukhov theory were a function of friction velocity. Thus, an optimal criterion of friction velocity was determined to be greater than 0.2-0.3 m s-1 for nocturnal fluxes so that the eddy covariance flux measurement was under high turbulent mixing conditions. Energy balance closure reached about 72%-81% at the studied site, which was comparable to the 10%-30% of energy imbalance reported in the literature. However, the energy balance closure could be only used as a useful reference criterion.     

Composite eddy structures on both sides of the Luzon Strait and influence factors

Combining Argo observations with satellite remote sensing data during the period of 2002–2014, the mean three-dimensional structures of mesoscale eddies on both sides of the Luzon Strait (LS) were obtained via a composite method and analyzed to statistically examine the influences of background marine environment and the Kuroshio current on the eddy structures. The significant signals of temperature and salinity anomalies within the composite eddies extend much deeper in the region east of the LS (zone E) than those in the region west of the strait (zone W) because of stronger eddy intensity and larger vertical gradients of background temperature and salinity in the deep layer in zone E. In the vertical structure of temperature anomaly within the eddies, two cores occur at around 200 and 400 dbar depths, respectively, in zone E and only one core is centered at about 100 dbar in zone W. There is a clear three-core sandwich pattern in the vertical structure of salinity anomaly within the eddies in zone E. The Kuroshio water trapped in the eddy is responsible for abnormally positive salinity anomaly in the surface layer of the anticyclonic eddy center in zone W. On both sides of the LS, an asymmetric dipole structure in the surface layer gradually turns into a monopole one at depths, which resulted from the competition between horizontal advection effect and eddy pumping effect. The Kuroshio current influences the distribution patterns of isotherms and isohalines and enhances background temperature and salinity horizontal gradients on both sides of the LS, determining the orientations of dipole temperature and salinity structures within eddies.     

Observations of submesoscale eddies using high-frequency radar-derived kinematic and dynamic quantities

The spatio-temporal variability of submesoscale eddies off southern San Diego is investigated with two-year observations of subinertial surface currents [O(1) m depth] derived from shore-based high-frequency radars. The kinematic and dynamic quantities — velocity potential, stream function, divergence, vorticity, and deformation rates — are directly estimated from radial velocity maps using optimal interpolation. For eddy detection, the winding-angle approach based on flow geometry is applied to the calculated stream function. A cluster of nearly enclosed streamlines with persistent vorticity in time is identified as an eddy. About 700 eddies were detected for each rotation (clockwise and counter-clockwise). The two rotations show similar statistics with diameters in the range of 5–25 km and Rossby number of 0.2–2. They persist for 1–7 days with weak seasonality and migrate with a translation speed of 4–15 cm s⁻¹ advected by background currents. The horizontal structure of eddies exhibits nearly symmetric tangential velocity with a maximum at the defined radius of the eddy, non-zero radial velocity due to background flows, and Gaussian vorticity with the highest value at the center. In contrast divergence has no consistent spatial shape. Two episodic events are presented with other in situ data (subsurface current and temperature profiles, and local winds) as an example of frontal-scale secondary circulation associated with drifting submesoscale eddies.     

Low-frequency variability in atmospheric middle latitudes

A short review of research trends in the study of low-frequency mid-latitude variations is presented. Theoretical developments have been concentrated upon with the major themes of multiple equilibria, flow stability and eddy-mean flow interaction reflecting the authors main interests. A new interpretation of the role of transient eddies in maintaining atmospheric blocking is also suggested in which eddy potential vorticity fluxes are considered to mediate a downstream transition between a zonal and a steady free Rossby wave flow. This treatment avoids emphasizing local balances and fluxes by the transients which are often entirely or partially reversible. The consequences of this interpretation are explored in the barotropic model of blocking first presented by Shutts (1983). This interpretation is used to suggest conditions in which the jetstream may be unlikely to undergo transition to a blocked weather regime.     

Experimental and numerical modelling of sedimentation in a rectangular shallow basin

Numerical simulation of flows in shallow reservoirs has to be checked for its consistency in predicting real flow conditions and sedimentation patterns. Typical flow patterns may exhibit flow separation at the inlet, accompanied by several recirculation and stagnation areas all over the reservoir surface. The aim of the present research project is to study the influence of the geometry of a reservoir on sediment transport and deposition numerically and experimentally, focusing on a prototype reservoir depth between 5 and 15 m as well as suspended sediment transport.
A series of numerical simulations is presented and compared with scaled laboratory experiments, with the objective of testing the sensitivity to different flow and sediment parameters and different turbulence closure schemes. Different scenarios are analyzed and a detailed comparison of preliminary laboratory tests and some selected simulations are presented.
The laboratory experiments show that suspended sediment transport and deposition are determined by the initial flow pattern and by the upstream and downstream boundary conditions. In the experiments, deposition in the rectangular basin systematically developed along the left bank, although inflow and outflow were positioned symmetrically along the centre of the basin. Three major horizontal eddies developed influencing the sediment deposition pattern. Although asymmetric flow patterns are privileged, a symmetric pattern can appear from time to time. This particular behaviour could also be reproduced by a two-dimensional depth-averaged flow and sediment transport model （CCHE2D）. The paper presents numerical simulations using different turbulence closure schemes （k-ε and eddy viscosity models）. In spite of the symmetric setup, these generally produced an asymmetric flow pattern that can easily switch sides depending on the assumptions made for the initial and boundary conditions. When using the laboratory experiment as a reference, the most reliable numerical results have been obtai     

Application of a sigma coordinate sea model to the calculation of wind-induced currents

A three-dimensional numerical sea model is formulated in terms of sigma coordinates in the vertical. The vertical grid spacing in the model is arbitrary and can be refined to give enhanced resolution in high shear regions (e.g., close to the sea surface in wind-driven flows, and/or across the thermocline in stratified flows). A method of accurately determining surface currents and indicating how fine a grid is required in the surface layer is described.The problem of determining a suitable formulation of vertical eddy viscosity to use in a model of wind-induced flow in a tidal sea is considered in detail. A formulation in which surface eddy viscosity depends upon the roughness of the sea surface and the transfer of momentum to depth by surface waves appears reasonable. Below the surface layer turbulence is related to the current at depth.Idealized calculations are performed to demonstrate the accuracy and stability of the sigma coordinate model. Results of these calculations indicate that the formulation of eddy viscosity developed in this paper can explain the high surface shears reported in lake measurements of wind-induced surface currents, and the lack of shear under strong wind conditions in the open sea (GORDON, 1982, Journal of Geophysical Research, 87, 1939–1951).Surface current to surface wind ratio are also computed.     

An enhanced depth-averaged tidal model for morphological studies in the presence of rotary currents

A simple and efficient method to improve morphological predictions using depth-averaged tidal models is presented. The method includes the contribution of secondary flows in sediment transport using the computed flow field from a depth-averaged model. The method has been validated for a case study using the 3D POLCOMS model and ADCP data. The enhanced depth-averaged tidal model along with the SWAN wave model are applied to morphological prediction around the Lleyn Peninsula and Bardsey Island as a case study in the Irish Sea. Due to the presence of a headland in this area two asymmetrical tidal eddies are developed in which the cyclonic eddy is stronger as a result of Coriolis effects. The results show that the enhanced model can effectively predict formation of sand banks at the centre of cyclonic eddies, while the depth-averaged model, due to its inability to accommodate secondary flow, is inadequate in this respect.     

Stochastic particle based models for suspended particle movement in surface flows

Modeling of suspended sediment particle movement in surface water can be achieved by stochastic particle tracking model approaches.In this paper,different mathematical forms of particle tracking models are introduced to describe particle movement under various flow conditions,i.e.,the stochastic diffusion process,stochastic jump process,and stochastic jump diffusion process.While the stochastic diffusion process can be used to represent the stochastic movement of suspended particles in turbulent flows,the stochastic jump and the stochastic jump diffusion processes can be used to describe suspended particle movement in the occurrences of a sequence of extreme flows.An extreme flow herein is defined as a hydrologic flow event or a hydrodynamic flow phenomenon with a low probability of occurrence and a high impact on its ambient flow environment.In this paper,the suspended sediment particle is assumed to immediately follow the extreme flows in the jump process（i.e.the time lag between the flow particle and the sediment particle in extreme flows is considered negligible）.In the proposed particle tracking models,a random term mainly caused by fluid eddy motions is modeled as a Wiener process,while the random occurrences of a sequence of extreme flows can be modeled as a Poisson process.The frequency of occurrence of the extreme flows in the proposed particle tracking model can be explicitly accounted for by the Poisson process when evaluating particle movement.The ensemble mean and variance of particle trajectory can be obtained from the proposed stochastic models via simulations.The ensemble mean and variance of particle velocity are verified with available data.Applicability of the proposed stochastic particle tracking models for sediment transport modeling is also discussed.     

Impacts of the Kuroshio intrusion on the two eddies in the northern South China Sea in late spring 2016

During mid-May to early June 2016, a cold eddy and a warm eddy were captured on the continental slope of the northern South China Sea by the in situ measurements. A salty lens-shaped water mass in the subsurface layer existed in these two detected eddies, which indicated they had a Kuroshio water origin. The trajectories of the observed eddies from satellite altimeter data show that the cold eddy was generated in the central part of the Luzon Strait, while the warm eddy was formed southwest of Taiwan. The genesis of the cold eddy is related to a weak Kuroshio loop current, while that of the warm eddy is associated with a strong Kuroshio loop current. The warm eddy east of the Luzon Strait may trigger the Kuroshio from a leaping path to a looping path. During the evolution of these detected eddies, they had interactions with the Kuroshio and Luzon Gyre. Energy analysis from ocean reanalysis data showed that the baroclinic conversion between the cold eddy and the Kuroshio was stronger than that between the cold eddy and Luzon Gyre. During the eddy shedding stage, the warm eddy mainly acquired energy from the Kuroshio loop current through the baroclinic conversion.     

On the meridional circulation and balance of momentum in the Southern Ocean of POP

 The circulation of the Southern Ocean is studied in the eddy-resolving model POP (Parallel Ocean Program) by an analysis of zonally integrated balances. The TEM formalism (Transformed Eulerian Mean) is extended to include topography and continental boundaries, thus deviations from a zonally integrated state involve transient and standing eddies. The meridional circulation is presented in terms of the Eulerian, eddy-induced, and residual streamfunctions. It is shown that the splitting of the meridional circulation into Ekman and geostrophic transports and the component induced by subgrid and Reynolds stresses is identical to a particular form of the zonally integrated balance of zonal momentum. In this balance, the eddy-induced streamfunctions represent the interfacial form stresses by transient and standing eddies and the residual streamfunction represents the acceleration of the zonal current by density fluxes in a zonally integrated frame. The latter acceleration term is directly related to the surface flux of density and interior fluxes due to the resolved and unresolved eddies. The eddy-induced circulation is extremely vigorous in POP. In the upper ocean a shallow circulation, reversed in comparison to the Deacon cell and mainly due to standing eddies, appears to the north of Drake Passage latitudes, and in the Drake Passage belt of latitudes a deep-reaching cell is induced by transient eddies. In the resulting residual circulation the Deacon cell is largely cancelled and the residual advection of the zonal mean potential density is balanced by diapycnal eddy and subgrid fluxes which are strong in the upper few hundred meters but small in the ocean interior. The balance of zonal momentum is consistent with other eddy-resolving models; a new aspect is the clear identification of density effects in the zonally integrated balance. We show that the wind stress and the stress induced by the residual circulation drive the eastward current, whereas both eddy species result in a braking. Finally, we extend the Johnson–Bryden model of zonal transport to incorporate all relevant terms from the zonal momentum balance. It is shown that wind stress and induction by the residual circulation carry an eastward transport while bottom form stress and the stress induced by standing eddies yield westward components of transport. Received: 26 June 2001 / Accepted: 2 November 2001     

LES of turbulent surface shear stress and pressure-gradient-driven flow on shallow continental shelves

Turbulent shear flows on shallow continental shelves (here shallow means that the interaction with the solid, no-slip bottom is important) are of great importance because tide- and wind-driven flows on the shelf are drivers of the transfer of momentum, heat, and mass (gas) across the air–sea interface. These turbulent flows play an important role because vertical mixing and current are vectors for the transport of sediment and bioactive material on continental shelves. Understanding the dynamics of this class of flows presents complications because of the presence of a free surface and also because the flow can be driven by a pressure gradient (a tidal current), a stress at the free surface (a wind-driven current), or a combination of both. In addition, the flow can be modified by the presence of a wave field that can induce Langmuir circulation (Langmuir, Science 87:119–123, 1938). Large eddy simulation is used to quantify the effects of pressure gradient and wind shear on the distinctive structures of the turbulent flow. From these computations, an understanding of the physics governing the turbulence of pressure-driven and wind-driven flows, how they can interact in a normal or a tangential direction, and the effect of wave forcing on these flows is obtained.