Reynolds Flux Research Articles

On the definition, evolution, and properties of the outer edge of gravity currents: A direct-numerical and large-eddy simulation study

Gravity currents are flows driven by the action of gravity over fluids with different densities. Here, we focus on gravity currents where heavier fluid travels along the bottom of a sloping bed, underneath a large body of stagnant lighter ambient fluid. The thickness of the current increases due to entrainment of ambient fluid into the current. Direct numerical and large eddy simulations of gravity currents and a wall-jet transporting a passive scalar field are performed. We focus on the rate of penetration of mean momentum and mean concentration of the agent responsible for the density difference (temperature, salinity, or sediment volume fraction) into the ambient fluid. The rates of penetration of turbulence-related quantities (i.e., turbulent kinetic energy, Reynolds flux, and stress) into the ambient are analyzed. A robust methodology for defining the upper edge of these quantities and thereby defining the current thickness using these different mean and turbulent quantities is presented. A comparison between downstream evolution of the gravity current with the corresponding behaviors of canonical wall-bounded turbulent flows is presented. The present understanding of turbulent/non-turbulent interface (TNTI) is extended to include subcritical flows where, due to the strong effect of stratification, the TNTI is buried well within the upper edge of the current and confined right above the inner near-bed layer. The present work sheds light on the striking difference between the different definitions of thickness (momentum, concentration, turbulence, etc.) in subcritical gravity currents, where stratification suppresses turbulence in the upper region of the current.

Application of Reynolds flux modeling in CFD simulation of 45$$^{\circ}$$ inclined negatively buoyant jets

Application of Reynolds flux modeling in CFD simulation of 45$$^{\circ}$$ inclined negatively buoyant jets

Large eddy simulation of the hydrodynamic behavior of horizontal side jets in compound open channels with vegetated floodplain.

Understanding the hydrodynamic behavior of side jets in compound open channels with vegetated floodplain is crucial to jet dilution, sediment transport, and bank stability. Large eddy simulation was used to study horizontal side jets in compound open channels with vegetated floodplain. Predicted mean velocity, turbulent kinetic energy, and secondary currents were compared with experimental data, with a good agreement between measured and calculated data. Analyses of bed shear stress showed that vegetation in the floodplain increases the total drag and decreases bed shear stress, thus governing sediment transport and protecting the bank. The transport mechanism was quantitatively investigated by the quadrant analysis, concentration, and Reynolds flux. The ejection and sweep events were major contributors to the momentum and scalar flux transport. Analyses of concentration and Reynolds flux showed that the secondary flow influenced the spreading of the jet and the location of the concentration peaks, and the distribution of concentration and Reynolds flux did not strictly follow Fickian law in the whole region due to the effect of secondary flow on the concentration distributions. Additionally, the typical vortexes and spatiotemporal evolution of vortex structures in compound open channels, especially those near the junction between the main channel and floodplain, were successfully demonstrated.

Mesoscale contribution to the long-range offshore transport of organic carbon from the Canary Upwelling System to the open North Atlantic

Abstract. Several studies in upwelling regions have suggested that mesoscale structures, such as eddies and filaments, contribute substantially to the long-range transport of the organic carbon from the nearshore region of production to the offshore region of remineralization. Yet a comprehensive analysis of this mesoscale flux and of its impact across the Canary Upwelling System (CanUS) has not been provided. Here, we fill this gap using simulations with the Regional Oceanic Modeling System (ROMS) coupled to a Nutrient, Phytoplankton, Zooplankton and Detritus (NPZD) ecosystem model. We run climatological simulations on an Atlantic telescopic grid with an eddy-resolving resolution in the CanUS. Using both a Reynolds flux decomposition and structure-identification algorithms, we quantify and characterize the organic carbon fluxes driven by filaments and eddies within the upper 100 m and put them in relationship to the total offshore transport. Our analysis reveals that both coastal filaments and eddies enhance the offshore flux of organic carbon, but that their contribution is very different. Upwelling filaments, with their high speeds and high concentrations, transport the organic carbon offshore in a very intense, but coastally confined manner, contributing nearly 80 % to the total flux of organic carbon at 100 km offshore. The filament contribution tapers off quickly to near zero values at 1000 km off the coast, leading to a strong offshore flux divergence that is the main lateral source of organic carbon in the coastal waters up to 1000 km offshore. Some of this divergence is also due to the filaments inducing a substantial vertical subduction of the organic carbon below 100 m. Owing to the temporal persistence and spatial recurrence of filaments, the filament transport largely constitutes a time-mean flux, while the time-varying component, i.e., the turbulent flux, is comparatively small. At distances beyond 500 km from the coast, eddies dominate the mesoscale offshore transport. Although their contribution represents only 20 % of the total offshore flux and its divergence, eddies, especially cyclones, transport organic carbon offshore to distances as great as 2000 km from the coast. The eddy transport largely represents a turbulent flux, but striations in this transport highlight the existence of typical formation spots and recurrent offshore propagation pathways. While they propagate slowly, eddies are an important organic carbon reservoir for the open waters, as they contain, on average, a third of the organic carbon in this region, two thirds of which is found in cyclones. Our analysis confirms the importance of mesoscale processes for the offshore organic carbon transport and the fueling of the heterotrophic activity in the eastern subtropical North Atlantic, and highlights the need to consider the mesoscale flux in order to fully resolve the three-dimensionality of the marine organic carbon cycle.

Differentiating the effects of advection and resuspension on suspended sediment concentrations in a turbid estuary

Suspended sediment concentration (SSC) has a significant impact on the estuarine environment and its morphological evolution. At any given location, the temporal variability of depth-averaged SSC is due to a combination of two processes: horizontal advection and local resuspension. In this study, we investigated the sediment dynamics at three anchored monitoring stations close to the maximum turbidity zone of the Changjiang Estuary, and developed a box model to differentiate the effects of advection and resuspension. Further, settling velocities were estimated using the ADV Reynolds flux method, excluding the advection SSC component. We found that predicted changes in advection- and resuspension-induced SSCs were consistent with the bottom shear stress and accretion/erosion observations. The combination of observed bed accretion/erosion changes and the predicted advection-induced SSCs indicates that the advective transport of suspended sediment is an important process in accelerating persistent erosion at the monitoring stations. Although SSC variations due to advection and resuspension are of similar magnitudes, our model results indicate that if resuspension dominates, the resuspension-induced component can reach up to twice the magnitude of the advection-induced component. We conclude that the box model is a valuable tool for evaluating subaqueous delta accretion/erosion in response to sediment reduction caused by upstream dam construction and climate change.

Effect of submerged vegetation on solute transport in an open channel using large eddy simulation

Existence of vegetation plays a significant effect on the flow velocity distributions, turbulence structures and solute mixing in an open channel. This paper has implemented a 3D large eddy simulation model for the flow and scalar transport in the open channel with vegetation. The model can produce a typical turbulence characteristics and concentration distribution with vegetation. The scalar transport mechanism is quantitatively explained by the turbulent Schmidt number, Reynolds flux, coherent structures and quadrant conditional analysis. A dominance of ejection-sweeping events occurs in the process of the momentum and scalar flux transport. The spectral analysis is used to identify the Kelvin–Helmholtz frequency. The turbulence characteristics of the length scale of vortexes, Kelvin–Helmholtz frequency and Reynolds stress etc. are analyzed with the vegetation density. The model quantitatively predicts the trend of decreasing in the concentration distribution along the flow direction with the increasing of vegetation density.

A test of the ADV-based Reynolds flux method for in situ estimation of sediment settling velocity in a muddy estuary

Under conditions common in muddy coastal and estuarine environments, acoustic Doppler velocimeters (ADVs) can serve to estimate sediment settling velocity (w s) by assuming a balance between upward turbulent Reynolds flux and downward gravitational settling. Advantages of this method include simple instrument deployment, lack of flow disturbance, and relative insensitivity to biofouling and water column stratification. Although this method is being used with increasing frequency in coastal and estuarine environments, to date it has received little direct ground truthing. This study compared in situ estimates of w s inferred by a 5-MHz ADV to independent in situ observations from a high-definition video settling column over the course of a flood tide in the bottom boundary layer of the York River estuary, Virginia, USA. The ADV-based measurements were found to agree with those of the settling column when the current speed at about 40 cm above the bed was greater than about 20 cm/s. This corresponded to periods when the estimated magnitude of the settling term in the suspended sediment continuity equation was four or more times larger than the time rate of change of concentration. For ADV observations restricted to these conditions, ADV-based estimates of w s (mean 0.48±0.04 mm/s) were highly consistent with those observed by the settling column (mean 0.45±0.02 mm/s). However, the ADV-based method for estimating w s was sensitive to the prescribed concentration of the non-settling washload, C wash. In an objective operational definition, C wash can be set equal to the lowest suspended solids concentration observed around slack water.

Study of parameters and entrainment of a jet in cross-flow arrangement with transition at two low Reynolds numbers

Investigation of the mixing process is one of the main issues in chemical engineering and combustion and the configuration of a jet into a cross-flow (JCF) is often employed for this purpose. Experimental data are gained for the symmetry plane in a JCF-arrangement of an air flow using a combination of particle image velocimetry (PIV) with laser-induced fluorescence (LIF). The experimental data with thoroughly measured boundary conditions are complemented with direct numerical simulations, which are based on idealized boundary conditions. Two similar cases are studied with a fixed jet-to-cross-flow velocity ratio of 3.5 and variable cross-flow Reynolds numbers equal to 4,120 and 8,240; in both cases the jet issues from the pipe at laminar conditions. This leads to a laminar-to-turbulent transition, which depends on the Reynolds number and occurs quicker for the case with higher Reynolds number in both experiments and simulations as well. It was found that the Reynolds number only slightly affects the jet trajectory, which in the case with the higher Reynolds number is slightly deeper. It is attributed to the changed boundary layer shape of the cross-flow. Leeward streamlines bend toward the jet and are responsible for the strong entrainment of cross-flow fluid into the jet. Velocity components are compared for the two Reynolds numbers at the leeward side at positions where strongest entrainment is present and a pressure minimum near the jet trajectory is found. The numerical simulations showed that entrainment is higher for the case with the higher Reynolds number. The latter is attributed to the earlier transition in this case. Fluid entrainment of the jet in cross-flow is more than twice stronger than for a similar flow of a jet issuing into a co-flowing stream. This comparison is made along the trajectory of the two jets at a distance of 5.5 jet diameters downstream and is based on the results from the direct numerical simulations and recently published experiments of a straight jet into a co-flow. Mixing is further studied by means of second-order statistics of the passive scalar variance and the Reynolds fluxes. Windward and leeward sides of the jet exhibit different signs for the time-averaged streamwise Reynolds flux 〈vx′c′〉. The large coherent structures which contribute to this effect are investigated by means of timely correlated instantaneous PIV-LIF camera snapshots and their contribution to the average statistics of 〈vx′c′〉 are discussed. The discussion on mixing capabilities of the jet in cross-flow is supported by simulation results showing the instantaneous three-dimensional coherent structures defined in terms of the pressure fluctuations.

Erratum for “Particle Image Velocimetry Measurements and Numerical Modeling of a Saline Density Current” by G. Gerber, G. Diedericks, and G. R. Basson

Fig. 9. Excess density variance profiles; measured hΔρ0Δρ0i profile at x=h 1⁄4 30 (circles with 95% confidence interval), measured hΔρ0Δρ0i profile at x=h 1⁄4 80 (triangles) Fig. 10. Anisotropic Reynolds flux profiles at x=h 1⁄4 30, showing maxima at the interface; measured hΔρ0u0i profiles (circles with 95% confidence interval), measured hΔρ0v0i profile (triangles), simulated hΔρ0v0i 1⁄4 ΓtdhΔρi=dy profile (solid line)

Modeling the transport of passive tracers in sea ice

A model for the vertical transport of passive tracers in sea ice is presented. Two Reynolds flux closure approximations are proposed for the tracer velocity dispersion term in the new ice tracer model (IceT). The schemes, “enhanced molecular diffusion” (EMD) and “mixing length diffusion” (MLD), are suggested parameterizations of gravity drainage, the dominant mechanism of desalination in growing sea ice. The performance of IceT using each parameterization is tested against two experimental studies: simulations I compare profiles of brine salinity with passive tracer concentrations during sea ice growth and melt, and simulations II compare bottom boundary salt and brine volume fluxes with passive tracer fluxes and bottom diffusivities. IceT behavior is evaluated under three salinity forcing prescriptions. Both schemes successfully reproduce expected tracer concentrations in simulations I when the salinity forcing evolves logarithmically. However in simulations II, the MLD scheme outperforms EMD in two significant ways: 1) growth rate trends in the MLD diffusivity parallel measurements of brine volume flux, while EMD bottom diffusivities remain almost constant; and 2) MLD bottom tracer concentrations decrease with ice growth rate similar to excluded brine salinity, while EMD trends are contrary. Hence, enhanced molecular diffusion is highly questionable for implementation in models of reactive passive tracers. The IceT mixing length diffusivity is a viable choice in sea ice biogeochemical modeling. It remains a challenge to assess whether MLD can provide quantitative estimates of desalination at each time step for use in forcing IceT or for implementation in a model of sea ice salinity.

Measurement and Simulation of Turbulent Mixing in a Jet in Crossflow

Computational fluid dynamics (CFD) has an important role in current research. While large eddy simulations (LES) are now common practice in academia, Reynolds-averaged Navier–Stokes (RANS) simulations are still very common in the industry. Using RANS allows faster simulations, however, the choice of the turbulence model has a bigger impact on the results. An important influence of the turbulence modeling is the description of turbulent mixing. Experience has shown that often inaccurate simulations of combustion processes originate from an inadequate description of the mixing field. A simple turbulent flow and mixing configuration of major theoretical and practical importance is the jet in crossflow (JIC). Due to its good fuel-air mixing capability over a small distance, JIC is favored by gas turbine manufacturers. As the design of the mixing process is the key to creating stable low NOx combustion systems, reliable predictive tools and detailed understanding of this basic system are still demanded. Therefore, the current study has re-investigated the JIC configuration under engine relevant conditions both experimentally and numerically using the most sophisticated tools available today. The combination of planar particle image velocimetry and laser induced fluorescence was used to measure the turbulent velocity and concentration fields as well as to determine the correlations of the Reynolds stress tensor ui′uj′¯ and the Reynolds flux vector ui′c′¯. Boundary conditions were determined using laser Doppler velocimetry. The comparisons between the measurements and simulation using RANS and LES showed that the mean velocity field was well described using the SST turbulence model. However, the Reynolds stresses and more so, the Reynolds fluxes deviate substantially from the measured data. The systematic variation of the turbulent Schmidt number reveals the limited influence of this parameter indicating that the basic modeling is amiss. The results of the LES simulation using the standard Smagorinsky model were found to provide much better agreement with the experiments also in the description of turbulent mixing.

Particle Image Velocimetry Measurements and Numerical Modeling of a Saline Density Current

Particle image velocimetry scalar measurements were carried out on the body of a stably stratified density current with an inlet Reynolds number of 2,300 and bulk Richardson number of 0.1. These measurements allowed the mass and momentum transport between the current and the less dense ambient fluid to be investigated. Reynolds stress, Reynolds flux, and shear production of turbulent kinetic-energy profiles revealed local maxima at the bed, as well as at the interface with the ambient fluid. Profiles of excess density variance and buoyancy production of turbulent kinetic energy revealed only local maxima at the interface with the ambient. These maxima decreased downstream as the stable density gradient reduced the turbulent intensities, until turbulence collapsed. A two-dimensional, unsteady, Reynolds-averaged Navier-Stokes (2DV-URANS) simulation was also performed on this density current. Good agreement was found between the modeled and measured normalized mean flow profiles. A comparison was also made between the measured and modeled outer flow scales of the density current. DOI: 10.1061/(ASCE)HY.1943-7900.0000304. © 2011 American Society of Civil Engineers. CE Database subject headings: Density currents; Flow measurement; Turbulence; Reynolds stress; Diffusion; Numerical models. Author keywords: Density current; Flow measurement; Navier-Stokes equations; Turbulence; Reynolds stress; Turbulent diffusion.

Turbulent mass and momentum transport of a circular offset dense jet

Turbulence characteristics of a circular dense jet offset by a small distance from a parallel horizontal boundary have been studied using the combined particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) method. The cross-sectional profiles of the turbulence intensity, Reynolds shear stress and Reynolds flux reveal the characteristics of the flow transition from a dense-jet regime to a wall-dense-jet regime. In the dense-jet regime, the profiles at different downstream locations collapse after normalization, and the turbulent. Self-similarity has not been reached in the covered transitional regime. Turbulent mass and momentum transport are found to be weaker than in the unbounded vertical buoyant jet, but are growing with the transition to the wall jet. In the transitional regime, the turbulence characteristics grow stronger but self-similarity was not observed. The associated turbulent viscosity, ν t , turbulent diffusivity, D t as well as the turbulent Schmidt number, Sc t , have been derived from the presented experimental data.

Observations of sediment resuspension and settling off the mouth of Jiaozhou Bay, Yellow Sea

We deployed bottom-mounted quadrapod equipped with acoustic Doppler current profiler (ADCP), acoustic Doppler velocimeter (ADV), and optical backscatter sensor (OBS) over two semidiurnal tidal cycles along the western coast of the Yellow Sea, China. In combination with shipboard profiling of CTD and LISST-100, we resolved the temporal and spatial distributions of tidal currents, turbulent kinetic energy (TKE), suspended sediment concentration (SSC) and particle size distributions. During the observations, tidal-induced bottom shear stress was the main stirring factor. However, weak tidal flow during the ebb phase was accompanied by two large SSC and median size events. The interactions of seiche-induced oscillations with weak ebb flow induced multiple flow reversals and provided a source of turbulence production, which stripped up the benthic fluff layers (only several millimeters) around the Jiaozhou Bay mouth. Several different methods for inferring mean suspended sediment settling velocity agreed well under peak currents, including estimates using LISST-based Stokes’ settling law, and ADCP-based Rouse profiles, ADV-based inertial-dissipation balance and Reynolds flux. Suspended particles in the study site can be roughly classified into two types according to settling behavior: a smaller, denser class consistent with silt and clay and a larger, less dense class consistent with loosely aggregated flocs. In the present work, we prove that acoustic approaches are robust in simultaneously and non-intrusively estimating hydrodynamics, SSC and settling velocities, which is especially applicable for studying sediment dynamics in tidal environments with moderate concentration levels.

Numerical simulation of forced convective evaporation system for tannery effluent

A numerical technique for evaluating the performance of forced convective evaporation system for tannery effluent is presented. The paper describes a mathematical model, which treats the airflow to be two dimensional and liquid flow to be one-dimensional. The turbulence in airflow is modeled with low Reynolds number k– ε model. The interface heat and mass transfer are represented by Reynolds flux model. The governing equations are solved using a modified MAC (Marker and Cell) method. The model is embodied into a computer code, which is applicable to forced convective evaporation system as well as mechanical draft cooling towers of both counter flow and cross flow types. Predicted results compare well with the available data in the literature and with that of experimental data and give closer results than the existing models. Distributions of air velocities, pressure, moisture fraction and air and water temperatures have been presented. The model can be used as design as well as optimization tool.

Predictions of solute transport in a compound channel using turbulence models

Prediction of solute distributions in an asymmetric compound channel is carried out using two turbulence models. Results of the numerical models are compared with turbulence data recently obtained using laser Doppler anemometer (LDA) and laser induced fluorescence (LIF) in a small laboratory flume. The predicted distributions of solute and Reynolds flux using a k-s model and an algebraic stress model for various injection points near the water surface are used to identify different mixing mechanisms. A skewed distribution of solute on the floodplain observed in the experimental data is well predicted by the algebraic stress model but not by the k-ε model. The cause of the skewed distribution is examined through the variations of secondary flow and eddy diffusivity. The predicted eddy viscosity and diffusivity and the turbulent Schmidt number are discussed with the experimental data. As a result, solute concentration distribution can be well predicted by adjusting the turbulent Schmidt number even if the eddy viscosity was not correctly calculated by any particular model. An effect of secondary flow on peak concentration in the shear layer along the channel is also demonstrated.

Turbulence Measurements of Dye Concentration and Effects of Secondary Flow on Distribution in Open Channel Flows

This paper presents simultaneous turbulence measurements of velocity and tracer concentration using a combination of laser Doppler anemometer (LDA) and laser induced fluorescence (LIF) in rectangular and compound channels. Secondary flow, Reynolds stresses, Reynolds fluxes, and dye concentration distributions were measured near the water surface in both channels. An investigation of the effect of secondary flow on passive contaminant diffusion processes was carried out with relatively weak secondary flow in the rectangular channel and relatively strong secondary flow in the compound channel. The results show that the secondary flow clearly influences the spreading of the tracer concentration and the location of concentration peak, being different from the injection location. The transport rate of solute due to the secondary flow is not significant in the rectangular channel case but significant in the compound channel case. The transverse eddy viscosity is demonstrated to be equal to the transverse eddy diffusivity. The transverse eddy diffusivity near the water surface is larger than the vertical one. The Fickian law is valid in most regions investigated, but there are some regions where the Reynolds flux and concentration gradients are locally of the same sign due to the influence of secondary flow on the concentration distribution.

Numerical Investigation of a Bluff-Body Stabilised Nonpremixed Flame with Differential Reynolds-Stress Models

A numerical investigation of a bluff-body stabilised nonpremixedflame, and the corresponding nonreacting flow, has been performed withdifferential Reynolds-stress models (DRSMs). The equilibrium chemistry model is employed and an assumed-shape beta function PDFapproach is used to represent the interaction between turbulence andchemistry. The Reynolds flux of the mixture fraction is obtained from atransport equation, hence a full second moment closure is used. Toclarify the applicability of the existing DRSMs in this complex flame,several models, including LRR-IP model, JM model, SSG model as well as amodified LRR-IP model, have been applied and evaluated. The existingmodels, with default values of the coefficients, cannot provide overallsatisfactory predictions for this challenging test case. The standardLRR-IP model over predicts the centreline velocity decay rate, andtherefore does not perform satisfactory. The modified LRR-IP model, withmodel constant C ∈1 = 1.6 instead of the standard value1.44 (here named BM-M1), gives better results for the mean velocity.However in the nonreacting case this does not lead to improvement inpredicting rms fluctuating velocities especially downstream of therecirculation zone. Motivated by the need to improve the prediction, anew modification of the LRR-IP model is proposed (BM-M2), with modelconstant C 2 = 0.7in the pressure strain correlation rather thanthe standard value 0.6. With the new modified model, a verysignificant improvement of the prediction of flow field is obtained inthe nonreacting case, whereas in the reacting case the prediction ofthe flow field is of the same overall quality as with BM-M1. This showsthat some DRSMs have different behaviour in the nonreacting case andthe reacting case. In the reacting case also the mean and variance ofmixture fraction are considered and it is found that the best resultsare obtained with the BM-M1 model, with SSG as second best. Combiningthe results for flow field and mixture fraction field it is concludedthat the BM-M1 model is recommended for further studies of thisbluff-body stabilised flame. Grid independence of the result isdemonstrated.

On the relevance of diapycnal mixing for the stability of frontal meanders

SUMMARY: This work examines the possible importance of shear-induced diapycnal mixing in controlling the evolution and stability of meanders in oceanic frontal jets. We first review the conditions necessary for vortex stability and investigate how these may be modified in the presence of diapycnal mixing. The procedure used is rather crude but provides a measure of the relative importance of diapycnal mixing. It consists in constructing a simplified equation for the radial velocity that retains the density tendency and examining under what circumstances this velocity may grow in time. Next, we use a simple two-dimensional isopycnic model to examine the intensity of diapycnal mixing in meanders. In the model the alongfront velocity is in geostrophic balance and the ageostrophic contributions are an oscillating deformation field and diapycnal mass exchange. The horizontal deformation field increases the slope of the isopycnals in temporal scales typical of Gulf Stream meanders, causing a reduction of the gradient Richardson number, Ri. The diapycnal flux is calculated as the divergence of the density Reynolds flux, which is parameterized in terms of Ri. The results of the model show that diapycnal mixing increases during the frontogenetical stages, reaching density tendency values of the order of 10 -4 kg m -3 s -1 and convergence/divergence values of the order of 10 -3 s -1 . It turns out that diapycnal mixing in meanders may be intense enough to control the separation and slope of the isopycnals and to condition the possibility of barotropic instability.

On the structure of supercritical western boundary currents

Abstract The structure of supercritical western boundary currents is investigated using a quasi-geostrophic numerical model. The basic flow is of meridional Munk balance, and the input boundary is perturbed by the most unstable wave solution obtained from linear spatial instability calculations. Self-preserving (or equilibrium) solutions are obtained for the model runs at Re =30, 60, 90, and 120, and their energy and vorticity budgets are analyzed. In an analogy with the laboratory turbulence of wall boundary layers, the western boundary layer is divided into inner and outer layers. In the inner layer, the mean energy is dissipated via direct viscous dissipation, while in the outer layer it is converted to the eddy energy via turbulence production. The main scenario is that the mean energy is produced in the inner layer via ageostrophic pressure work divergence, and it is partly removed due to viscous action within a narrow region near the wall, defined here as viscous sub-layer. The remaining portion is converted to the eddy energy via turbulence production in the outer layer, which is in turn transported to the inner layer, then again to the viscous sub-layer where it is ultimately dissipated. In the near-wall side, the vorticity balance of the mean flow is maintained by viscous effect and Reynolds flux divergence, while in the offshore side it is maintained by beta effect and Reynolds flux divergence. The length scale of the supercritical boundary current is roughly ∼ 0.2 Re L M , where L M is the Munk length, as observed from a dimensional analysis.