Baroclinic adjustment in coarse‐resolution numerical ocean models

Abstract

The propagation of baroclinic Kelvin and Rossby waves in a fairly coarse‐resolution numerical reduced‐gravity ocean model is investigated using simple geostrophic adjustment experiments in a box‐like domain. Numerical experiments using three different horizontal resolutions (4° × 5°,2° × 2.5° and l° × 1.25°) with properly scaled eddy viscosity coefficients show that the phase speed of the model Kelvin waves is almost exactly proportional to the grid resolution, but is virtually independent of the model viscosity. These results are consistent with the findings of Hsieh et al. (1983) and Wajsowicz and Gill (1986). It is also shown that the two relevant parameters that govern the propagation and decay of these waves, namely the grid‐resolution parameter Δ = Δx/a (where Δx is the grid size and a is the baroclinic Rossby radius, viz. a = C/f, with C being the phase speed of inviscid internal gravity waves in a continuum) and the viscosity parameterΔ = A_mλ/2πfa³ (where A_m is the eddy viscosity coefficient and λ is the alongshore wavelength) can be replaced with Δ only. This is because in Munk (1950)‐type models, the viscosity parameter Δ scales with Δ³. For Δ³ >1, the Kelvin wave phase speed is c_K ΔC/Δ and the alongshore decay length scale is of the order of the perimeter of the basin, viz., 0(10⁴) km.

In contrast to the case for Kelvin waves, the phase speed of the model Rossby waves is not that much different from its value in a continuum and depends only weakly on the model resolution. This is in good agreement with the theoretical results of Wajsowicz (1986). On the other hand, the model Rossby waves are severely damped, within a distance of the order of a wavelength, by the large eddy viscosity of the model. We therefore extrapolate that for a proper simulanon of Kelvin and Rossby waves in this type of numerical ocean model, we need a grid size smaller than 1° × 1°, and a higher‐order turbulent closure scheme that will reduce the eddy viscosity coefficient.     

Neutrally Stratified Turbulent Ekman Boundary Layer: Universal Similarity for a Transitional Rough Surface

The geostrophic Ekman boundary layer for large Rossby number (Ro) has been investigated by exploring the role played by the mesolayer (intermediate layer) lying between the traditional inner and outer layers. It is shown that the velocity and Reynolds shear stress components in the inner layer (including the overlap region) are universal relations, explicitly independent of surface roughness. This universality of predictions has been supported by observations from experiment, field and direct numerical simulation (DNS) data for fully smooth, transitionally rough and fully rough surfaces. The maxima of Reynolds shear stresses have been shown to be located in the mesolayer of the Ekman boundary layer, whose scale corresponds to the inverse square root of the friction Rossby number. The composite wall-wake universal relations for geostrophic velocity profiles have been proposed, and the two wake functions of the outer layer have been estimated by an eddy viscosity closure model. The geostrophic drag and cross-isobaric angle predictions yield universal relations, which are also supported by extensive field, laboratory and DNS data. The proposed predictions for the geostrophic drag and the cross-isobaric angle compare well with data for Rossby number Ro ≥ 10⁵. The data show low Rossby number effects for Ro < 10⁵ and higher-order effects due to the mesolayer compare well with the data for Ro ≥ 10³.     

Marginal mixing theories

Abstract

Mixing near the sloping boundaries of oceans or lakes may be a significant mechanism of diapycnal transport. The basic physics of this is reviewed, with emphasis on the reduction of the effectiveness of the process due to both reduced stratification and the restratifying secondary circulation driven by buoyancy forces. This re stratification is shown to reduce the effectiveness of intermittent mixing events as well as steady mixing. It is argued that for boundary mixing to be effective in the abyssal ocean it must extend sufficiently far from the boundary that the stratification can be maintained; this may be true for breaking bottom‐reflected internal waves. The alongslope flow implied by steady‐state boundary mixing theories is downwelling‐favourable and has a magnitude related to the thickness and other properties of the boundary layer. Mixing near a boundary may thus tend to drive a downwelling‐favourable mean circulation in the interior. If the interior circulation is imposed by other forces, the bottom boundary layer may evolve to a steady state if the interior flow is downwelling‐favourable, but if it is upwelling‐favourable initially a steady state seems unlikely and the downwelling‐favourable alongslope flow induced by the boundary mixing will tend to diffuse slowly into the interior. The nature of the solution in all these cases is sensitive to the Burger number, N² sin² θ/f², where θ is the bottom slope, and to the eddy Prandtl number.     

The algebraic decay of equatorial Rossby waves in a shear flow

Through numerical integration, we show that equatorial Rossby waves, like their midlatitude counterparts, decay algebraically in the limit t → ∞ in a linear shear flow. For small times, the growth expected for some components does not translate into any growth of the wave disturbance as a whole when the initial conditions has a broad Fourier spectrum. The conclusion is that Rossby waves will amplify with time only when the mean flow has an inflection point or when the initial eddy field is strongly concentrated in long waves tilted against the shear.     

Dynamics of the Leeuwin Current: Part 2. Impacts of mixing,friction, and advection on a buoyancy-driven eastern boundary current over a shelf

The boundary currents over the Western Australian continental shelf and slope consist of the poleward flowing Leeuwin Current (LC) and the equatorward flowing Leeuwin Undercurrent (LUC). Key properties of the LC are its poleward strengthening, deepening to the south, and shelfbreak intensification. The alongshore flow reverses direction below about 300 m, forming the LUC at greater depths. To investigate the processes that cause these features, we obtain solutions to an idealized, regional ocean model of the South Indian Ocean. Solutions are forced by relaxing surface density to a prescribed, meridionally varying density profile ρ^*(y) with a timescale of δt. In addition, vertical diffusion is intensified near the ocean surface. This diffusion establishes the minimum thickness over which density is well-mixed. We define this thickness as the “upper layer”. Solutions are obtained with and without a continental shelf and slope off Western Australia and for a range of values of δt and mixing parameters. Within this upper layer, there is a meridional density gradient that balances a near-surface, eastward geostrophic flow. The eastward current downwells near the eastern boundary, leading to westward flow at depth. The upper layer's meridional structure and zonal currents crucially depend on coastal processes, including the presence of topography near the eastern boundary. Kelvin waves inhibit the upper layer from deepening at the coast. Rossby waves propagate the coastal density structure offshore, hence modifying the interior currents. A comparison of the solutions with or without a continental shelf and slope demonstrate that topographic trapping of Rossby waves is a necessary process for maintaining realistic eastern boundary current speeds. Significant poleward speeds occur only onshore of where the upper layer intersects the slope, that is, at a grounding line. Its poleward transport increases when surface-enhanced vertical mixing is applied over a greater depth. When the timescale δt is sufficiently short, the poleward current is nearly barotropic. The current's spatial structure over the shelf is controlled by horizontal mixing, having the structure of a Munk layer. Increasing vertical diffusion deepens the upper layer thickness and strengthens the alongshore current speed. Bottom drag leads to an offshore flow along the bottom, reducing the net onshore transport and weakening the current's poleward acceleration. When δt is long, poleward advection of buoyancy forms a density front near the shelf break, intensifying poleward speeds near the surface. With bottom drag, a bottom Ekman flow advects density offshore, shifting the jet core offshore of the shelf break. The resulting cross-shelf density gradient reverses the meridional current's direction at depth, leading to an equatorward undercurrent.     

黄海典型气旋与反气旋式海洋涡旋特征及影响机制模拟研究

为探讨黄海海洋涡旋的三维结构特征、能量输送与转换及影响机制,对黄海海域典型台风海洋气旋与近海海湾反气旋式涡旋个例进行数值模拟和时空诊断分析。采用FVCOM(Finite Volume Community Ocean Model)区域海洋数值模式精细化描述台风海洋涡旋与近海海洋中小尺度涡旋系统。对涡旋能量传输特征模拟显示,气旋式和反气旋式海洋涡旋中,非对称强流区动能能量下传比涡旋中心部位的强度更强,维持时间更长,下传深度更深。反气旋式海洋涡旋因Ekman流动形成的向中心辐合作用,造成此类差异更显著。气旋涡的动能主要来源于台风的近海面风应力动能和海洋涡旋有效位能的转换,反气旋涡旋区域风动力偏弱,其动能强度维持在低位,其涡旋增强伴随着有效位能的增加。环境因子影响机制从风浪,底摩擦和地形三方面讨论。结果显示:耦合波浪模块后,台风强风应力和风浪的综合作用扩大台风海洋涡旋尺度,并增强涡旋环流强度,同时对相邻的反气旋涡有压缩和减弱作用。风浪效应对台风海洋涡旋有正贡献。强台风过程表层环流响应台风应力而浅水地形和底摩擦强烈影响涡旋下层,造成台风海洋涡旋结构在垂直方向上偏移,并影响到下层环流速度减小,流向与表层相反。在海洋气旋涡和反气旋涡的显著辐散区,其混合层下方有温盐要素的涌升对应,辐合区有温盐要素的下沉对应;同时海底地形的升降也造成温盐强迫上升与下降,其强度与地形起伏尺度成正比,较环流系统作用更强。     

On the interactions between planetary geostrophy and mesoscale eddies

Multiscale asymptotics are used to derive three systems of equations connecting the planetary geostrophic (PG) equations for gyre-scale flow to a quasigeostrophic (QG) equation set for mesoscale eddies. Pedlosky (1984), following similar analysis, found eddy buoyancy fluxes to have only a small effect on the large-scale flow; however, numerical simulations disagree. While the impact of eddies is relatively small in most regions, in keeping with Pedlosky’s result, eddies have a significant effect on the mean flow in the vicinity of strong, narrow currents.First, the multiple-scales analysis of Pedlosky is reviewed and amplified. Novel results of this analysis include new multiple-scales models connecting large-scale PG equations to sets of QG eddy equations. However, only introducing anisotropic scaling of the large-scale coordinates allows us to derive a model with strong two-way coupling between the QG eddies and the PG mean flow. This finding reconciles the analysis with simulations, viz. that strong two-way coupling is observed in the vicinity of anisotropic features of the mean flow like boundary currents and jets. The relevant coupling terms are shown to be eddy buoyancy fluxes. Using the Gent-McWilliams parameterization to approximate these fluxes allows solution of the PG equations with closed tracer fluxes in a closed domain, which is not possible without mesoscale eddy (or other small-scale) effects. The boundary layer width is comparable to an eddy mixing length when the typical eddy velocity is taken to be the long Rossby wave phase speed, which is the same result found by Fox-Kemper and Ferrari (2009) in a reduced gravity layer.     

Interaction of internal waves and turbulence in the ocean

Within the framework of the semiempirical theory of turbulence for stratified fluids some aspects of the problem of internal wave-turbulence interaction in the upper layer of the ocean are discussed. The conditions of amplification and sustaining of turbulence by internal waves are investigated. Stationary distributions of turbulent energy are found for a stratified fluid with a shear flow produced, for example, by a low-frequency internal wave. The internal wave damping due to both turbulent viscosity and turbulent diffusion in the thermocline is studied. For a two-layer model damping constant is determined as a function of the wave number. The variation of surface turbulence by internal waves is estimated and the role of this process in slick formation is considered.     

Growing interfacially coupled oscillations of the ocean–atmosphere

A stability analysis of the coupled ocean–atmosphere is presented which shows that the potential energy (PE) of the upper layer of the ocean is available to generate coupled growing planetary waves. An independent analysis suggests that the growth of these waves would be maintained in the presence of oceanic friction. The growing waves are a consequence of relaxing the rigid lid approximation on the ocean, thus allowing an upward transfer of energy across the sea surface. Using a two and a half layer model consisting of an atmospheric planetary boundary layer, coupled with a two layer ocean comprising an active upper layer and a lower layer in which the velocity perturbation is vanishingly small, it is shown that coupled unstable waves are generated, which extract PE from the main thermocline. The instability analysis is an extension of earlier work [Tellus 44A (1992) 67], which considered the coupled instability of an atmospheric planetary boundary layer coupled with an oceanic mixed layer, in which unstable waves were generated which extract PE from the seasonal thermocline. The unstable wave is an atmospheric divergent barotropic Rossby wave, which is steered by the zonal wind velocity, and has a wavelength of about 6000 km, and propagates eastward at the speed of the deep ocean current. It is argued that this instability, which has a multidecadal growth time constant, may be generated in the Southern Ocean, and that its properties are similar to observations of the Antarctic Circumpolar Wave (ACW).     

On the transient adjustment of a mid-latitude abyssal ocean basin with realistic geometry: the constant depth limit

The early stages in the adjustment of a mid-latitude abyssal basin with realistic geometry are studied using an inverted one and one-half layer model of the Eastern Mediterranean Sea as a natural test basin. The model is forced with a localized sidewall mass source and a compensating distributed mass sink. A flat bottom basin is investigated for comparison with existing theories on abyssal gyral spin-up, and as a precursor to a study with realistic topography. As in existing theories, the early adjustment is dominated by sub-inertial Kelvin and Rossby waves. Obstacles and the varying coastal geometry do not impede the passage of the Kelvin wave, though the circuit time of the main Kelvin wave signal is reduced by an aggregate 6% for the abyssal Eastern Mediterranean basin. The scattering of the Kelvin wave due to small-scale variations in the coastline is also shown not to be significant to the adjustment. The relatively short period of time needed to reach a statistical steady state is attributed to western boundary current formation in response to local Kelvin wave dynamics. Upon cessation of the sidewall forcing, sub-inertial motion controls the spin-down adjustment with basin-scale Rossby waves becoming the most pronounced feature of the flow. Two dynamical issues of particular interest emerge in these simulations: the retardation of Kelvin wave propagation around the abyssal basin and the roles of detrainment and sidewall forcing in the interior vorticity balance. An idealized simulation using an elliptical basin is used to illustrate that the mechanism for Kelvin wave retardation is a geometrically induced dispersion due to large-scale variations in the coastline. A dynamical analysis of the interior circulation shows that detrainment alone does not develop a Sverdrup response. Both the localized sidewall injection and the detrainment are needed to describe the interior dynamics, with both poleward and equatorward flows developing during the adjustment.     

热带气旋强度与结构研究新进展

主要回顾热带气旋(TC)强度与结构变化的研究发展近况。以往热带气旋的理论研究认为在给定的大气和海洋热状况下,存在着一个TC所能达到的最大可能强度(MPI)。但实际上,海洋生成的热带气旋达到的最大强度普遍要比由MPI理论计算得到最大强度要低。近几年的研究表明,存在着内部和外部的不利因子通过对TC结构的改变来阻碍其加强,从而限制TC的强度。以往认为在诸多因子中,垂直风切变产生的内核区非对称结构与眼墙区下方海水上涌造成的海面冷却是制约TC达到MPI的主要因子。最新的研究进一步指出,产生TC非对称性的中尺度过程对其强度与结构的变化至关重要。中尺度过程包含有对流耦合的涡旋Rossby波、内外圈螺旋雨带、嵌于TC环流内的中尺度涡旋。外部的环境气流也是通过这些眼墙的中尺度过程影响到TC的强度与结构变化。     

On eddy diffusion profiles in oceanic bottom boundary layers associated with cold eddies and filaments

The oceanic bottom boundary-layer model of Weatherly and Martin (1978) is used to study the vertical structure of the eddy diffusivity in a region with initially imposed bottom mixed-layer thickness. Because of near-bottom oceanic features, such as the Cold Filament (Weatherly and Kelley, 1982) and cold eddies (Ebbesmeyer et al., 1988), the bottom mixed-layer thickness is not the sole result of boundary-layer mixing; this is the incentive for this study. For a given geostrophic forcing and imposed mixed-layer depth, a formula for the eddy diffusion coefficient is found. This parameterization of the eddy diffusivity improves previous formulas used in oceanic and atmospheric boundary layers in the upper portion of the boundary layer. A simple model of a Cold Filament-like feature demonstrates the structure of the bottom boundary layer, the bottom mixed layer, and the relation between the two. A lens-like cross section of cold blobs, often used in analytical models, may be inappropriate if bottom friction is important.     

Observations of the energy-containing oceanic Eddies,and theoretical models of waves and turbulence

Two of the best available observed frequency spectra of energy-containing oceanic motions are summarized. Without provoking any simple explanation, they affirm that an efficient, homogeneous cascade of energy to small scales isnot occurring. The way is left open for interpretation as a mixture of geostrophic turbulence and waves.Detailed models are given which yield plausible behavior of various parts of the wave-number and frequency spectra, and illustrate the workings of nonlinearity and wave dispersion: (i) simple dispersion of linear, wind-generated internal waves gives at depths an inertial peak and a steeply sloping high-frequency spectrum (the inertial peak at the very top of the ocean is a direct response of the mixed layer to the wind); (ii) at longer periods,two-dimensional turbulence subjected to the beta effect produces well-ordered motions from a chaotic initial state, with dominant length and time-scale independent of initial conditions. The turbulence evolves quickly and naturally into Rossby waves, leaving a peaky, quasi-stationary spectrum; (iii) inone dimension, the Korteweg de Vries equation again shows how waves may sharpen and fix the wave-number spectrum while dispersing the energy in physical space; (iv) possible application of the ideas tothree-dimensional turbulence and waves is discussed.The most general result is that the scale-dependent boundary, at which the wave steepness is about unity, often divides energy-frequency/wave-number space into regions in which the mobility of energy is vastly different; depending on the direction and speed of nonlinear migration within these regions, energy may pile up at this boundary. Thus, wave-restoring forces can concentrate spectra at certain wave numbers while dispersing the fields in physical space.Now at Woods Hole Oceanographic Institution.     

简单的热带海气耦合波——Rossby波的相互作用

在本文中分析了当大气和海洋中未经耦合前的自由波均为Rossby模时,经相互作用后所激发出的耦合波的物理性质。结果表明,由于大气和海洋的背景状态不同,可以激发出两类不稳定耦合Rossby波。一类波要求大气的背景场是斜压的,而海洋的混合层较深,即热容量较大。这是一类弱相互作用的不稳定波。另一类要求大气的背景场趋于正压性,而海洋的混合层较浅,即热容量较小。这是一类强相互作用的不稳定波。色散关系的计算表明,这两类不稳定波产生的物理机制也不相同。文中对解不同截断模的本征值问题提出了几种数学方法,同时还进一步提出了一种使大气和海洋自由Rossby模的色散关系不受歪曲的处理方法。     

Effects of Sea-Surface Waves and Ocean Spray on Air-Sea Momentum Fluxes

The effects of sea-surface waves and ocean spray on the marine atmospheric boundary layer(MABL) at different wind speeds and wave ages were investigated. An MABL model was developed that introduces a wave-induced component and spray force to the total surface stress. The theoretical model solution was determined assuming the eddy viscosity coefficient varied linearly with height above the sea surface. The wave-induced component was evaluated using a directional wave spectrum and growth rate. Spray force was described using interactions between ocean-spray droplets and wind-velocity shear. Wind profiles and sea-surface drag coefficients were calculated for low to high wind speeds for wind-generated sea at different wave ages to examine surface-wave and ocean-spray effects on MABL momentum distribution. The theoretical solutions were compared with model solutions neglecting wave-induced stress and/or spray stress. Surface waves strongly affected near-surface wind profiles and sea-surface drag coefficients at low to moderate wind speeds. Drag coefficients and near-surface wind speeds were lower for young than for old waves. At high wind speeds, ocean-spray droplets produced by wind-tearing breaking-wave crests affected the MABL strongly in comparison with surface waves, implying that wave age affects the MABL only negligibly. Low drag coefficients at high wind caused by ocean-spray production increased turbulent stress in the sea-spray generation layer, accelerating near-sea-surface wind. Comparing the analytical drag coefficient values with laboratory measurements and field observations indicated that surface waves and ocean spray significantly affect the MABL at different wind speeds and wave ages.     

A coupled surface boundary-layer-quasigeostrophic model

A three-dimensional model of the mesoscale surface boundary layer of the open ocean is developed through scale analysis of the primitive equations with mixing included. A set of surface boundary-layer equations appropriate for a broad range of oceanic and atmospheric scales is thereby derived. The essential basis of the model is a coupling between quasigeostrophic dynamics away from the boundary layer and arbitrary mixing models within the mixed layer. The coupling consists of advection of the boundary layer by the horizontal and vertical components of the interior quasigeostrophic flow and forcing of the interior by the boundary layer in the form of divergence within the boundary layer which leads to vortex stretching/compression in the interior. The divergence is generalized for mesoscale wind-driven flows and includes nonlinear interaction between the directly wind-driven boundary-layer flow and the interior flow in the form of interior relative vorticity advection by the wind-driven flow. The nature of the equations leads us to apply a numerical algorithm to their solution. This algorithm is calibrated through application to idealized problems to determine the temporal and spatial grid requirements. The model is initialized with a realistic ocean flow having the properties of the Gulf Stream.     

Atmospheric Response to Mesoscale Ocean Eddies over the South China Sea

The South China Sea(SCS) is an eddy-active area. Composite analyses based on 438 mesoscale ocean eddies during 2000–2012 revealed the status of the atmospheric boundary layer is influenced remarkably by such eddies. The results showed cold-core cyclonic(warm-core anticyclonic) eddies tend to cool(warm) the overlying atmosphere and cause surface winds to decelerate(accelerate). More than 5% of the total variance of turbulent heat fluxes, surface wind speed and evaporation rate are induced by mesoscale eddies. Furthermore, mesoscale eddies locally affect the columnar water vapor, cloud liquid water, and rain rate. Dynamical analyses indicated that both variations of atmospheric boundary layer stability and sea level pressure are responsible for atmospheric anomalies over mesoscale eddies. To reveal further details about the mechanisms of atmospheric responses to mesoscale eddies, atmospheric manifestations over a pair of cold and warm eddies in the southwestern SCS were simulated. Eddy-induced heat flux anomalies lead to changes in atmospheric stability. Thus, anomalous turbulence kinetic energy and friction velocity arise over the eddy dipole, which reduce(enhance) the vertical momentum transport over the cold(warm) eddy, resulting in the decrease(increase) of sea surface wind. Diagnoses of the model's momentum balance suggested that wind speed anomalies directly over the eddy dipole are dominated by vertical mixing terms within the atmospheric boundary layer, while wind anomalies on the edges of eddies are produced by atmospheric pressure gradient forces and atmospheric horizontal advection terms.     

Coastal-trapped waves with finite bottom friction

Coastal-trapped waves with finite-amplitude bottom friction are explored. “Finite-amplitude” in this context means that the bottom stresses are large enough to change the wave modal structure. The importance of bottom friction is measured by the nondimensional number r/(ωh), where r is a bottom resistance coefficient, ω the wave frequency and h the water depth. Increasing bottom drag causes free wave modes to adjust by having their amplitude maxima for alongshore current translate offshore to the point that, with relatively large bottom stress, the alongshore current variance is trapped entirely on the slope, even though pressure variations remain substantial right up to the coast. In conjunction with these adjustments, wave frequency, hence propagation speed, varies and the wave damping is usually less than would be expected based on a weak-friction perturbation calculation. Stronger density stratification increases wave damping, all else being the same. A mean alongshore flow can strongly affect modal structure and wave damping, although general trends are difficult to discern. Results suggest that bottom friction may cause an observed tendency for lower frequency alongshore current fluctuations to become relatively more important with distance offshore.     

Circulation and boundary layers in differentially heated rotating stratified fluid

Recent laboratory experiments with rotating stratified water in a cylinder have revealed many of the predictions of linearized, analytic theory. Earlier measurements of the velocity field generated in a cylinder by top heating compared well with theory. Large stratification clearly suppressed Ekman pumping so that the interior velocity field (primarily azimuthal) responded by satisfying no-slip top and bottom boundary conditions without the need for Ekman layers. This interior flow also occupied a boundary layer of greater thickness than the Ekman layer under some conditions. Theory and experiments have now been conducted for sidewall heating. As before, experiment and theory agree well over some parameter ranges. But for some parameters, the flow is unstable. The exact nature of the instability remains poorly understood. The size of one combination of both vertical and horizontal boundary layers is governed by the Rossby radius of deformation multiplied by the square root of the Prandtl number. Sidewall boundary layers and their scales will be reviewed with the present results in mind.     

Rectified flow along a vertical coastline

Laboratory experiments are conducted on a physical system in which an oscillatory, along-shore, free stream flow of a homogeneous fluid occurs in the vicinity of a long coastline with vertical slope; the model sea-floor is horizontal. Particular attention is given to the resulting rectified (mean) current which is along the coastline with the shore on the right, facing downstream. In the lateral far field region defined by (1), where y is the offshore coordinate and H is the depth of the fluid, the motion field is approximately independent of the lateral distance from the coast. The vertical structure of the cross-stream motion in this region consists of Ekman layers near the sea-floor and interior adjustment flows, both periodic in time. In the near field, defined by (1), the motion is strongly dependent on the cross-stream coordinate as well as time, and rectified currents are observed. The mechanism responsible for the rectification is a complex nonlinear coupling between laterally directed adjustment flows driven by the transport in the bottom Ekman layers, and the free stream motion field. The rectified current is found to be substantially wider than the Stewartson layer thickness but much narrower than the Rossby deformation radius. The characteristic width, δ_y, of the rectified current is shown to scale as , where Ro is the Rossby number Ro_t is the temporal Rossby number and E is the Ekman number. Experiments are presented which support this scaling.