Thickness Of Bottom Boundary Layer Research Articles

Parametric optimization of vortex generator configuration for flow control in an intake duct for waterjet propulsion

Vortex generators (VG) are simple miniature devices that suppress flow separation in aeronautical elements. In this study, VG device operation in a submerged flush waterjet inlet was numerically investigated to improve the flow quality entering the jet pump at low Inlet Velocity Ratio (IVR). Steady Reynolds-averaged Navier-Stokes equations are solved using the SST k-ω turbulence model and used to simulate the flow field, with the effects of the orientation, angle of attack, height and installation position of VGs thoroughly analyzed. The hydrodynamic performance of the intake duct was assessed over the operational range. The results show that VGs arranged in a divergent configuration better suppress flow separation. The zonal magnitude of the high turbulent kinetic energy on the ramp side was reduced, with the non-uniformity in the pump face plane reduced from 0.41 to 0.26. Excessive angles of attack and VG heights have negative effects. Through parametric studies, VGs were found to have best performance in the target duct with an angle of attack of 40⁰ and a height measuring 20% of the bottom boundary layer thickness. In addition, VGs installed along the keel of a ship can effectively suppress the flow distortion and improve the overall efficiency of the intake duct.

The Near‐Bed Flow Structure and Bed Shear Stresses Within Emergent Vegetation

AbstractThe structure of the bottom boundary layer (BBL) in aquatic flows influences a range of biophysical processes, including sediment transport, hyporheic exchange, and biofilm formation. While the structure of BBL above bare sediment beds has been well studied, little is known about the complex near‐bed flow structure within aquatic vegetation. In this study, we used high‐resolution laboratory measurements and numerical Large Eddy Simulations to investigate the near‐bed mean and turbulent flow properties within staggered‐ordered emergent vegetation under a wide range of flow conditions and densities. There is strong spatial variability of key near‐bed flow characteristics on the scale of the vegetation elements. Measurement locations that provide single‐point flow characteristics closest to the spatially averaged values were identified. The spatially averaged BBL thickness is influenced strongly by vegetation density. This impact of vegetation density is engendered through its direct control of near‐bed turbulent kinetic energy (TKE), which in turn is negatively correlated with BBL thickness, both locally in a given flow and across the range of flow conditions studied here. A model based on the near‐bed TKE is developed to predict the BBL thickness and, ultimately, the bed shear stress. Model predictions were in close agreement with the experimental and numerical results. These findings provide new insights into the physical links between near‐bed flow variables and therefore contribute to the understanding of some of the complex biophysical processes present in vegetated flows.

A local eddy viscosity parameterization for wind-driven estuarine exchange flow. Part I: Stratification dependence

A new parameterization for the estuarine turbulent eddy viscosity coefficient is developed considering the influence of wind forcing and feedback between stratification and shear. The emerging tidally averaged eddy viscosity profile AvT is parameterized as parabolic under well-mixed conditions, and is composed of a skewed-Gaussian-like form for the upper layer, and a parabolic form for the bottom layer under stratified conditions. The precise shape of the profiles depends parametrically on the bottom boundary layer thickness, the bulk Richardson number, and the Wedderburn number. The parameterized AvT profiles show excellent agreement with profiles obtained from numerical models. To explore the importance of vertically varying AvT with regard to exchange processes, an analytical model is designed. This one-dimensional model is based on a balance between frictional forces and pressure gradient. The resulting exchange flow is analyzed over the relevant parameter space that is associated with horizontal and vertical stratification through the bulk Richardson number, and the bi-directional wind stress via the Wedderburn number. Down-estuary wind enhances the up-estuary flow near the bottom and down-estuary flow near the surface driving an exchange flow pattern typically associated with gravitational circulation. Up-estuary wind results in either a two-layer inverted circulation opposing the gravitational circulation, or a three-layer flow that is up-estuarine at the surface with classical two-layer circulation underneath. Three-layer flow emerges with a weak wind. With increasing runoff velocity, three-layer flow transitions to a single layer flow under weak stratification conditions.

Wave flume experiments on dynamics of the bottom boundary layer in silty seabed

The objectives of this study are carried out a series of controlled large wave flume experiments using fine-grained sediment from the Huanghe River Delta, exploring the complete sequence of sediment behavior in the bottom boundary layer (BBL) during wave-induced liquefaction. The results show that: (1) The BBL in silty seabed is exposed to a progressive wave, goes through a number of different stages including compaction before liquefaction, sediment liquefaction, and compaction after liquefaction, which determines the range and thickness of BBL. (2) With the introduction of waves, first, the sediment surface has settled by an amount S (S=1–2 cm) in the course of wave loadings with an insufficient accumulation of pore water pressure. And a thin high concentration layer formed the near-bed bottom. (3) Once the liquefaction sets in, the liquefied sediment with an ‘orbital motion’ and the sub-liquefied sediment form a two-layer-sediment region. The range of BBL extends downwards and stopped at a certain depth, subsequently, develops upwards with the compaction process. Meanwhile, re-suspended sediments diffuse to the upper water column. (4) During the dynamics process of the BBL beneath progressive waves, the re-suspended sediment increment ranked as sediment liquefaction > erosion before liquefaction > compaction after liquefaction.

Three-dimensionality of shallow island wakes

Island wakes are thought to play a significant role in the vertical and cross-shelf mixing processes in strong tidally forced coastal regions. This paper describes a comprehensive laboratory study of shallow water wakes behind islands of circular cross section forced by a sinusoidal tidal flow. The wake structure and vertical circulation are determined through novel three-dimensional particle imaging velocimetry measurements. Four archetypal wake forms (symmetric, asymmetric, unsteady bubble, and vortex shedding) are observed. Through examination of the vertical structure of each of these wake forms, we demonstrate the dependence of vertical transport in island wakes on three key parameters: (1) the tidal excursion relative to the island size, (2) the bottom boundary layer thickness relative to the flow depth and (3) the aspect ratio of the island size to the flow depth. The importance of secondary vortices in island upwelling is highlighted by local peaks in vertical velocity that exceed 40% of the peak external tidal velocity. This study fundamentally changes the view of island wake upwelling from a weak ‘tea cup’-like recirculation process to one where primary and secondary flow structures vigorously stir the water column over the full depth. This has fundamental implications for the fate of passive biological tracers and the time scales that determine productivity in topographically-complex continental shelf regions.

Internal-Wave-Driven Mixing: Global Geography and Budgets

AbstractInternal-wave-driven dissipation rates ε and diapycnal diffusivities K are inferred globally using a finescale parameterization based on vertical strain applied to ~30 000 hydrographic casts. Global dissipations are 2.0 ± 0.6 TW, consistent with internal wave power sources of 2.1 ± 0.7 TW from tides and wind. Vertically integrated dissipation rates vary by three to four orders of magnitude with elevated values over abrupt topography in the western Indian and Pacific as well as midocean slow spreading ridges, consistent with internal tide sources. But dependence on bottom forcing is much weaker than linear wave generation theory, pointing to horizontal dispersion by internal waves and relatively little local dissipation when forcing is strong. Stratified turbulent bottom boundary layer thickness variability is not consistent with OGCM parameterizations of tidal mixing. Average diffusivities K = (0.3–0.4) × 10−4 m2 s−1 depend only weakly on depth, indicating that ε = KN2/γ scales as N2 such that the bulk of the dissipation is in the pycnocline and less than 0.08-TW dissipation below 2000-m depth. Average diffusivities K approach 10−4 m2 s−1 in the bottom 500 meters above bottom (mab) in height above bottom coordinates with a 2000-m e-folding scale. Average dissipation rates ε are 10−9 W kg−1 within 500 mab then diminish to background deep values of 0.15 × 10−9 W kg−1 by 1000 mab. No incontrovertible support is found for high dissipation rates in Antarctic Circumpolar Currents or parametric subharmonic instability being a significant pathway to elevated dissipation rates for semidiurnal or diurnal internal tides equatorward of 28° and 14° latitudes, respectively, although elevated K is found about 30° latitude in the North and South Pacific.

Fortnightly Variation in the Bottom Thermal Front and Associated Circulation in a Semienclosed Sea

AbstractSummer hydrographic data from 1971 to 2000 demonstrate the presence of bottom cold water (BCW) and a bottom thermal front around the BCW in a semienclosed sea in the Seto Inland Sea of Japan. The horizontal gradient of water temperature across the bottom front was larger in neap tide than in spring tide, which is the opposite the pattern observed in the fortnightly variations in other areas (e.g., the Irish Sea). A numerical model for the Inland Sea reproduced the presence of BCW and a bottom front as well as the same fortnightly variation in the horizontal gradient of water temperature across the bottom front as in observational data. Being the same BCW as those in other areas, the presence of BCW in the Inland Sea is also caused by spatial variation in tidal mixing. The intensification of the bottom front in neap tide in the Inland Sea results from a combination of tidal mixing and horizontal advection of warm water to the BCW. The presence of a bottom residual current in the direction across the bottom front results in the horizontal advection of warm water to the BCW, and its fortnightly variation is responsible for the fortnightly variation of the bottom front in the Inland Sea. The presence of the BCW induces a surface cyclonic circulation in the direction approximately along the bottom front; the intensification and weakening of the bottom front with the spring–neap tidal cycle, combined with the fortnightly variation in the bottom boundary layer thickness, produce a slightly stronger surface cyclonic circulation in neap tide than in spring tide.

On the role of infiltration and exfiltration in swash zone boundary layer dynamics

AbstractBoundary layer dynamics are investigated using a 2‐D numerical model that solves the Volume‐Averaged Reynolds‐Averaged Navier‐Stokes equations, with a VOF‐tracking scheme and a k ‐ ϵ turbulence closure. The model is validated with highly resolved data of dam break driven swash flows over gravel impermeable and permeable beds. The spatial gradients of the velocity, bed shear stress, and turbulence intensity terms are investigated with reference to bottom boundary layer (BL) dynamics. Numerical results show that the mean vorticity responds to flow divergence/convergence at the surface that result from accelerating/decelerating portions of the flow, bed shear stress, and sinking/injection of turbulence due to infiltration/exfiltration. Hence, the zero up‐crossing of the vorticity is employed as a proxy of the BL thickness inside the shallow swash zone flows. During the uprush phase, the BL develops almost instantaneously with bore arrival and fluctuates below the surface due to flow instabilities and related horizontal straining. In contrast, during the backwash phase, the BL grows quasi‐linearly with less influence of surface‐induced forces. However, the infiltration produces a reduction of the maximum excursion and duration of the swash event. These effects have important implications for the BL development. The numerical results suggest that the BL growth rate deviates rapidly from a quasi‐linear trend if the infiltration is dominant during the initial backwash phase and the flat plate boundary layer theory may no longer be applicable under these conditions.

Thickness of the mixed bottom layer in the Northern Atlantic

The thickness of the mixed bottom boundary layer (BBL) has been analyzed based on the CTD data at transoceanic sections in abyssal waters of the Northern Atlantic. The measurements were carried out at two transoceanic sections approximately along 48° N (ASV-99) and 5° N (AI-2000) in 1999 and 2000. These data, and the WOCE data obtained at four zonal sections (AR7E and AR12 along 57° N, AR01 along 24.5° S, and A06 along 7.5° N), were used for the calculation of the statistical characteristics of the BBL’s thickness HB. The probability distribution function F(HB) was close to lognormal. The mean value 〈HB〉 at different latitudes was in the range from 30 to 60 m. The averaged BBL thickness = 46.1 m. The BBL’s thickness was about 1% of the ocean’s depth D; the ratio HB/D was the minimum (0.8%) near the equator and increased up to 1.6% in the polar latitudes.

Viscous flows in a muddy seabed induced by a solitary wave

Liu & Chan (J. Fluid Mech.vol. 579, 2007, p. 467, hereinafter referred to as LC) derived analytical solutions for the interactions between shallow water waves and a viscous fluid seabed. In this paper we present a set of new experimental data on the solitary-wave-induced flows in a viscous muddy seabed so as to validate LC's theory and the approximations employed. In the experiments a clear silicone fluid was used as the viscous mud and particle image velocimetry was employed to measure the velocity field inside the viscous mud. The shear stress along the bottom of the mud bed and the displacement of the water--mud interface were also deduced from data. Experimental results showed excellent agreement with the theoretical solutions. Additional analyses were performed to show that the ratio of the muddy seabed thickness to the corresponding bottom boundary-layer thickness,$\dbar$, plays an important role in characterizing mud flow regimes. When$\dbar\,{\leq}\,1$, the vertical profile of the horizontal velocity in the mud bed can be parameterized as a parabola. On the other hand, when$\dbar\,{\gg}\,1$, the velocity profile appears as a plug flow above a thin viscous layer. When$ \dbar\,{\sim}\,O(1)$, the flow patterns are more complex than the other two regimes and flow reversal can occur inside the viscous mud bed.

Tidal currents, energy flux and bottom boundary layer thickness in the Clyde Sea and North Channel of the Irish Sea

A high-resolution three-dimensional model of the Clyde Sea and the adjacent North Channel of the Irish Sea is used to compute the major diurnal and semidiurnal tides in the region, the associated energy fluxes and thickness of the bottom boundary layer. Initially, the accuracy of the model is assessed by performing a detailed comparison of computed tidal elevations and currents in the region, against an extensive database that exists for the M2, S2, N2, K1 and O1 tides. Subsequently, the model is used to compute the tidal energy flux vectors in the region. These show that the major energy flux is confined to the North Channel region, with little energy flux into the Clyde Sea. Comparison with the observed energy flux in the North Channel shows that its across-channel distribution and its magnitude are particularly sensitive to the phase difference between elevation and current. Consequently, small changes in the computed values of these parameters due to slight changes of the order of the uncertainty in the open-boundary values to the model, can significantly influence the computed energy flux. The thickness of the bottom boundary layer in the region is computed using a number of formulations. Depending upon the definition adopted, the empirical coefficient C used to determine its thickness varies over the range 0.1 to 0.3, in good agreement with values found in the literature. In the North Channel, the boundary layer thickness occupies the whole water depth, and hence tidal turbulence produced at the sea bed keeps the region well mixed. In the Clyde Sea, the boundary layer thickness is a small fraction of the depth, and hence the region stratifies.

Plume capture by divergent plate motions: implications for the distribution of hotspots, geochemistry of mid-ocean ridge basalts, and estimates of the heat flux at the core–mantle boundary

The coexistence of stationary mantle plumes with plate-scale flow is problematic in geodynamics. We present results from laboratory experiments aimed at understanding the effects of an imposed large-scale circulation on thermal convection at high Rayleigh number (10 6≤Ra≤10 9) in a fluid with a temperature-dependent viscosity. In a large tank, a layer of corn syrup is heated from below while being stirred by large-scale flow due to the opposing motions of a pair of conveyor belts immersed in the syrup at the top of the tank. Three regimes are observed, depending on the ratio V of the imposed horizontal flow velocity to the rise velocity of plumes ascending from the hot boundary, and on the ratio λ of the viscosity of the interior fluid to the viscosity of the hottest fluid in contact with the bottom boundary. When V≪1 and λ≥1, large-scale circulation has a negligible effect on convection and the heat flux is due to the formation and rise of randomly spaced plumes. When V>10 and λ>100, plume formation is suppressed entirely, and the heat flux is carried by a sheet-like upwelling located in the center of the tank. At intermediate V, and depending on λ, established plume conduits are advected along the bottom boundary and ascending plumes are focused towards the central upwelling. Heat transfer across the layer occurs through a combination of ascending plumes and large-scale flow. Scaling analyses show that the bottom boundary layer thickness and, in turn, the basal heat flux q depend on the Peclet number, Pe, and λ. When λ>10, q∝Pe 1/2 and when λ→1, q∝(Pe λ) 1/3, consistent with classical scalings. When applied to the Earth, our results suggest that plate-driven mantle flow focuses ascending plumes towards upwellings in the central Pacific and Africa as well as into mid-ocean ridges. Furthermore, plumes may be captured by strong upwelling flow beneath fast-spreading ridges. This behavior may explain why hotspots are more abundant near slow-spreading ridges than fast-spreading ridges and may also explain some observed variations of mid-ocean ridge basalt (MORB) geochemistry with spreading rate. Moreover, our results suggest that a potentially significant fraction of the core heat flux is due to plumes that are drawn into upwelling flows beneath ridges and not observed as hotspots.

A Numerical Study of the Adjustment of a Narrow Stratified Current over a Sloping Bottom*

The adjustment of a narrow, stratified, cyclonic along-isobath current over a uniformly sloping bottom and the coupling between the current and the bottom boundary layer that develops beneath are investigated using a primitive-equation numerical model. The current generates a bottom Ekman layer immediately downstream of its origin, with downslope transport everywhere beneath the current, carrying lighter water under heavier water to produce a vertically well-mixed bottom boundary layer. At the top of the boundary layer, Ekman suction on the shallow side and pumping on the deep side lead to density advection in the vertical, tilted interior isopycnals, and thermal-wind shear of the interior along-isobath velocity. Flow above the bottom boundary layer is nearly perfectly geostrophic and along isopycnals. Buoyancy advection in the bottom boundary layer continues to cause growth of the boundary layer downstream, with subsequent reduction in bottom stress, until the flow reaches a steady downstream equilibrium beyond which only gradual changes occur as a result of viscosity and mixing. The numerical results are compared with the idealized model of this adjustment process previously proposed by Chapman and Lentz. The same basic dynamics dominate, and some of the scales and parameter dependencies predicted by the idealized model apply to the numerical results. For example, the distance to the downstream equilibrium decreases with increasing buoyancy frequency and/or bottom slope, and the equilibrium structure is nearly independent of the bottom friction coefficient. The equilibrium bottom boundary layer thickness and the interior along-isobath velocity just above the boundary layer closely obey the idealized model scales; that is, the boundary layer thickness decreases with increasing buoyancy frequency and is independent of bottom slope, and the overlying current decreases while its width increases as either the buoyancy frequency or bottom slope decreases. However, the interior vertical shear in the numerical model tends to decouple the overlying current from the bottom boundary layer, so the structure of the bottom boundary layer in the downstream equilibrium is different from the idealized model, and neither the current width nor the surface currents are as sensitive to parameter variations as the idealized model suggests. Finally, the along-isobath current is not geostrophic near the bottom of the bottom boundary layer, as assumed in the idealized model, so the bottom boundary layer is not fully arrested, that is, bottom stress never quite vanishes downstream, suggesting that a completely frictionless downstream equilibrium is unlikely to be achieved.

Modelling of turbulent mixing at the shelf edge

A two-dimensional cross-sectional model of the shelf slope, initially in the form of a single point model on the slope is used to investigate the sensitivity of the bottom boundary layer thickness, and along and across slope flows to the parameterization of vertical mixing and the magnitude of bottom friction. A range of formulations for determining bottom mixing, from simple, in terms of a Richardson-number-dependent mixing, through both one and two equation turbulence energy models are considered. Calculations using both upwelling and downwelling favourable along slope flows together with the cascading of dense water down the shelf slope, show that the solution in the downwelling case is significantly influenced by convective mixing rather than turbulent mixing and consequently is not particularly sensitive to the form of the turbulence energy closure model. In the upwelling case convective mixing does not occur and the solution is more sensitive to the methods used to parameterize vertical mixing. In the case of cascading where there is a significant density gradient above a well mixed bottom boundary layer the solution is particularly sensitive to the parameterization of mixing, and bottom friction. This suggests that measurements of boundary layer thickness, associated flow fields and bed stresses under upwelling or cascading conditions together with turbulence energy dissipation rates would yield a suitable data set for a rigorous validation of turbulence energy models, and hence improved parameterizations of mixing in shelf slope regions. Calculations using the model in cross shelf form show that in a more physically realistic situation, the assumption made in the single-point model that the flow above the bottom boundary layer is not influenced by changes in this layer is only correct on a short time scale (of order a few days). In the cross shelf calculation differences in shelf edge slope influence the thickness of the boundary layer, which varies from point to point. These changes in shelf slope and boundary layer thickness produce a circulation above the bottom boundary layer after a few days which invalidates the concept of this flow being independent of the boundary layer.

Processes influencing the circulation and bottom mixing across the shelf slope: the importance of the slope topography and the coast

A series of comparisons of across slope current, and growth of a well mixed bottom boundary layer, on a shelf slope using both a single point model and a cross shelf model, with and without a coastal boundary, are performed. The across slope flow is induced by either an upwelling favourable or downwelling favourable along slope flow. Calculations with the single point model show that for a given buoyancy frequency the bottom boundary layer thickness changes with time due to upwelling or downwelling across slope flows produced by near bed shear in the along slope flow. In the single point model, the assumption is made that the flow above the bottom boundary layer is independent of time and not influenced by the boundary layer. In the case of a shelf slope, where the steepness of the slope varies from ocean to shelf, then variations in the flow within the bottom boundary layer due to changes in shelf steepness, lead to regions of convergence and divergence up the slope giving rise to a circulation above the bottom boundary layer. This circulation varies with time and horizontal position. The calculations with the cross slope model show that the assumption in the single point model, that the flow outside the boundary layer is constant, is no longer valid after a few days. Also, the thickness of the bottom boundary layer, the across slope flow and hence cross shelf transport are influenced by the presence or absence of a coastline. The inclusion or omission of the coastline has a significant influence, through the associate free surface elevation gradient, and internal pressure gradients, upon the flow both within and above the bottom boundary layer.

Application of eddy viscosity closure models for the M 2 tide and tidal currents in the Yellow Sea and the East China Sea

A three-dimensional mode-splitting, σ-coordinate barotropic finite-difference model, with subgrid scale diffusion represented using a range of eddy viscosity closure models, is used to examine M 2 tidal elevation and currents in the Yellow Sea and the East China Sea. Four eddy viscosity formulations are considered: q 2- q 2 l turbulence energy model (Blumberg and Mellor, 1987), Prandtl mixing length model, Davies and Furnes’ (1980) simple flow-related model with mixing length which includes the bottom boundary layer thickness, and a time and space invariant eddy viscosity with 650 cm 2/s. The bottom friction at the sea bed is given in a quadratic form using a constant bottom friction coefficient, c f and near-bottom velocities. A series of M 2 tide model runs were carried out and optimal values of c f were determined through the comparison with tidal elevation amplitudes and phases at 203 stations. From these comparisons it is shown that the M 2 tidal charts computed with a range of eddy viscosity formulations are in good agreement with each other when optimal values of c f are chosen; comparing with M 2 tidal current amplitudes and phases at 15 stations, it is shown that tidal current distributions and its profiles are in reasonably good agreement with winter-time observations in the central part of the Yellow Sea; relatively poor results are obtained near the Chinese coast where non-tidal effects such as abrupt changes in tidal current phase in the vertical due to large freshwater discharge are pronounced. It is noted that the bottom friction coefficient has a major influence on tidal elevation and tidal currents and optimal values of bottom friction coefficient are closely related to the near-bottom eddy viscosity. The considered eddy viscosity closure models appear to work well for tidal problem when the bottom friction parameter is optimized. Results indicate that for a barotropic tide the Prandtl mixing length model which can account of the boundary layer thickness could be an useful alternative to a highly complex q 2- q 2 l model.

The bottom boundary layer structure in the vicinity of the Middle Atlantic Bight shelfbreak front

The velocity structure in the bottom boundary layer (BBL) in the Middle Atlantic Bight (MAB) is investigated using data derived from the Shelf Edge Exchange Processes (SEEP-II) experiment to test theoretical predictions of the effects of cross-shelf buoyancy flux on the BBL which are thought to contribute to frontogenesis at the shelfbreak. The cross-shelf flow is bottom intensified with a direction veering consistent with that of a frictional boundary layer with rotation. The BBL thickness based on veering angle ranges from 8 to 40 m with a velocity dependence complicated by stratification that is dependent on frontal position. There is evidence of the asymmetry in the BBL thickness expected for the cross-shelf buoyancy flux during up- and downwelling events. However, the velocity structure does not define a sharp upper boundary to the BBL as given by simple one-dimensional model calculations and suggests that there must be other sources of turbulence in addition to bottom friction.

Measurements of internal wave band eddy fluxes above a sloping bottom

The boundary layer near a sloping bottom may have a major influence on the ocean’s interior density structure (due to “boundary mixing”) and on its circulation (because of the arrest of the Ekman layer by buoyancy forces). As a first attempt to measure eddy fluxes of momentum and buoyancy, in order to quantify the mixing in this region, we have carried out a S-day pilot experiment on a sloping side of Emerald Basin on the Scotian Shelf. A moored upward-looking 1.2 MHz ADCP and a thermistor chain mounted along its vertical axis returned analyzable data between 8 and 17 m above the bottom at one-minute intervals. An extensive set of microstructure profiles was also obtained. The predominantly tidal flow regime causes the bottom boundary layer thickness to vary between 3 < z < 30 m, with most high frequency activity during the upslope phase. A bottom-normal momentum flux significantly different from zero is found in the crossisobath direction only. The main contribution comes from a band near the buoyancy frequency N, possibly indicative of advective or Kelvin-Helmholtz instability. When cast in terms of mean-flow shear, the stress yields an eddy viscosity A = 9 x 10e3 m* s-l within the boundary layer and twice this value at z = 15 m, the average height of the pycnocline that caps the boundary layer. The buoyancy flux also seems to be dominated by fluctuating signals near N, but is countergradient and only significantly different from zero at a height of about 15 m. The associated restratification occurs in short periods of approximately one hour when isotherms rise rapidly. Indirect evidence for the importance of the tertiary circulation within the boundary layer is found from the gradient of stress divergence and the mean bottom-normal velocity. An approximate turbulent kinetic energy balance has been investigated, with the currents split into three parts (mean, tidal, and the high frequency part of the internal waveband (“turbulence”)). Production balances viscous dissipation within a factor of 2. Turbulent kinetic energy production by interaction between the turbulent Reynolds stress and the mean flow shear and tidal shear are of the same order of magnitude, but the buoyancy term appears to be of equal importance at the pycnocline.

On the interaction of the bottom boundary layer and deep rings

The interaction of rings extending down to the ocean bottom and the bottom boundary layer (BBL) is studied numerically with a primitive equation model in which the BBL is resolved using the Mellor Yamada level-2.5 closure scheme. The lower portions, below the thermocline, of rings with radii of ≈50, 100 and 200 km, are considered. For rings of comparable strength, the larger ones are found to have the stronger velocity “footprint” on the bottom. The BBL is found to spin down this portion of rings by ≈60% in times 0(6 months), with most of the energy transfer lost irretrievably to bottom friction for the larger rings and to potential energy for the smaller rings. The classical constant eddy viscosity BBL formulation is found to yield similar spindown results as the model, provided the eddy viscosity is chosen to give realistic bottom stress rather than BBL thickness. The numerical model indicates that Ekman pumping out of the BBL affects the bottom mixed layer thickness more so than the Ekman pumping into the BBL, and that maximum bottom mixed layer thicknesses are found not in regions of maximum flows but in upwelling regions of relatively strong flows. Because of the presence of the Cold Filament, the HEBBLE site is found to be unsuitable for testing the model conclusions about bottom layers.

A note on the locus of a shelf front

It is suggested that the locus of a shelf front is where the water depth is equal to the thickness of the tidal frictional bottom boundary layer. From this, it follows that the locus of the front should be given by a critical value of h / U t , where h is the water depth and U t is the tidal stream amplitude. This result differs from that suggested by Simpson and Hunter who argued that a critical value of h / U 3 t determines the locus of the front. The parameterization suggested here implies that the locus of a shelf front (1) does not adjust in response to the seasonal heating cycle and (2) responds only weakly to the spring-neap cycle. Utilizing established empirical constants, we predict that the locus of a shelf front should be where h / U t ≅ 80 s. All these predicted features conform well with observed properties of shelf fronts. The bottom boundary layer thickness conformant with these results is equal to λ( C d ∫ U t 2 ) 1/2 / f , where λ = 0.20 and C d = 0.003. DOI: 10.1111/j.1600-0870.1988.tb00361.x