Oceanic Bottom Boundary Layer Research Articles

Observation of Near-Inertial Waves in the Bottom Boundary Layer of an Abyssal Seamount

Abstract The bottom boundary layer (BBL) contributes significantly to the global energy dissipation of low-frequency flows in the abyssal ocean, but how this dissipation occurs remains poorly understood. Using in situ data collected near the BBL at an abyssal seamount in the western Pacific Ocean, we demonstrate that strong bottom-trapped flows over sloping topography can lose their energy to near-inertial waves (NIWs) generated via the adjustment of the bottom Ekman layer. The NIWs with near-resonant frequencies corresponding to internal waves with propagation direction parallel to the topographic slope are observed. These waves are strongest in the BBL and have a correlation with the off-seamount subinertial flows largely attributed to the Ekman transport driven by the bottom-trapped anticyclonic circulation over the seamount. The bottom-intensified NIWs are observed to have dominant upward-propagating energy and hypothesized to be generated via Ekman flow–topography interactions in the BBL. Energy loss from the near-bottom flows to radiating NIWs (∼8 × 10−4 W m−2) is estimated to be substantially larger than that due to bottom drag dissipation (∼2 × 10−4 W m−2), suggesting the important role of internal-wave generation via the Ekman transport adjustment in damping the subinertial flows over the sloping seafloor. Significance Statement Dissipation of geostrophic currents and eddies via the oceanic bottom boundary layer (BBL) plays an important role in modulating the global oceanic mechanical energy budget. The bottom drag has long been considered a key process in inducing such dissipation, but it is recently suggested to be less effective at a sloping bottom. This study suggests another potentially important mechanism that can remove energy from the geostrophic flows at the sloping bottom. This mechanism is depicted as the resonant generation of near-inertial internal waves by near-bottom flows. Generation of internal waves due to near-bottom flows over sloping topography should be common in the global ocean and therefore have significant implications for the oceanic mechanical energy budget.

Impacts of Instrumented Bottom Frame on Flow and Turbulence Measurements

Abstract A series of laboratory experiments are carried out to demonstrate the impacts of instrumented bottom frame legs on flow and turbulence. The magnitudes of vertical velocity, turbulent kinetic energy, dissipation, and shear stress induced by the frame legs depend on several factors, including the diameter and number of the frame legs, distances between the legs and the observational location, and the magnitude of the incoming flow and its direction with respect to the layout of the frame. In situ observations were carried out near the mouth of the Yellow River using two acoustic Doppler velocimeters mounted on a bottom frame. The estimated vertical velocity and turbulent kinetic energy dissipation rate show a significant asymmetry with flood and ebb tidal flows. This asymmetry can be partly explained by the influences of the bottom frame legs. Finally, the design and deployment principles of bottom frames are discussed for the purpose of reducing the impacts of the frame legs. Significance Statement Instrumented bottom frames are widely used for observations in the oceanic bottom boundary layer and above. However, the impacts of frame legs on the observed flow and turbulence have rarely been investigated. A series of laboratory experiments demonstrate that frame legs can induce vertical flow and enhanced turbulence, and the magnitudes of these influences vary with the size and layout of the frame legs and the magnitude and direction of the background flow. The results of the laboratory experiments can partially explain an “asymmetry” behavior of the vertical flow and turbulent kinetic energy with the flood and ebb tidal flows, derived from in situ observations near the mouth of the Yellow River.

Internal tide-induced turbulent mixing and suspended sediment transport at the bottom boundary layer of the South China Sea slope

Internal tides produce significant vertical and horizontal flows in the ocean and cause strong turbulent mixing that is essential for the energy cascade of multiscale dynamic processes. However, the effects of internal tides on turbulent mixing and sediment transport in the ocean bottom boundary layer remain unclear due to limited observations. In this study, a seabed-based monitoring platform was placed on the continental slope of the South China Sea (118° 09.80′E, 22° 03.78′N, water depth: 1145 m) to observe the internal tides and their influence on turbulent mixing and sediment transport at the bottom boundary layer for the first time. A primarily east-west direction of movement was observed with a maximum velocity of 0.41 m/s, which is much higher than regular barotropic tidal velocity (approximately 0.08 m/s) at the observation site. Influenced by the internal tides, the shear stress and the turbulent kinetic energy dissipation rate of the bottom boundary layer increased from 0.01 to 0.41 Pa and from 7.6 ×10−6 to 5.6 ×10−4 W/kg, respectively. The enhanced shear stress and turbulent mixing led to the resuspension of seabed sediment, and the bottom suspended sediment concentration increased from 3.6 to 12.7 mg/L. In the process of upward propagation, the internal tides also carried the bottom sediment to a height of more than 300 m from the seabed. The sediment transport flux caused by internal tides reached 2.4 g/s/m2.

Observational study on drag reduction of continental-shelf bottom boundary layer

Long-term and high-frequency observing of the oceanic bottom boundary layer was implemented using a seabed-mounted tripod equipped with multiple high-frequency instruments in a semidiurnal tide-dominated channel around the Zhoushan Islands, China. The estimated turbulent parameters, e.g., turbulent intensity, friction velocity, and bottom drag coefficient, varied with quarter-diurnal frequency. The amplitudes of turbulent intensity, bottom stress, and friction velocity were larger in spring tide than those in neap tide. As the Reynolds number increased from 103 to 105, the measured bottom drag coefficient initially increased, peaked at a Reynolds number of approximately 1.4 × 105, and then decreased. The observed drag reduction is similar to the variations of drag coefficient of cross-flow around a circular cylinder and the fluid friction of the pipe flow in the transitional state, which can provide a necessary and important proof for further theoretical and experimental investigations. Several plausible explanations are raised for this reduction: the stratification caused by the gradient of salinity or sediment suspension and the occurrence of recirculation vortices generated by seabed topography.

Note on the Bulk Estimate of the Energy Dissipation Rate in the Oceanic Bottom Boundary Layer

The dissipation of the kinetic energy (KE) associated with oceanic flows is believed to occur primarily in the oceanic bottom boundary layer (BBL), where bottom drag converts the KE from mean flows to heat loss through irreversible mixing at molecular scales. Due to the practical difficulties associated with direct observations on small-scale turbulence close to the seafloor, most up-to-date estimates on bottom drag rely on a simple bulk formula (CdU3) proposed by G.I. Taylor that relates the integrated BBL dissipation rate to a drag coefficient (Cd) as well as a flow magnitude outside of the BBL (U). Using output from several turbulence-resolving direct numerical simulations, it is shown that the true BBL-integrated dissipation rate is approximately 90% of that estimated using the classic bulk formula, applied here to the simplest scenario where a mean flow is present over a flat and hydrodynamically smooth bottom. It is further argued that Taylor’s formula only provides an upper bound estimate and should be applied with caution in the future quantification of BBL dissipation; the performance of the bulk formula depends on the distribution of velocity and shear stress near the bottom, which, in the real ocean, could be disrupted by bottom roughness.

The Evolution and Arrest of a Turbulent Stratified Oceanic Bottom Boundary Layer over a Slope: Upslope Regime and PV Dynamics

AbstractThe influence of a sloping bottom and stratification on the evolution of an oceanic bottom boundary layer (BBL) in the presence of a mean flow is explored. As a complement to an earlier study by Ruan et al. (https://doi.org/10.1175/JPO-D-18-0079.1) examining Ekman arrest in a downslope regime, this paper describes turbulence and BBL dynamics during Ekman arrest in the upslope regime. In the upslope regime, an enhanced stratification develops in response to the upslope Ekman transport and suppresses turbulence. Using a suite of large-eddy simulations, we show that the BBL evolution can be described in a self-similar framework based on a nondimensional number X/Xa. This nondimensional number is defined as the ratio between the lateral displacement of density surfaces across the slope X and a displacement Xa required for Ekman arrest; the latter can be predicted from external parameters. Additionally, the evolution of the depth-integrated potential vorticity is considered in both upslope and downslope regimes. The PV destruction rate in the downslope regime is found to be twice the production rate in the upslope regime, using the same definition for the bottom mixed layer thickness. It is shown that this asymmetry is associated with the depth scale over which turbulent stresses are active. These results are a step toward improving parameterizations of BBL properties and evolution over sloping topography in coarse-resolution ocean models.

Nongeostrophic Baroclinic Instability over Sloping Bathymetry: Buoyant Flow Regime

AbstractBaroclinic instabilities are important processes that enhance mixing and dispersion in the ocean. The presence of sloping bathymetry and the nongeostrophic effect influence the formation and evolution of baroclinic instabilities in oceanic bottom boundary layers and in coastal waters. This study explores two nongeostrophic baroclinic instability theories adapted to the scenario with sloping bathymetry and investigates the mechanism of the instability suppression (reduction in growth rate) in the buoyant flow regime. Both the two-layer and continuously stratified models reveal that the suppression is related to a new parameter, slope-relative Burger number Sr ≡ (M2/f2)(α + αp), where M2 is the horizontal buoyancy gradient, α is the bathymetry slope, and αp is the isopycnal slope. In the layer model, the instability growth rate linearly decreases with increasing Sr {the bulk form Sr = [U0/(H0f)](α + αp)}. In the continuously stratified model, the instability suppression intensifies with increasing Sr when the regime shifts from quasigeostrophic to nongeostrophic. The adapted theories are intrinsically applicable to deep ocean bottom boundary layers and could be conditionally applied to coastal buoyancy-driven flow. The slope-relative Burger number is related to the Richardson number by Sr = δrRi−1, where the slope-relative parameter is δr = (α + αp)/αp. Since energetic fronts in coastal zones are often characterized by low Ri, that implies potentially higher values of Sr, which is why baroclinic instabilities may be suppressed in the energetic regions where they would otherwise be expected to be ubiquitous according to the quasigeostrophic theory.

The Evolution and Arrest of a Turbulent Stratified Oceanic Bottom Boundary Layer over a Slope: Downslope Regime

AbstractThe dynamics of a stratified oceanic bottom boundary layer (BBL) over an insulating, sloping surface depend critically on the intersection of density surfaces with the bottom. For an imposed along-slope flow, the cross-slope Ekman transport advects density surfaces and generates a near-bottom geostrophic thermal wind shear that opposes the background flow. A limiting case occurs when a momentum balance is achieved between the Coriolis force and a restoring buoyancy force in response to the displacement of stratified fluid over the slope: this is known as Ekman arrest. However, the turbulent characteristics that accompany this adjustment have received less attention. We present two estimates to characterize the state of the BBL based on the mixed layer thickness: Ha and HL. The former characterizes the steady Ekman arrested state, and the latter characterizes a relaminarized state. The derivation of HL makes use of a newly defined slope Obukhov length Ls that characterizes the relative importance of shear production and cross-slope buoyancy advection. The value of Ha can be combined with the temporally evolving depth of the mixed layer H to form a nondimensional variable H/Ha that provides a similarity prediction of the BBL evolution across different turbulent regimes. The length scale Ls can also be used to obtain an expression for the wall stress when the BBL relaminarizes. We validate these relationships using output from a suite of three-dimensional large-eddy simulations. We conclude that the BBL reaches the relaminarized state before the steady Ekman arrested state. Calculating H/Ha and H/HL from measurements will provide information on the stage of oceanic BBL development being observed. These diagnostics may also help to improve numerical parameterizations of stratified BBL dynamics over sloping topography.

Behavior of Suspended Particulate Matter Near the Ocean Bottom Boundary Layer

Behavior of Suspended Particulate Matter Near the Ocean Bottom Boundary Layer

The Bottom Boundary Layer.

The oceanic bottom boundary layer extracts energy and momentum from the overlying flow, mediates the fate of near-bottom substances, and generates bedforms that retard the flow and affect benthic processes. The bottom boundary layer is forced by winds, waves, tides, and buoyancy and is influenced by surface waves, internal waves, and stratification by heat, salt, and suspended sediments. This review focuses on the coastal ocean. The main points are that (a) classical turbulence concepts and modern turbulence parameterizations provide accurate representations of the structure and turbulent fluxes under conditions in which the underlying assumptions hold, (b) modern sensors and analyses enable high-quality direct or near-direct measurements of the turbulent fluxes and dissipation rates, and

Direct measurement of hairpin‐like vortices in the bottom boundary layer of the coastal ocean

AbstractLaboratory measurements and numerical modeling at low Reynolds numbers (Reθ<7700) indicate the energy‐containing turbulence of boundary layer flows comprises coherent packets of hairpin vortices. Here direct measurements in the bottom boundary layer of the coastal ocean at higher Reynolds numbers (Reθ = 266,150) show tidal flows also contain packets of large vortices separated by periods of more quiescent conditions. The 1452 vortices recorded within a 20 min period are typically aligned along stream (∼8.0° from the mean flow direction) and inclined to the horizontal (∼27.0° from the seabed), with a mean period of occurrence of 4.3 s. These results lend three‐dimensional, in situ support to an interpretation of the coastal ocean bottom boundary layer as comprising coherent packets of hairpin vortices. This demonstrates a direct linkage from low Reynolds number experiments to higher Reynolds number flows, permitting fine‐scale details of particle transport and pollutant dispersion to be inferred from lower Reynolds number data.

On the wave and current interaction with a rippled seabed in the coastal ocean bottom boundary layer

Interactions of currents and waves with a rippled seabed in the inner part of the coastal ocean bottom boundary layer are studied using particle image velocimetry, ADV, and bottom roughness measurements. Mean velocity profiles collapse with appropriate scaling in the log layer, but vary substantially in the roughness sublayer. When wave-induced motions are similar or greater than the mean current, the hydrodynamic roughness ( z0) determined from velocity profiles is substantially larger than directly measured values. The roughness signature in turbulent energy spectra persists with elevation when its scale falls in the dissipation range, but decays in the log layer for larger roughness elements. Reynolds shear stress profiles peak in the lower parts of the log layer, diminishing below it, and gradually decaying at higher elevations. In contrast, wave shear stresses are negligible within the log layer, but become significant within the roughness sublayer. This phenomenon is caused by an increase in the magnitude and phase lag of the vertical component of wave-induced motion. No single boundary layer length scale collapses the Reynolds stresses, but both the Prandtl mixing length and eddy viscosity profiles agree well with the classical model of linear increase with elevation, especially near the seabed. Within the log region, profiles of shear production and dissipation rates of turbulence converge. Below it, dissipation rapidly increases, peaking near the seabed. Conversely, the shear production decays near the seabed, in agreement with the eddy viscosity model, but in contrast to both laboratory and computational rough wall studies.

Friction law and turbulent properties in a laboratory Ekman boundary layer

We use spin-up/spin-down laboratory experiments to study the neutrally stratified Ekman boundary layer. The experiments are performed in the 13 m diameter, 1 m deep Coriolis rotating tank of the LEGI in Grenoble, France. A global flow rotation is produced by an initial change in the tank rotation speed. It then slowly decays under the effect of Ekman friction, evolving from the turbulent state to the laminar state. It is checked that the Ekman layer itself remains in a quasi-steady state during this decay. The velocity is measured by Particle Imaging Velocimetry (PIV) at two scales: the global rotation in a horizontal plane, and the vertical profile inside the boundary layer, where the three velocity components are obtained by stereoscopic PIV. The friction law is obtained by relating the decay rate of the bulk velocity to the velocity itself. This method is justified by the fact that this bulk velocity is independent of height beyond the top of the boundary layer (a few cm), as expected from the Taylor-Proudman theorem for rotating fluids. The local measurements inside the boundary layer provide profiles of the mean velocity and Reynolds stress components, in particular the cross-isobar angle between the interior and near surface velocities. In the laminar regime, good agreement is obtained with the classical Ekman's theory, which validates the method. In the turbulent regime, the results are found consistent with the classical Atmospheric Boundary Layer (ABL) model based on the von Karman logarithmic layer. Our experiments therefore indicate that this theory, in principle valid for very large Reynolds numbers, is already relevant close to the transitional regimes. A fit of the empirical coefficients A and B appearing in this theory yields A = 3.3 and B = 3.0. Extrapolating the results to the atmospheric case gives a friction velocity u* about 12% higher than the traditional fit for the ABL. We may safely deduce that for the oceanic bottom boundary layer, corresponding to lower Reynolds numbers than the atmosphere, our result provides a correct estimate within 10%. The previous laboratory results of Caldwell et al. [“A laboratory study of the turbulent Ekman layer,” Geophys. Fluid Dyn. 3, 125–160 (1972)10.1080/03091927208236078] provided frictions velocities about 20% higher than in our experiments, and slightly higher cross-isobar angles. We attribute this difference to the higher vortical Rossby number Rot in those experiments, and maybe also to roughness effects. We take into account the effect of this vortical Rossby number within the framework of the Ekman layer (Rot → 0) by replacing the tank rotation rate by the fluid rotation rate.

A numerical investigation of the turbulent Stokes–Ekman bottom boundary layer

AbstractIn the present paper turbulent mixing in the Stokes–Ekman bottom boundary layer is investigated analytically and by wall-resolving large-eddy simulations (LES). The analytical solution shows that when the Rossby number $\mathit{Ro}\ensuremath{\sim} 1$ oscillation and rotation interact with each other, this gives rise to a thickening of the boundary layer compared with the purely oscillating or the purely rotating case. The solution also shows the presence of elliptical patterns developing on the horizontal planes that shrink when approaching the low latitudes. In the turbulent regime, a LES was applied for an east–west tidal current, considered at three different latitudes in the Northern Hemisphere, namely, the polar case, the mid-latitude case ($4{5}^{\ensuremath{\circ} } $) and the quasi-equatorial case (${5}^{\ensuremath{\circ} } $). The Reynolds number of the simulation, based on the viscous penetration depth and the frequency of the purely oscillatory flow, was set equal to ${\mathit{Re}}_{\delta } = 1790$. The analysis suggests that rotation has two main effects on the flow field: in the polar case, rotation tends to delay the cyclic re-transition to turbulence and to narrow the turbulent phases of the cycle. Also, rotation suppresses vertical fluctuations of velocity and redistributes energy from the streamwise direction to the spanwise direction. It is noteworthy that the high-latitude effect makes the turbulent field substantially different from the reference Stokes boundary layer case, whereas the low-latitude effects appear to be of secondary importance, owing to the weakness of the rotation rate. Consequently, the study shows that the Stokes boundary layer may be representative of the oceanic bottom boundary layer in the low-latitude cases ($\mathit{Ro}\gt 1$ cases in our simulations). Conversely, it cannot be considered as archetypal of the oceanic boundary layer at high latitudes ($\mathit{Ro}\lt 1$ case of our study), where the vertical background vorticity profoundly modifies the turbulent field.

Effect of Finite Spatial Resolution on the Turbulent Energy Spectrum Measured in the Coastal Ocean Bottom Boundary Layer

Abstract The effect of finite spatial resolution on the measured energy spectrum is examined via a parametric study using in situ particle image velocimetry (PIV) measurements performed in the bottom boundary layer on the Atlantic continental shelf. Two-dimensional (2D) box spatial filters of various scales are applied to the data, and these filtered distributions are used to compute 1D energy spectra in both frequency and wavenumber domains. It is found that energy levels are attenuated by more than 15% at all length scales that are smaller than 10 times the scale of the filter. Filtering both in the direction of the spectrum as well as perpendicular to it contributes to the extent of attenuation, the latter via implicit integration over all wavenumbers. At scales larger than that of the filter, Gaussian, nonlinear Butterworth, and median filters attenuate less energy than the box filter. When frequency spectra are converted using Taylor’s hypothesis, wave energy appears in wavenumber space at a location different than its true physical scale, which is much larger than the filter sizes. Consequently, wave energy is not attenuated and dominates over the turbulence through this spectral range. Because wave energy and turbulence respond differently to the filtering, modified spectral slopes at the transition between wave- and turbulence-dominated regions occur, resulting in inordinately steep spectral slopes. Finally, removal of the pressure-coherent part of the velocity signal is not sufficient to reveal the turbulence within the wave peak spectral range. Remaining energy in this range is still dominated by much larger scales.

Wave-induced steady streaming, mass transport and net sediment transport in rough turbulent ocean bottom boundary layers

The interaction between two important mechanisms which causes streaming has been investigated by numerical simulations of the seabed boundary layer beneath both sinusoidal waves and Stokes second order waves, as well as horizontally uniform bottom boundary layers with asymmetric forcing. These two mechanisms are streaming caused by turbulence asymmetry in successive wave half-cycles (beneath asymmetric forcing), and streaming caused by the presence of a vertical wave velocity within the seabed boundary layer as earlier explained by Longuet-Higgins. The effect of wave asymmetry, wave length to water depth ratio, and bottom roughness have been investigated for realistic physical situations. The streaming induced sediment dynamics near the ocean bottom has been investigated; both the resulting suspended load and bedload are presented. Finally, the mass transport (wave-averaged Lagrangian velocity) has been studied for a range of wave conditions. The streaming velocities beneath sinusoidal waves (Longuet-Higgins streaming) is always in the direction of wave propagation, while the streaming velocities in horizontally uniform boundary layers with asymmetric forcing are always negative. Thus the effect of asymmetry in second order Stokes waves is either to reduce the streaming velocity in the direction of wave propagation, or, for long waves relative to the water depth, to induce a streaming velocity against the direction of wave propagation. It appears that the Longuet-Higgins streaming decreases as the wave length increases for a given water depth, and the effect of wave asymmetry can dominate, leading to a steady streaming against the wave propagation. Furthermore, the asymmetry of second order Stokes waves reduces the mass transport (wave-averaged Lagrangian velocity) as compared with sinusoidal waves. The boundary layer streaming leads to a wave-averaged transport of suspended sediments and bedload in the direction of wave propagation.

The effect of waves on subgrid-scale stresses, dissipation and model coefficients in the coastal ocean bottom boundary layer

Six sets of particle image velocimetry (PIV) data from the bottom boundary layer of the coastal ocean are examined. The data represent periods of high, moderate and weak mean flow relative to the amplitude of wave-induced motion, which correspond to high, moderate and low Reynolds numbers based on the Taylor microscale (Re). The two-dimensional PIV velocity distributions enable spatial filtering to calculate some of the subgrid-scale (SGS) stresses, from which we can estimate the SGS dissipation, and evaluate the performance of typically used SGS stress models. The previously reported mismatch between the SGS and viscous dissipation at moderate and low Reynolds numbers appears to be related to the sparsity of large vortical structures that dominate energy fluxes.Conditional sampling of SGS stresses and dissipation based on wave phase using Hilbert transforms demonstrate persistent and repeatable direct effects of large-scale but weak straining by the waves on the SGS energy flux at small scales. The SGS energy flux is phase-dependent, peaking when the streamwise-wave-induced velocity is accelerating, and lower when this velocity is decelerating. Combined with strain rate generated by the mean flow, the streamwise wave strain causes negative energy flux (backscatter), whereas the vertical wave strain causes a positive flux. The phase-dependent variations and differences between horizontal and vertical contributions to the cascading process extend to strains that are substantially higher than the wave-induced motion. These trends may explain the measured difference between spatial energy spectra of streamwise velocity fluctuations and spectra of the wall-normal component, i.e. the formation of spectral bumps in the spectra of the streamwise component at the wavenumbers for the transition between inertial and dissipation scales.All the model coefficients of typical SGS stress models measured here are phase dependent and show similar trends. Thus, the variations of measured SGS dissipation with phase are larger than those predicted by the model variables. In addition, the measured coefficients of the static Smagorinsky SGS stress model decrease with decreasing turbulence levels, and increase with filter size. The dynamic model provides higher correlation coefficients than the Smagorinsky model, but the substantial fluctuations in their values indicate that ensemble averaging is required. The ‘global’ dynamic model coefficients indicate that the use of a scale-dependent dynamic model may be appropriate. The structure function model yields poor correlation coefficients and is found to be over-dissipative under all but the highest turbulence levels. The nonlinear model has higher correlations with measured stresses, as expected, but it also does not reproduce the trends with wave phase.

Capturing the bottom boundary layer in finite element ocean models

The goal of this paper is to develop and compare numerical discretizations that explicitely take into account the logarithmic behaviour of the velocity field in the oceanic bottom boundary layer. This is achieved by discretizing the governing equations by means of the finite element method and either enriching or modifying the set of shape functions used to approximate the velocity field. The first approach is based on the extended finite element formalism and requires additional “enriched” degrees of freedom near the bottom. The second approach amounts to using logarithmic shape functions in the bottom element instead of the usual linear ones. Both approaches are compared with analytical and classical finite element solutions in the case of rotating and non-rotating bottom boundary layer flows.

A modified law‐of‐the‐wall applied to oceanic bottom boundary layers

Near the bottom, the velocity profile in the bottom boundary layer over the continental shelf exhibits a characteristic law‐of‐the‐wall that is consistent with local estimates of friction velocity from near‐bottom turbulence measurements. Farther from the bottom, the velocity profile exhibits a deviation from the law‐of‐the‐wall. Here the velocity gradient continues to decrease with height but at a rate greater than that predicted by the law‐of‐the‐wall with the local friction velocity. We argue that the shape of the velocity profile is made consistent with the local friction velocity by the introduction of a new length scale that, near the boundary, asymptotes to a value that varies linearly from the bottom. Farther from the boundary, this length scale is consistent with the suppression of velocity fluctuations either by stratification in the upper part of the boundary layer or by proximity to the free surface. The resultant modified law‐of‐the‐wall provides a good representation of velocity profiles observed over the continental shelf when a local estimate of the friction velocity from coincident turbulence observations is used. The modified law‐of‐the‐wall is then tested on two very different sets of observations, from a shallow tidal channel and from the bottom of the Mediterranean outflow plume. In both cases it is argued that the observed velocity profile is consistent with the modified law‐of‐the‐wall. Implicit in the modified law‐of‐the‐wall is a new scaling for turbulent kinetic energy dissipation rate. This new scaling diverges from the law‐of‐the‐wall prediction above 0.2D(whereDis the thickness of the bottom boundary layer) and agrees with observed profiles to 0.6D.

Turbulence spectra and local similarity scaling in a strongly stratified oceanic bottom boundary layer

In the turbulence inertial subrange, wavenumber spectra of vertical velocity and streamwise velocity in a strongly stratified oceanic bottom boundary layer agree with the local similarity scaling laws found previously in the stable atmospheric boundary layer. At scales greater than the turbulence inertial subrange, oceanic velocity spectra exceed the universal spectra. This additional energy at large scales could be due either to internal waves, inappropriate estimates of turbulence parameters, or non-stationarity of the data. Providing that the energy containing eddies in the stratified boundary layer have a scale close to the Ozmidov scale, ε 1/2 N −3/2, where ε is the turbulence kinetic energy dissipation rate and N is the buoyancy frequency, the universal model spectrum leads to a turbulent scaling ε= βNσ w 2, where β is a dimensionless constant 0.6–1.5 and σ w 2 is the vertical velocity variance. This scaling law of ε has been found in free shear flows in the ocean and atmosphere. The turbulence Reynolds stress is related to the vertical velocity variance as −〈 u′ w′〉=1/4 σ w 2. The strong stratification in the observed tidal bottom boundary layer is maintained by the advective density gradient. Results reported here include the effects of horizontal advection.