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

2019 ◽  
Vol 49 (2) ◽  
pp. 469-487 ◽  
Author(s):  
Xiaozhou Ruan ◽  
Andrew F. Thompson ◽  
John R. Taylor
Keyword(s):  
Boundary Layer ◽  
Mixed Layer ◽  
Three Dimensional ◽  
Wall Stress ◽  
Bottom Boundary Layer ◽  
Ekman Transport ◽  
Momentum Balance ◽  
Bottom Boundary ◽  
Obukhov Length ◽  
Turbulent Characteristics

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.

scholarly journals Rapid Generation of Upwelling at a Shelf Break Caused by Buoyancy Shutdown

2015 ◽  
Vol 45 (1) ◽  
pp. 294-312 ◽  
Author(s):  
Jessica Benthuysen ◽  
Leif N. Thomas ◽  
Steven J. Lentz
Keyword(s):  
Boundary Layer ◽  
Vertical Mixing ◽  
Shelf Break ◽  
Bottom Boundary Layer ◽  
Ekman Transport ◽  
Bottom Boundary ◽  
Middle Atlantic ◽  
Time Period ◽  
Rapid Generation ◽  
Offshore Transport

AbstractModel analyses of an alongshelf flow over a continental shelf and slope reveal upwelling near the shelf break. A stratified, initially uniform, alongshelf flow undergoes a rapid adjustment with notable differences onshore and offshore of the shelf break. Over the shelf, a bottom boundary layer and an offshore bottom Ekman transport develop within an inertial period. Over the slope, the bottom offshore transport is reduced from the shelf’s bottom transport by two processes. First, advection of buoyancy downslope induces vertical mixing, destratifying, and thickening the bottom boundary layer. The downward-tilting isopycnals reduce the geostrophic speed near the bottom. The reduced bottom stress weakens the offshore Ekman transport, a process known as buoyancy shutdown of the Ekman transport. Second, the thickening bottom boundary layer and weakening near-bottom speeds are balanced by an upslope ageostrophic transport. The convergence in the bottom transport induces adiabatic upwelling offshore of the shelf break. For a time period after the initial adjustment, scalings are identified for the upwelling speed and the length scale over which it occurs. Numerical experiments are used to test the scalings for a range of initial speeds and stratifications. Upwelling occurs within an inertial period, reaching values of up to 10 m day−1 within 2 to 7 km offshore of the shelf break. Upwelling drives an interior secondary circulation that accelerates the alongshelf flow over the slope, forming a shelfbreak jet. The model results are compared with upwelling estimates from other models and observations near the Middle Atlantic Bight shelf break.

scholarly journals The evolution and arrest of a turbulent stratified oceanic bottom boundary layer over a slope: Upslope regime and PV dynamics

2021 ◽  
Author(s):  
XIAOZHOU RUAN ◽  
ANDREW F. THOMPSON ◽  
JOHN R. TAYLOR
Keyword(s):  
Boundary Layer ◽  
Lateral Displacement ◽  
Large Eddy Simulations ◽  
Bottom Boundary Layer ◽  
Ekman Transport ◽  
Mean Flow ◽  
Bottom Boundary ◽  
Large Eddy ◽  
Depth Scale ◽  
Self Similar

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 (Ruan et al. 2019) 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 non-dimensional number X/Xa. This non-dimensional 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 towards improving parameterizations of BBL properties and evolution over sloping topography in coarse-resolution ocean models.

scholarly journals Buoyancy Arrest and Bottom Ekman Transport. Part II: Oscillating Flow

2010 ◽  
Vol 40 (4) ◽  
pp. 636-655 ◽  
Author(s):  
K. H. Brink ◽  
S. J. Lentz
Keyword(s):  
Boundary Layer ◽  
Mixed Boundary ◽  
Broad Band ◽  
Bottom Boundary Layer ◽  
Ekman Transport ◽  
Buoyancy Frequency ◽  
Bottom Boundary ◽  
Bottom Stress ◽  
Interior Flow ◽  
Lower Frequencies

Abstract The effects of a sloping bottom and stratification on a turbulent bottom boundary layer are investigated for cases where the interior flow oscillates monochromatically with frequency ω. At higher frequencies, or small slope Burger numbers s = αN/f (where α is the bottom slope, N is the interior buoyancy frequency, and f is the Coriolis parameter), the bottom boundary layer is well mixed and the bottom stress is nearly what it would be over a flat bottom. For lower frequencies, or larger slope Burger number, the bottom boundary layer consists of a thick, weakly stratified outer layer and a thinner, more strongly stratified inner layer. Approximate expressions are derived for the different boundary layer thicknesses as functions of s and σ = ω/f. Further, buoyancy arrest causes the amplitude of the fluctuating bottom stress to decrease with decreasing σ (the s dependence, although important, is more complicated). For typical oceanic parameters, arrest is unimportant for fluctuation periods shorter than a few days. Substantial positive (toward the right when looking toward deeper water in the Northern Hemisphere) time-mean flows develop within the well-mixed boundary layer, and negative mean flows exist in the weakly stratified outer boundary layer for lower frequencies and larger s. If the interior flow is realistically broad band in frequency, the numerical model predicts stress reduction over all frequencies because of the nonlinearity associated with a quadratic bottom stress. It appears that the present one-dimensional model is reliable only for time scales less than the advective time scale that governs interior stratification.

scholarly journals Submesoscale Baroclinic Instability in the Bottom Boundary Layer

2018 ◽  
Vol 48 (11) ◽  
pp. 2571-2592 ◽  
Author(s):  
Jacob O. Wenegrat ◽  
Jörn Callies ◽  
Leif N. Thomas
Keyword(s):  
Boundary Layer ◽  
Mixed Layer ◽  
Baroclinic Instability ◽  
Slope Angle ◽  
Deep Ocean ◽  
Bottom Boundary Layer ◽  
Surface Mixed Layer ◽  
Nonlinear Simulation ◽  
Bottom Boundary ◽  
Topographic Slope

AbstractWeakly stratified layers over sloping topography can support a submesoscale baroclinic instability mode, a bottom boundary layer counterpart to surface mixed layer instabilities. The instability results from the release of available potential energy, which can be generated because of the observed bottom intensification of turbulent mixing in the deep ocean, or the Ekman adjustment of a current on a slope. Linear stability analysis suggests that the growth rates of bottom boundary layer baroclinic instabilities can be comparable to those of the surface mixed layer mode and are relatively insensitive to topographic slope angle, implying the instability is robust and potentially active in many areas of the global oceans. The solutions of two separate one-dimensional theories of the bottom boundary layer are both demonstrated to be linearly unstable to baroclinic instability, and results from an example nonlinear simulation are shown. Implications of these findings for understanding bottom boundary layer dynamics and processes are discussed.

The tidally induced bottom boundary layer in the rotating frame: development of the turbulent mixed layer under stratification

2009 ◽  
Vol 619 ◽  
pp. 235-259 ◽  
Author(s):  
KEI SAKAMOTO ◽  
KAZUNORI AKITOMO
Keyword(s):  
Boundary Layer ◽  
Mixed Layer ◽  
Interfacial Layer ◽  
Rapid Development ◽  
Tidal Mixing ◽  
Bottom Boundary Layer ◽  
Buoyancy Frequency ◽  
Rotating Frame ◽  
Three Dimensional Model ◽  
Bottom Boundary

To investigate turbulent properties and the developing mechanisms of the tidally induced bottom boundary layer in the linearly stratified ocean, numerical experiments have been executed with a non-hydrostatic three-dimensional model in the rotating frame, changing the temporal Rossby number Rot = |σ/f|, i.e. the ratio of the tidal frequency σ to the Coriolis parameter f. After the flow transitions to turbulence, the entire water column can be characterized by three layers: the mixed layer where density is homogenized and the flow is turbulent (z < zm); the stratified layer where the initial stratification remains and the flow is laminar (z > zt); and the interfacial layer between them where the flow is turbulent but the stratification remains (zm < z < zt). Turbulence is scaled by the frictional velocity uτ and the mixed-layer thickness zm (uτ and uτ/N where N is the buoyancy frequency) in the mixed (interfacial) layer, and has similarity. The mixed layer is thickened by the process where light water of the upper stratified layer is mixed with the lower unstratified layer water through the interfacial layer. As Rot approaches unity, i.e. near the critical latitude, the mixed layer develops more rapidly according to the following mechanism. As becomes Rot closer to unity, the current shear in the interfacial layer is intensified, since the difference of velocity becomes larger between the lower turbulent mixed and upper laminar stratified layers, and this leads to thickening of the interfacial layer. As a result, density deviation of the water entrained from above becomes larger, and this causes more rapid development of the mixed layer. In terms of the energy conversion from the eddy kinetic energy (EKE) to the potential energy (PE), the efficiency factor β which is the ratio of the conversion rate from EKE to PE to that from the tidal shear to EKE increased from 0.25% for Rot = 0.5 to 3.5% for Rot = 1.05 on average. When the time is normalized by the period required for the mixed layer to be thickened to the unstratified turbulent boundary layer δ = uτ/|f+σ|, the mixed layer development occurred in a similar manner in all cases. This similarity suggests the possibility of universal formulation for the turbulent tidal mixing under stratification.

Large eddy simulation of a stratified boundary layer under an oscillatory current

2009 ◽  
Vol 643 ◽  
pp. 233-266 ◽  
Author(s):  
BISHAKHDATTA GAYEN ◽  
SUTANU SARKAR ◽  
JOHN R. TAYLOR
Keyword(s):  
Boundary Layer ◽  
Large Eddy Simulation ◽  
Mixed Layer ◽  
Numerical Study ◽  
Bottom Boundary Layer ◽  
Mean Velocity ◽  
Bottom Boundary ◽  
Eddy Simulation ◽  
Large Eddy ◽  
The Mean

A numerical study based on large eddy simulation is performed to investigate a bottom boundary layer under an oscillating tidal current. The focus is on the boundary layer response to an external stratification. The thermal field shows a mixed layer that is separated from the external stratified fluid by a thermocline. The mixed layer grows slowly in time with an oscillatory modulation by the tidal flow. Stratification strongly affects the mean velocity profiles, boundary layer thickness and turbulence levels in the outer region although the effect on the near-bottom unstratified fluid is relatively mild. The turbulence is asymmetric between the accelerating and decelerating stages. The asymmetry is more pronounced with increasing stratification. There is an overshoot of the mean velocity in the outer layer; this jet is linked to the phase asymmetry of the Reynolds shear stress gradient by using the simulation data to examine the mean momentum equation. Depending on the height above the bottom, there is a lag of the maximum turbulent kinetic energy, dissipation and production with respect to the peak external velocity and the value of the lag is found to be influenced by the stratification. Flow instabilities and turbulence in the bottom boundary layer excite internal gravity waves that propagate away into the ambient. Unlike the steady case, the phase lines of the internal waves change direction during the tidal cycle and also from near to far field. The frequency spectrum of the propagating wave field is analysed and found to span a narrow band of frequencies clustered around 45°.

scholarly journals Centrifugal and Symmetric Instability during Ekman Adjustment of the Bottom Boundary Layer

2020 ◽  
Vol 50 (6) ◽  
pp. 1793-1812 ◽  
Author(s):  
Jacob O. Wenegrat ◽  
Leif N. Thomas
Keyword(s):  
Boundary Layer ◽  
Flow Field ◽  
Potential Vorticity ◽  
Lower Boundary ◽  
Bottom Boundary Layer ◽  
Ekman Transport ◽  
Surface Boundary ◽  
Layer Potential ◽  
Bottom Boundary ◽  
Symmetric Instability

AbstractFlow along isobaths of a sloping lower boundary generates an across-isobath Ekman transport in the bottom boundary layer. When this Ekman transport is down the slope it causes convective mixing—much like a downfront wind in the surface boundary layer—destroying stratification and potential vorticity. In this manuscript we show how this can lead to the development of a forced centrifugal or symmetric instability regime, where the potential vorticity flux generated by friction along the boundary is balanced by submesoscale instabilities that return the boundary layer potential vorticity to zero. This balance provides a strong constraint on the boundary layer evolution, which we use to develop a theory that explains the evolution of the boundary layer thickness, the rate at which the instabilities extract energy from the geostrophic flow field, and the magnitude and vertical structure of the dissipation. Finally, we show using theory and a high-resolution numerical model how the presence of centrifugal or symmetric instabilities alters the time-dependent Ekman adjustment of the boundary layer, delaying Ekman buoyancy arrest and enhancing the total energy removed from the balanced flow field. Submesoscale instabilities of the bottom boundary layer may therefore play an important, largely overlooked, role in the energetics of flow over topography in the ocean.

scholarly journals NEAR BOTTOM VELOCITIES IN WAVES WITH A CURRENT; ANALYTICAL AND NUMERICAL COMPUTATIONS

1984 ◽  
Vol 1 (19) ◽  
pp. 79 ◽  
Author(s):  
W.G.M. Van Kesteren ◽  
W.T. Bakker
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Bottom Friction ◽  
Bottom Boundary Layer ◽  
Two Dimensional ◽  
Layer Model ◽  
Bottom Boundary ◽  
Waves And Currents ◽  
A Current ◽  
Bottom Velocities

In this paper, starting from the Prandtl hypothesis a three-dimensional numerical bottom boundary layer model has been developed, which allows to calculate bottom friction by a combination of waves and currents. The model has been compared with two-dimensional analytical computations which gave similar results. The bottom friction values found are comparable to the ones, found by Lundgren (1972), however in the most relevant cases somewhat less. Furthermore in the two-dimensional case the model has been compared with measurements of Bakker and Van Doom (1978). With respect to the oscillatory motion, still some minor deviations occur between theory and measurements, due to deficiencies of the Prandtl theory.

Sand ripples under sea waves. Part 4. Tile ripple formation

2001 ◽  
Vol 447 ◽  
pp. 227-246 ◽  
Author(s):  
P. C. ROOS ◽  
P. BLONDEAUX
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Resonant Interaction ◽  
Bottom Boundary Layer ◽  
Small Scale ◽  
Sea Waves ◽  
Nonlinear Stability Analysis ◽  
Sandy Bottom ◽  
Bottom Boundary ◽  
Ripple Formation

We investigate the formation of small-scale three-dimensional bedforms due to interactions of an erodible bed with a sea wave that obliquely approaches the coast, being partially reflected at the beach. In this case the trajectories of fluid particles at the top of the bottom boundary layer are ellipses in the horizontal plane, the axes of which depend on the angle of wave incidence and the distance from the shore. A weakly nonlinear stability analysis of an initially flat, cohesionless, sandy bottom is performed. We focus on the resonant interaction of three perturbation components. The results show that these elliptical forcing conditions are responsible for the formation of both brick-pattern ripples and tile ripples. In particular tile ripples are associated with a flow at the top of the bottom boundary layer which is near-circular (ellipticity close to one), whereas brick-pattern ripples are related to a unidirectional oscillatory flow (zero ellipticity).

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