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.

scholarly journals Accelerating Dense-Water Flow down a Slope

2009 ◽  
Vol 39 (6) ◽  
pp. 1495-1511 ◽  
Author(s):  
John M. Huthnance
Keyword(s):  
Boundary Layer ◽  
Density Gradient ◽  
Slope Angle ◽  
Deep Ocean ◽  
Bottom Boundary Layer ◽  
Bottom Slope ◽  
Initial Value ◽  
Bottom Boundary ◽  
Downslope Flow ◽  
Horizontal Density Gradient

Abstract Where water is denser on a shallow shelf than in the adjacent deep ocean, it tends to flow down the slope from shelf to ocean. The flow can be in a steady bottom boundary layer for moderate combinations of upslope density gradient −ρx∞ and bottom slope (angle θ to horizontal):Here g is acceleration due to gravity, ρ0 is a mean density, and f is twice the component of the earth’s rotation normal to the sloping bottom. For stronger combinations of the horizontal density gradient and bottom slope, the flow accelerates. Analysis of an idealized initial value problem shows that, when b ≥ 1, there is a bottom boundary layer with downslope flow, intensifying exponentially at a rate fb2(1 + b)−1/2/2, and slower-growing flow higher up. For stronger stratification b > 21/2, that is, a relatively weak Coriolis constraint, the idealized problem posed here may not be the most apposite but suggests that the whole water column accelerates, at a rate [ρ0−1|ρx∞|g sinθ]1/2 if f is negligible.

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 Stratified Inertial Subrange Inferred from In Situ Measurements in the Bottom Boundary Layer of the Rockall Channel

2010 ◽  
Vol 40 (11) ◽  
pp. 2401-2417 ◽  
Author(s):  
Pascale Bouruet-Aubertot ◽  
Hans van Haren ◽  
M. Pascale Lelong
Keyword(s):  
Boundary Layer ◽  
Energy Levels ◽  
Deep Ocean ◽  
Energy Dissipation Rate ◽  
Bottom Boundary Layer ◽  
Inertial Subrange ◽  
Buoyancy Frequency ◽  
Bottom Boundary ◽  
Wide Range ◽  
Taylor Hypothesis

Abstract Deep-ocean high-resolution moored temperature data are analyzed with a focus on superbuoyant frequencies. A local Taylor hypothesis based on the horizontal velocity averaged over 2 h is used to infer horizontal wavenumber spectra of temperature variance. The inertial subrange extends over fairly low horizontal wavenumbers, typically within 2 × 10−3 and 2 × 10−1 cycles per minute (cpm). It is therefore interpreted as a stratified inertial subrange for most of this wavenumber interval, whereas in some cases the convective inertial subrange is resolved as well. Kinetic energy dissipation rate ε is inferred using theoretical expressions for the stratified inertial subrange. A wide range of values within 10−9 and 4 × 10−7 m2 s−3 is obtained for time periods either dominated by semidiurnal tides or by significant subinertial variability. A scaling for ε that depends on the potential energy within the inertio-gravity waves (IGW) frequency band PEIGW and the buoyancy frequency N is proposed for these two cases. When semidiurnal tides dominate, ε ≃ (PEIGWN)3/2, whereas ε ≃ PEIGWN in the presence of significant subinertial variability. This result is obtained for energy levels ranging from 1 to 30 times the Garrett–Munk energy level and is in contrast with classical finescale parameterization in which ε ∼ (PEIGW)2 that applies far from energy sources. The specificities of the stratified bottom boundary layer, namely a weak stratification, may account for this difference.

Simulations of coastal upwelling on the Sydney Continental Shelf

2000 ◽  
Vol 51 (6) ◽  
pp. 577 ◽  
Author(s):  
Patrick Marchesiello ◽  
Mark T. Gibbs ◽  
Jason H. Middleton
Keyword(s):  
Boundary Layer ◽  
Coastal Upwelling ◽  
Deep Ocean ◽  
Bottom Boundary Layer ◽  
Return Flow ◽  
Pressure Gradients ◽  
Bottom Boundary ◽  
Eastern Australia ◽  
Flow Through ◽  
Good Agreement

Two-dimensional numerical simulations of the response of the coastal waters of Sydney, south-eastern Australia, to idealized upwelling-favourable winds are presented. The spin up of the upwelling circulation is investigated, in particular the structure of the nearshore circulation. The intensity of the final upwelling state is found to be strongly linked to the activation of the return flow through the bottom boundary layer, which is also related to the strength of imposed alongshore pressure gradients. Results from a simulation of upwelling forced by a deep-ocean alongshore-current jet also show the final upwelling state to be weak in comparison with upwelling states produced by the action of the local wind stress. Bottom boundary layer shut-down in the presence of such a forcing jet is also discussed. A simulation of a real upwelling event was also performed and good agreement was found between the simulation and observations from a field experiment performed during summer 1994 in the Sydney coastal ocean.

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.

The bottom boundary layer of the deep ocean

1976 ◽  
Vol 81 (27) ◽  
pp. 4983-4990 ◽  
Author(s):  
Laurence Armi ◽  
Robert C. Millard
Keyword(s):  
Boundary Layer ◽  
Deep Ocean ◽  
Bottom Boundary Layer ◽  
Bottom Boundary

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°.

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