Velocity Profiles Above and Within the Wave Bottom Boundary Layer Over a Sloping Bottom

Diapycnal motion, diffusion, and stretching of tracers in the ocean

10.31223/x59p84 ◽

2022 ◽

Author(s):

Henri Drake ◽

Xiaozhou Ruan ◽

Raffaele Ferrari

Keyword(s):

Numerical Simulation ◽

Boundary Layer ◽

Bottom Boundary Layer ◽

Small Scale ◽

Leading Order ◽

Release Experiment ◽

Bottom Boundary ◽

In Situ Diffusion ◽

Sloping Bottom

Small-scale mixing drives the diabatic upwelling that closes the abyssal ocean overturning circulation. Measurements of in-situ turbulence reveal that mixing is bottom-enhanced over rough topography, implying downwelling in the interior and stronger upwelling in a sloping bottom boundary layer. However, in-situ mixing estimates are indirect and the inferred vertical velocities have not yet been confirmed. Purposeful releases of inert tracers, and their subsequent spreading, have been used to independently infer turbulent diffusivities; however, these Tracer Release Experiments (TREs) provide estimates in excess of in-situ ones. In an attempt to reconcile these differences, Ruan and Ferrari (2021) derived exact buoyancy moment diagnostics, which we here apply to quasi-realistic simulations. We show in a numerical simulation that tracer-averaged diapycnal motion is directly driven by the tracer-averaged buoyancy velocity, a convolution of the asymmetric upwelling/downwelling dipole. Diapycnal spreading, however, involves both the expected contribution from the tracer-averaged in-situ diffusion and an additional non-linear diapycnal stretching term. These diapycnal stretching effects, caused by correlations between buoyancy and the buoyancy velocity, can either enhance or reduce tracer spreading. Diapycnal stretching in the stratified interior is compensated by diapycnal contraction near the bottom; for simulations of the Brazil Basin Tracer Release Experiment these nearly cancel by coincidence. By contrast, a numerical tracer released near the bottom experiences leading-order stretching that varies in time. These results suggest mixing estimates from TREs are not unambiguous, especially near topography, and that more attention should be paid towards the evolution of tracers' first moments.

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Acceleration of a Stratified Current over a Sloping Bottom, Driven by an Alongshelf Pressure Gradient*

Journal of Physical Oceanography ◽

10.1175/jpo2744.1 ◽

2005 ◽

Vol 35 (8) ◽

pp. 1305-1317 ◽

Cited By ~ 14

Author(s):

David C. Chapman ◽

Steven J. Lentz

Keyword(s):

Boundary Layer ◽

Pressure Gradient ◽

Vertical Shear ◽

Bottom Boundary Layer ◽

Buoyancy Frequency ◽

Coriolis Parameter ◽

Model Calculations ◽

Bottom Boundary ◽

Bottom Stress ◽

Sloping Bottom

Abstract An idealized theoretical model is developed for the acceleration of a two-dimensional, stratified current over a uniformly sloping bottom, driven by an imposed alongshelf pressure gradient and taking into account the effects of buoyancy advection in the bottom boundary layer. Both downwelling and upwelling pressure gradients are considered. For a specified pressure gradient, the model response depends primarily on the Burger number S = Nα/f, where N is the initial buoyancy frequency, α is the bottom slope, and f is the Coriolis parameter. Without stratification (S = 0), buoyancy advection is absent, and the alongshelf flow accelerates until bottom stress balances the imposed pressure gradient. The e-folding time scale to reach this steady state is the friction time, h/r, where h is the water depth and r is a linear bottom friction coefficient. With stratification (S ≠ 0), buoyancy advection in the bottom boundary layer produces vertical shear, which prevents the bottom stress from becoming large enough to balance the imposed pressure gradient for many friction time scales. Thus, the alongshelf flow continues to accelerate, potentially producing large velocities. The acceleration increases rapidly with increasing S, such that even relatively weak stratification (S > 0.2) has a major impact. These results are supported by numerical model calculations.

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