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

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.

On the Structure of Turbulence in the Bottom Boundary Layer of the Coastal Ocean

2005 ◽  
Vol 35 (1) ◽  
pp. 72-93 ◽  
Author(s):  
W. A. M. Nimmo Smith ◽  
J. Katz ◽  
T. R. Osborn
Keyword(s):  
Boundary Layer ◽  
Energy Spectrum ◽  
Coastal Ocean ◽  
Bottom Boundary Layer ◽  
Small Scale ◽  
Shear Stresses ◽  
Weak Turbulence ◽  
Conditional Sampling ◽  
Bottom Boundary ◽  
Dissipation Rates

Abstract Six sets of particle image velocimetry (PIV) data from the bottom boundary layer of the coastal ocean are examined. The data represent periods when the mean currents are higher, of the same order, and much weaker than the wave-induced motions. The Reynolds numbers based on the Taylor microscale (Reλ) are 300–440 for the high, 68–83 for the moderate, and 14–37 for the weak mean currents. The moderate–weak turbulence levels are typical of the calm weather conditions at the LEO-15 site because of the low velocities and limited range of length scales. The energy spectra display substantial anisotropy at moderate to high wavenumbers and have large bumps at the transition from the inertial to the dissipation range. These bumps have been observed in previous laboratory and atmospheric studies and have been attributed to a bottleneck effect. Spatial bandpass-filtered vorticity distributions demonstrate that this anisotropy is associated with formation of small-scale, horizontal vortical layers. Methods for estimating the dissipation rates are compared, including direct estimates based on all of the gradients available from 2D data, estimates based on gradients of one velocity component, and those obtained from curve fitting to the energy spectrum. The estimates based on vertical gradients of horizontal velocity are higher and show better agreement with the direct results than do those based on horizontal gradients of vertical velocity. Because of the anisotropy and low turbulence levels, a −5/3 line-fit to the energy spectrum leads to mixed results and is especially inadequate at moderate to weak turbulence levels. The 2D velocity and vorticity distributions reveal that the flow in the boundary layer at moderate speeds consists of periods of “gusts” dominated by large vortical structures separated by periods of more quiescent flows. The frequency of these gusts increases with Reλ, and they disappear when the currents are weak. Conditional sampling of the data based on vorticity magnitude shows that the anisotropy at small scales persists regardless of vorticity and that most of the variability associated with the gusts occurs at the low-wave-number ends of the spectra. The dissipation rates, being associated with small-scale structures, do not vary substantially with vorticity magnitude. In stark contrast, almost all the contributions to the Reynolds shear stresses, estimated using structure functions, are made by the high- and intermediate-vorticity-magnitude events. During low vorticity periods the shear stresses are essentially zero. Thus, in times with weak mean flow but with wave orbital motion, the Reynolds stresses are very low. Conditional sampling based on phase in the wave orbital cycle does not show any significant trends.

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

2005 ◽  
Vol 35 (8) ◽  
pp. 1305-1317 ◽  
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.

scholarly journals A Self-Contained Acoustic Scintillation Instrument for Path-Averaged Measurements of Flow and Turbulence with Application to Hydrothermal Vent and Bottom Boundary Layer Dynamics

2005 ◽  
Vol 22 (10) ◽  
pp. 1602-1617 ◽  
Author(s):  
D. Di Iorio ◽  
D. Lemon ◽  
R. Chave
Keyword(s):  
Boundary Layer ◽  
Hydrothermal Vent ◽  
Acoustic Scattering ◽  
Temperature Fluctuations ◽  
Energy Dissipation Rate ◽  
Bottom Boundary Layer ◽  
The Black Sea ◽  
Small Scale ◽  
Bottom Boundary

Abstract A self-contained acoustical scintillation instrument is described that has been used to measure flow and turbulence characteristics in two diverse oceanographic settings. This instrument is a battery-operated and internally logging acoustic propagation system that is ideally suited to monitor long-term flow and small-scale effective refractive index fluctuations. When the temperature variability dominates the acoustic scattering, as is the case of a hydrothermal vent plume, then a measure of the vertical buoyancy-driven flow, together with the root-mean-square temperature fluctuations, can be obtained. Results for vent structure Hulk of the Main Endeavour vent field of the Juan de Fuca Ridge show that the long-term (71 days) temperature fluctuations, together with the vertical flow, can be used to estimate heat flux density. Measurements also show oscillations in the log-amplitude variance that result from plume advection by the ambient tidal currents and demonstrate the need for a long time series measurement. When the turbulent velocity dominates the acoustic scattering, as is the case in some energetic bottom boundary layer flows, then the turbulent kinetic energy dissipation rate is derived, assuming isotropic and homogeneous models. The methodology and results are summarized from an application to the Bosporus Canyon of the Black Sea, to monitor the flow and turbulence associated with Mediterranean seawater inflow.

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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