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Shear Instability and Turbulent Mixing in the Stratified Shear Flow Behind a Topographic Ridge at High Reynolds Number
Observations on the lee of a topographic ridge show that the turbulence kinetic energy (TKE) dissipation rate due to shear instabilities is three orders of magnitude higher than the typical value in the open ocean. Laboratory-scale studies at low Reynolds number suggest that high turbulent dissipation occurs primarily within the core region of shear instabilities. However, field-scale studies indicate that high turbulence is mainly populated along the braids of shear instabilities. In this study, a high-resolution, resolving the Ozmidov-scale, non-hydrostatic model with Large Eddy Simulation (LES) turbulent closure is applied to investigate dominant mechanisms that control the spatial and temporal scales of shear instabilities and resulting mixing in stratified shear flow at high Reynolds number. The simulated density variance dissipation rate is elevated in the cusp-like bands of shear instabilities with a specific period, consistent with the acoustic backscatter taken by shipboard echo sounder. The vertical length scale of each cusp-like band is nearly half of the vertical length scale of the internal lee wave. However, it is consistent with instabilities originating from a shear layer based on linear stability theory. The model results indicate that the length scale and/or the period of shear instabilities are the key parameters to more »
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Publication Date:
NSF-PAR ID:
10355953
Journal Name:
Frontiers in Marine Science
Volume:
9
ISSN:
2296-7745
1. Abstract Direct numerical simulations are performed to compare the evolution of turbulent stratified shear layers with different density gradient profiles at a high Reynolds number. The density profiles include uniform stratification, two-layer hyperbolic tangent profile and a composite of these two profiles. All profiles have the same initial bulk Richardson number ( $$Ri_{b,0}$$ R i b , 0 ); however, the minimum gradient Richardson number and the distribution of density gradient across the shear layer are varied among the cases. The objective of the study is to provide a comparative analysis of the evolution of the shear layers in term of shear layer growth, turbulent kinetic energy as well as the mixing efficiency and its parameterization. The evolution of the shear layers in all cases shows the development of Kelvin–Helmholtz billows, the transition to turbulence by secondary instabilities followed by the decay of turbulence. Comparison among the cases reveals that the amount of turbulent mixing varies with the density gradient distribution inside the shear layer. The minimum gradient Richardson number and the initial bulk Richardson number do not correlate well with the integrated TKE production, dissipation and buoyancy flux. The bulk mixing efficiency for fixed $$Ri_{b,0}$$ R i b ,more »
3. Direct numerical simulations are performed to investigate a stratified shear layer at high Reynolds number ( $Re$ ) in a study where the Richardson number ( $Ri$ ) is varied among cases. Unlike previous work on a two-layer configuration in which the shear layer resides between two layers with constant density, an unbounded fluid with uniform stratification is considered here. The evolution of the shear layer includes a primary Kelvin–Helmholtz shear instability followed by a wide range of secondary shear and convective instabilities, similar to the two-layer configuration. During transition to turbulence, the shear layers at low $Ri$ exhibit a period of thickness contraction (not observed at lower $Re$ ) when the momentum and buoyancy fluxes are counter-gradient. The behaviour in the turbulent regime is significantly different from the case with a two-layer density profile. The transition layers, which are zones with elevated shear and stratification that form at the shear-layer edges, are stronger and also able to support a significant internal wave flux. After the shear layer becomes turbulent, mixing in the transition layers is shown to be more efficient than that which develops in the centre of the shear layer. Overall, the cumulative mixing efficiency ( $E^C$ )more »