Vertical Shear Processes in River Plumes: Instabilities and Turbulent Mixing

Adam Ayouche,Guillaume Charria,Xavier Carton

doi:10.3390/sym14020217

Adam Ayouche, Guillaume Charria + Show 1 more

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https://doi.org/10.3390/sym14020217

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Abstract

In this paper, the problem of vertical shear flow instabilities at the base of a river plume and their consequences in terms of turbulent energy production and mixing is addressed. This study was carried out using 2D non-hydrostatic simulations and a linear stability analysis. The initial conditions used in these simulations were similar to those observed in river plumes near estuaries. Unstable stratified sheared flows follow three stages of evolution: (i) the generation of billows induced by vertical shear instabilities, (ii) intensification, and (iii) elongation. The elongation of the generated billows is related to the strain intensity, which depends on the physical setting involved (velocity shear, stratification thickness, and bottom slope). Two vertical shear instabilities were found in our study: the Holmboe and Kelvin–Helmholtz instabilities. The Kelvin–Helmholtz instability has a smaller growth time and longer wavelengths; the Holmboe instability is characterized by a longer growth time and shorter wavelengths. The Kelvin–Helmholtz instability is intensified when the bottom is sloped and for large shears. The Holmboe instability is stronger when the stratification thickness is reduced compared to the shear thickness and when the bottom is sloped. For mixing, the flow can be: (i) pre-turbulent, (ii) quasi-turbulent, or (iii) turbulent. The pre-turbulent flow corresponds to more mass mixing than momentum mixing and to more Eddy Kinetic Energy dissipation than Eddy Available Potential Energy dissipation. Such a flow is encountered over a flat bottom whatever the initial shear is. The quasi-turbulent and turbulent flows are reached when the bottom is sloped and when the stratification thickness is reduced. Using turbulent mixing statistics (mixing coefficients, mixing efficiency, Eddy Kinetic Energy, and Eddy Available Potential Energy dissipation rates), we showed that, despite their slow growth, Holmboe instabilities contribute more efficiently to turbulent mixing than Kelvin–Helmholtz instabilities. Holmboe instabilities are the only source of turbulent mixing when sharp density gradients are observed (small buoyancy thickness experiment). Our simulations highlight the contribution of the Holmboe instability to turbulent mixing.

Highlights

IntroductionKelvin–Helmholtz (hereafter KH) instability was first proposed by Helmholtz in 1868 [1]
Kelvin–Helmholtz instability was first proposed by Helmholtz in 1868 [1]
The dynamics, instabilities, and turbulent mixing in stratified sheared flows were studied. We idealized these flows based on typical conditions of river estuaries and the near-field regions of river plumes

Summary

Introduction

Kelvin–Helmholtz (hereafter KH) instability was first proposed by Helmholtz in 1868 [1]. Using an analogy with electricity, he showed that the flow of two neighboring fluids results in surface separation This surface separation evolves as a discontinuity in the velocity field in the neighboring fluids. Thomson [2] showed that under the action of wind waves, disturbances can be observed below the ocean surface, which evolve into small waves that travel fast and cease, except when the disturbing force (the wind) continues to act. These growing waves are manifestations of the Kelvin–Helmholtz instability; they can roll up into vortices with horizontal axes, named “billows”. A condition for instability was obtained based on the Richardson number; the minimum Richardson number should be lower than a threshold of 0.25

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