Evidence for layered anisotropic stratified turbulence in a freely evolving horizontal shear flow

Abstract

We present evidence for layered anisotropic stratified turbulence (LAST) and mixing produced in a freely evolving uniformly stratified shear layer where the direction of shear is orthogonal to gravity. As originally reported by Basak & Sarkar (J. Fluid. Mech., vol. 568, 2006, pp. 19–54), such a flow develops a rich three-dimensional structure in the form of interlocking columnar vortices formed by horizontal shear instability that remain coherent at large scales due to the stabilising vertical stratification. Here, we modify the initial velocity field by introducing additional small-amplitude vertical perturbations designed to be representative of pre-existing horizontal layers often observed in strongly stratified ocean environments. This reveals a novel finite amplitude, non-normal mode growth mechanism through which the vertical shear between layers may be rapidly amplified by its interaction with the horizontal shear layer prior to the growth of shear instability, leading to a rapid turbulent transition instigated by the subsequent interaction of the layers with the emerging columnar vortices. Through a consideration of relevant flow statistics and associated dimensionless parameters, we demonstrate that turbulence can enter the LAST regime, thereby indicating a generic mechanism leading to the transient development of regions of strongly stratified turbulence in the ocean. We discuss the properties of mixing and the parameterisation of mixing efficiency in terms of the relationship between turbulent length scales in the flow, in particular highlighting links to models based on the classical vertical shear instability paradigm typically associated with more weakly stratified flows that produce isolated turbulent ‘patches’.