Nonlinear evolution of the zigzag instability in a stratified fluid

Abstract

In a strongly stratified fluid, a columnar counter-rotating vortex pair is subject to the zigzag instability which bends the vortices and ultimately produces layers. We have investigated the nonlinear evolution of this linear instability by means of DNS. We show that the instability grows exponentially without nonlinear saturation and therefore produces rapidly intense vertical shear. We show that this growth is only stopped when vertical viscous effects become important and that it occurs when F 2 h Re = O(1) where Fh is the horizontal Froude number and Re the Reynolds number. Energy is then rapidly dissipated through viscous effects. We also show that for sufficiently high initial values of F 2 h Re, the intense vertical shear created by the initial zigzag instability is not directly dissipated through viscous effects but first leads to Kelvin-Helmholtz instabilities. This makes the flow turbulent and again rapidly dissipates energy. In both cases, this means that the zigzag instability is a mechanism capable of directly transferring the energy from large scales to small vertical scales where it is dissipated. Key-words : stratified flow ; instability ; energy transfer