Transient evolution and high stratification scaling in horizontal mixing layers

Mixing layers (sheared flows in homogeneous or stratified fluid) are present in many geophysical contexts and may lead to turbulence and mixing. In several cases, mixing layers are known to exhibit the Kelvin-Helmholtz instability leading to the roll-up of spanwise vortices, the Kelvin-Helmholtz (KH) billows. This is an essentially two-dimensional (2D) process. In fact, in the homogeneous cases the Squire’s theorem implies that the most unstable mode is 2D. However, Squire’s theorem applies only for the exponentially growing perturbations that control the large time dynamics and is not valid for the transient dynamics at short time. Indeed, Iams et al.[1] have shown that, in the non-stratified case, the most amplified optimal perturbations for short times are three-dimensional (3D) and result from a cooperation between the lift-up and Orr mechanisms[2]. This provides a finite time mechanism for spanwise scale selection, scale that may persist at later times if nonlinearities are strong enough.