The effect of initial perturbations on the merging and mixing of Holmboe instabilities in stratified shear flows*

Initial perturbations are commonly used in direct numerical simulations to stimulate shear instabilities of stratified fluids. Without these perturbations, the velocity and density fields diffuse molecularly and no instabilities yield. We investigated the sensitivity of wave merging and mixing to initial perturbations in Holmboe instabilities through two- and three-dimensional simulations. Two-dimensional simulations are used to test the sensitivity of wave merging to the amplitude and phase difference between the primary Holmboe and subharmonic components of the perturbation. Three-dimensional simulations are used to investigate the effect of wave merging on mixing. The amplitude has a more significant effect on the merging of Holmboe instabilities compared to the initial phase difference. For a given amplitude of the primary component perturbation, a larger amplitude of subharmonic component perturbation results in an earlier merging event. In three-dimensional simulations, the subharmonic mode is incited if the subharmonic component perturbation is imposed, increasing the amplitude of the Holmboe instability and its associated cumulative mixing.