Sensitivity of wave merging and mixing to initial perturbations in Holmboe instabilities

Initial perturbations are commonly used in direct numerical simulations (DNS) to trigger the shear instability of stratified fluids. We investigate the effects of initial perturbations on the evolution of Holmboe instabilities with DNS. In particular, we model the interaction between a primary Holmboe wave and a subharmonic component that has a wavelength double that of the primary wave. We show that the phase difference and amplitude of the primary and subharmonic components of the initial perturbation controls the merging of Holmboe instabilities, which, in turn, influence diapycnal mixing in stratified flows. The amplitude difference has a more significant effect on the merging of Holmboe instabilities compared to the initial phase difference. For a given amplitude of the primary perturbation, a larger subharmonic perturbation results in an earlier merging event. In three-dimensional simulations, this preference of the subharmonic initial perturbation increased the amplitude of Holmboe waves by a factor of two. Although the subharmonic mode grows slower, it grows for longer producing more net mixing.