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

The effects of different initial perturbations on the evolution of Holmboe instabilities in stratified shear flows have been investigated through direct numerical simulations. The phase difference and amplitude of the primary and subharmonic Holmboe modes determine the development of Holmboe instabilities, which, in turn, influence diapycnal mixing in stratified flows. The amplitude has a more significant effect on the merging of primary Holmboe modes compared to the initial phase difference. For a given amplitude of the primary perturbation, a larger amplitude of subharmonic perturbation results in an earlier merging event. In three-dimensional simulations, the subharmonic mode is incited if the subharmonic perturbation is imposed, increasing the amplitude of Holmboe waves by a factor of 2. Although this Holmboe instability grows slower initially, the growing period is longer and the accumulated amount of mixing is also larger.