Spontaneous instability in internal solitary-like waves*

We study the onset of shear instability in internal solitary-like waves propagating in a quasi two-layer stratification, using high-resolution, two-dimensional direct numerical simulations with a spectral collocation method. We focus on large-amplitude, broadening limited waves whose minimum Richardson numbers are approximately 0.08. We demonstrate that, depending on the length of the high shear region (in which the local Richardson number is less than 0.25) relative to the width of the wave, instability can occur spontaneously along the wave's flat crest. We also show that, at least on the laboratory scale, the growth rate of the instability is Reynolds number dependent, such that for certain waves the onset of instability is possible only if the Reynolds number is sufficiently large. We further show that, for waves in which spontaneous instability does not occur, the onset of instability can still be triggered by small, but finite amplitude noise, and that the spatial structure and growth rate of the instability depends on the amplitude of the initial perturbation.