Abstract: Numerical simulation of shear instabilities in interfacial gravity waves



Authors: Oliver B. Fringer and Michael F. Barad

We present simulations of shear instabilities in solitary-like interfacial gravity waves of depression using a Navier-Stokes solver that employs adaptive mesh refinement. The adaptive technique enables resolution of 0.20 m in a 500 m long wave which allows simulation of meter-scale Kelvin-Helmholtz (KH)-like billows that develop at the interface. Due to the time-varying nature of the shear within the waves, instability occurs only when a parcel of fluid is subject to destabilizing shear long enough for KH-type billows to grow. While a necessary criterion for instability suggests that the Richardson number must fall below the canonical value of 1/4, we find that a sufficient condition for instability occurs when the minimum Richardson number within the waves falls below 0.1. Under this condition, two-dimensional billows form at the wave troughs, and these billows subsequently break down via three-dimensional motions that decay once the wave-induced shear subsides in the trailing edge of the waves. We analyze the instability with the Taylor Goldstein equation and then devise a criterion for instability based on bulk wave properties.