Wave Breaking and Transition to Turbulence in Stratified Shear Flows

Abstract

In a previous study the authors used a nonlinear, compressible, spectral collocation numerical model to examine the evolution of a breaking gravity wave in two and three dimensions. The present paper extends that effort to examine the implications of higher resolution and smaller dissipation for wave and instability evolutions, transports, and energetics in shear flows aligned with and having a component transverse to the direction of wave propagation. A component of mean shear transverse to the direction of wave propagation (denoted as a skew shear) results in the alignment of instability structures with the background shear flow rather than in the direction of wave propagation. This alignment leads to asymmetric instability structures and less rapid instability growth relative to the parallel shear flow. Slower instability evolution due to a skew shear has several implications for wave breakdown, including a delayed state of maximum instability, a larger wave amplitude prior to and throughout wave breaking, larger wave fluxes of energy and momentum, and more vigorous instability and small-scale energetics. The spectral evolutions of the motion fields exhibit the development of isotropy and the approach toward a spectrum having inertial character at smaller scales of motion due to instability within the breaking wave.