Gravity Wave Instability Dynamics at High Reynolds Numbers. Part I: Wave Field Evolution at Large Amplitudes and High Frequencies

Abstract

Abstract Direct numerical simulations are employed to examine gravity wave instability dynamics at a high intrinsic frequency, wave amplitudes both above and below nominal convective instability, and a Reynolds number sufficiently high to allow a fully developed turbulence spectrum. Assumptions include no mean shear, uniform stratification, and a monochromatic gravity wave to isolate fluxes due to gravity wave and turbulence structures from those arising from environmental shears or varying wave amplitudes. The results reveal strong wave breaking for both wave amplitudes, severe primary wave amplitude reductions within ∼1 or 2 wave periods, an extended turbulence inertial range, significant excitation of additional wave motions exhibiting upward and downward propagation, and a net positive vertical potential temperature flux due to the primary wave motion, with secondary waves and turbulence contributing variable and negative potential temperature fluxes, respectively. Turbulence maximizes within ∼1 buoyancy period of the onset of breaking, arises almost entirely owing to shear production, and decays rapidly following primary wave amplitude decay. Secondary waves are excited by wave–wave interactions and the turbulence dynamics accompanying wave breaking; they typically have lower frequencies and smaller momentum fluxes than the primary wave following breaking.