Effect of nonlinear instability on gravity-wave momentum transport

Abstract

In resonant interaction theory, an energetic, high-frequency, low-wavenumber wave is unstable to two waves of approximately half the frequency and is backscattered by a low-frequency wave or mean finestructure of twice the vertical wavenumber. By constrast, the Eikonal saturation model, as it is commonly used, ignores reflection by assuming a slowly varying basic state and does not question the longevity of the primary wave in the presence of local Kelvin-Helmholtz or convective instabilities. The resonant interaction formalism demands that the interactions be weakly nonlinear. The Eikonal saturation model allows strong, "saturated' waves but ignores reflection and eliminates nonlinear instability with respect to other horizontal wavenumbers by invoking the linear or quasi-linear assumption. To help bridge the gap between the two theories, results from prototype, nonlinear numerical simulations are presented. The numerical results establish the existence of a cascade in wavenumber space, which for hydrostatic waves proceed towards both higher and lower horizontal wavenumbers, in accord with theory. Substantial reductions in momentum flux are found relative to the linear values. -from Author