Inertia-gravity-wave breaking: primary and secondary instabilities

The three-dimensionalization of turbulence in the breaking of nearly vertically propagating inertia-gravity waves is investigated using singular vector analysis applied to the Boussinesq equations linearized about two-dimensional time-dependent basic states obtained from nonlinear simulations of breaking waves. The singular vectors are compared to integrations of the linear model using random initial conditions, and the leading few singular vectors are found to be representative of the structures that emerge in the randomly initialized integrations. A main result is that the length scales of the leading secondary instabilities are an order of magnitude smaller than the wavelengths of both the initial wave and the primary perturbation, suggesting that the essential dynamics of the breaking might be captured by tractable nonlinear three-dimensional simulations in a relatively small triply-periodic domain. A sub-grid-scale scheme is tested as to whether it is able to treat turbulence in such cases via parameterization, with encouraging results.