On the Flux Representation of Internal Wave Spectral Transports

Recent fine- and microstructure observations from the Brazil Basin indicate enhanced finescale shear and strain in conjunction with bottom intensified turbulent dissipation above rough bathymetry. Such observations implicate the bottom boundary as an energy source for the finescale oceanic internal wave field. An attempt is made here to lay the groundwork for simple models of the spatial evolution of finescale internal waves as they propagate away from a source. Nonlinearity is explicitly treated as a flux in the spectral domain and dissipation is implicitly viewed as the end result of nonlinear transfers to high wavenumber. A general formulation for the nonlinear transfers is discussed which conserves both energy and momentum. A specific formulation is given to these transfers which can be described as a relaxation to an equilibrium power law and a backscattering process.