WAVE-NUMBER TRANSPORT - SCATTERING OF SMALL-SCALE INTERNAL WAVES BY LARGE-SCALE WAVEPACKETS

In this work, we treat the problem of small-scale, small-amplitude, in ternal waves interacting nonlinearly with a vigorous, large-scale, und ulating shear. The amplitude of the background shear can be arbitraril y large, with a general profile, but our analysis requires that the am plitude vary on a length scale longer than the wavelength of the undul ations. In order to illustrate the method, we consider the ray-theoret ic model due to Broutman and Young (1986) of high-frequency oceanic in ternal waves that trap and detrap in a near-inertial wavepacket as a p rototype problem. The near-inertial wavepacket tends to transport the high-frequency test waves from larger to smaller wavenumber, and hence to higher frequency. We identify the essential physical mechanisms of this wavenumber transport, and we quantify it. We also show that, for an initial ensemble of test waves with frequencies between the inerti al and buoyancy frequencies and in which the number of test waves per frequency interval is proportional to the inverse square of the freque ncy, a single nonlinear wave-wave interaction fundamentally alters thi s initial distribution. After the interaction, the slope on a log-log plot is nearly flat, whereas initially it was -2. Our analysis capture s this change in slope. The main techniques employed are classical adi abatic invariance theory and adiabatic separatrix crossing theory.