On the energy spectra of a random field of internal waves

Several authors (e.g. Phillips, 1966; Voorhis, 1968; Fofonoff, 1969; Frankignoul, 1970) have attempted to interpret the energy spectra observed in the deep ocean as resulting from a random field of linear internal waves propagating in all directions. Further studies of erratic motions in the deep ocean by methods of weak turbulence theory (Nihoul, 1971) seem to suggest that, in fact, for frequencies smaller than the Brunt- Vaisalll frequency, the cogent factor responsible for the shape of the spectra may be the interaction of random internal waves with a weak mean shear. I n order to examine this suggestion, one investigates here the simple situation of a random field of linear internal waves super-imposed on a mean current which varies slowly (and, to be specific, in a linear way) with depth under the assumption that the Brunt-VaisalL frequency is constant.