The interaction of short-wavelength internal waves with a background current

Two approaches are used to explore the effects of shear on short-wavelength internal waves. In the first, the Taylor-Goldstein equation is solved exactly. The solutions reveal the inaccuracy of WKB predictions when applied to a curved velocity profile with a minimum Richardson number of order unity. To investigate internal waves in an inertial current, ray calculations are made. This second approach reveals that the process of refractive convergence, which includes the critical-layer interaction as a special case, operates at virtually all phases of the inertial oscillation and affects short waves of nearly all frequencies. It is also found, in contrast to the results of steady shear analyses, that short waves with phase speeds less that the mean flow maximum can propagate for several inertial periods without becoming unstable, and conversely that waves with initial phase speeds of two or three times the mean flow maximum can quickly become focussed to unstably high amplitudes. The final section examines the mean flow induced by three-dimensional, low-frequency, internal wave packets. Rotation alters the character of the flow so that the mean momentum is not equal to E/c, where c is the horizontal phase speed of the short waves and E is the intrinsic energy density. The generation of inertial waves by the internal wave field as found by Hasselmann (1970) for a wave field that is statistically homogeneous in the horizontal, is not predicted by a calculation that incorporates horizontal variations.