Abstract
In the linear approximation, we examine one-dimensional problems of long internal wave propagation in a stationary flow of two-layer fluids with free boundary in a channel of variable depth and width. We use the shallow-water approximation and assume that liquids in the layers are ideal, immiscible, and have a small relative density difference inherent to natural currents. The conditions the flow must satisfy for wave propagation without reflection are found and analyzed. It is shown that there are three classes of such flows, and the characteristic properties of each of them are studied and compared with those found earlier in a similar problem for surface waves. A general analysis of the problem is illustrated by a few particular solutions. The results obtained can be of interest for understanding natural phenomena in which internal waves play a significant role.
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