Transformation of internal waves over an uneven bottom: Analytical results

The transformation of internal waves over the oceanic shelf of variable depth is studied analytically within a linear theory of a two-layer flow. It is shown that, at a specific character of depth variation, the internal wave propagates without reflection from the slope even if it is sufficiently steep. The properties of such progressive waves are studied—their form and the current structure in the upper and lower layers. The transformation of the wave propagating from the open ocean, where the depth is assumed to be constant, is considered. It is shown that the wave is transformed at the shelf edge and does not change its form in the course of time during its further propagation over the shelf. The height and form of the internal wave are calculated at the interface of the transition of the two-layer flow into the one-layer flow. Applications of the developed analytical theory to the estimation of internal wave transformation over a real shelf are discussed.