Internal Gravity Wave Reflection by a Layered Density Anomaly

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Abstract
Exact solutions are obtained for internal gravity waves incident upon a layered density anomaly embedded in a stably stratified fluid with otherwise constant Brunt-Väisälä frequency:where z increases downward; and N2−∞, N2+∞ and NH2 are parameters. The reflection coefficient is a complicated function of the horizontal and vertical wavenumbers and the parameters related to the Brunt-Väisälä profile. It is found that all wave energy is transmitted through the anomalous layer for waves propagating almost horizontally and a significant amount is reflected for vertically propagating ones, while the validity of a low reflection, WKB description is demonstrated for waves which possess a vertical wave-length much smaller than the scale height σ−1. Further, there can exist for some stratification conditions certain other directions of propagation for which the conditions for energy transfer are more favorable than they are for nearly contiguous angles θ+∞. The transmission “windows” are seen to accumulate—in still more specialized cases—about the point θ+∞=0. The analytical form for N2 is shown to be of value in separating the influences upon the reflection of the various parameters specifying the stability frequency.

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