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Internal Gravity Wave Reflection by a Layered Density Anomaly

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  • 1 Ocean Sciences Division, Naval Research Laboratory, Washington, D. C. 20375
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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.

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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