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Internal Wave Tunnelling Through Non-uniformly Stratified Shear Flow (2006)
| Citations: | 3 - 0 self |
BibTeX
@MISC{Brown06internalwave,
author = {G. L. Brown and B. R. Sutherl},
title = {Internal Wave Tunnelling Through Non-uniformly Stratified Shear Flow},
year = {2006}
}
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Abstract
ABSTRACT We examine the transmission of internal gravity waves through a non-uniformly stratified fluid with vertically varying background shear. To quantify wave transmission we show that the appropriate measure is the ratio of the flux of transmitted to incident pseudoenergy, T. We derive an analytic prediction of T for the trans-mission of waves through a piecewise-linear shear flow in two cases. In both, the fluid is unstratified over the depth of the shear and uniformly stratified elsewhere. In one study, the density profile is continuous. Such a basic state is unstable but with vanishingly small growth rate as the bulk Richardson number, Ri, becomes large. In the limit of an infinitely large Richardson number (no shear), we recover the tunnelling prediction of Sutherland and Yewchuk (2004). In weak shear, incident waves can transmit weakly, even if the phase speed matches the flow speed within the shear layer (a critical level). However, no transmission occurs when the phase speed of incident waves exactly matches the flow speed on the opposite flank of the shear. In strong shear, with Ri 1, a transmission peak occurs where the incident wavenum-ber and frequency are close to, but different from, those associated with unstable modes. In a second study, the background density profile is discontinuous and representative of a well-mixed patch within a once uniformly stratified fluid. In this case, no transmission occurs for incident waves with phase speed matching the speed of the flow within the shear layer. However, a transmission spike occurs if the incident waves
Keyphrases
incident wave phase speed internal wave tunnelling non-uniformly stratified shear flow shear layer flow speed density profile appropriate measure basic state weak shear well-mixed patch analytic prediction non-uniformly stratified fluid critical level bulk richardson number infinitely large richardson number transmission peak incident wavenum-ber opposite flank internal gravity wave piecewise-linear shear flow background shear small growth rate wave transmission second study tunnelling prediction transmission spike strong shear unstable mode background density profile
