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Rayleigh Wave–Internal Wave Coupling and Internal Wave Generation above a Model Jet Stream

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  • 1 Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada
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Abstract

Linear theory for modes in a nonuniformly stratified, semi-infinite shear flow demonstrates that Rayleigh waves (stable waves propagating in fluid with spatially varying shear) couple with evanescent internal waves. If the bulk Richardson number (the squared ratio of the buoyancy frequency and shear) lies between 1/4 and 1, the waves have infinite e-folding depth for waves with critical relative horizontal wavenumbers. Fully nonlinear numerical simulations examine the effect of Rayleigh wave–internal wave coupling when the shear layer is localized and is thus Kelvin–Helmholtz unstable. Diagnostics examining profiles of the wave-induced mean flow show that if the bulk Richardson number is of order unity, significant momentum is extracted from a shear layer as a consequence of transport by waves. The work is extended to the study of unstable jet flows and applications of this work for internal wave generation by dynamic instability of the upper flank of the jet stream are discussed.

Corresponding author address: Bruce R. Sutherland, Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2G1, Canada. Email: bruce.sutherland@ualberta.ca

Abstract

Linear theory for modes in a nonuniformly stratified, semi-infinite shear flow demonstrates that Rayleigh waves (stable waves propagating in fluid with spatially varying shear) couple with evanescent internal waves. If the bulk Richardson number (the squared ratio of the buoyancy frequency and shear) lies between 1/4 and 1, the waves have infinite e-folding depth for waves with critical relative horizontal wavenumbers. Fully nonlinear numerical simulations examine the effect of Rayleigh wave–internal wave coupling when the shear layer is localized and is thus Kelvin–Helmholtz unstable. Diagnostics examining profiles of the wave-induced mean flow show that if the bulk Richardson number is of order unity, significant momentum is extracted from a shear layer as a consequence of transport by waves. The work is extended to the study of unstable jet flows and applications of this work for internal wave generation by dynamic instability of the upper flank of the jet stream are discussed.

Corresponding author address: Bruce R. Sutherland, Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2G1, Canada. Email: bruce.sutherland@ualberta.ca

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