Transient critical-level effect for internal gravity waves in a stably stratified shear flow with thermal forcing

Resonant interactions between triads of internal gravity waves propagating in a shear flow are considered for the case when the stratification and the background shear flow vary slowly with respect to typical wavelengths. If ωn, kn(n = 1, 2, 3) are the local frequencies and wavenumbers respectively then the resonance conditions are that ω1 + ω2 + ω3 = 0 and k1 + k2 + k3 = 0. If the medium is only weakly inhomogeneous, then there is a strong resonance and to leading order the resonance conditions are satisfied globally. The equations governing the wave amplitudes are then well known, and have been extensively discussed in the literature. However, if the medium is strongly inhomogeneous, then there is a weak resonance and the resonance conditions can only be satisfied locally on certain space-time resonance surfaces. The equations governing the wave amplitudes in this case are derived, and discussed briefly. Then the results are applied to a study of the hierarchy of wave interactions which can occur near a critical level, with the aim of determining to what extent a critical layer can reflect wave energy.

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Transient, Linear Dynamics of a Stably Stratified Shear Flow with Thermal Forcing and a Critical Level

Journal of the Atmospheric Sciences ◽

10.1175/1520-0469(1999)056<0483:tldoas>2.0.co;2 ◽

1999 ◽

Vol 56 (4) ◽

pp. 483-499 ◽

Cited By ~ 15

Author(s):

Jong-Jin Baik ◽

Hong-Sub Hwang ◽

Hye-Yeong Chun

Keyword(s):

Shear Flow ◽

Critical Level ◽

Thermal Forcing ◽

Linear Dynamics ◽

Stratified Shear Flow ◽

Stably Stratified Shear Flow

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Resonant wave interactions near a critical level in a stratified shear flow

Journal of Fluid Mechanics ◽

10.1017/s0022112094001461 ◽

1994 ◽

Vol 269 ◽

pp. 1-22 ◽

Cited By ~ 5

Author(s):

R. Grimshaw

Keyword(s):

Shear Flow ◽

Critical Level ◽

Harmonic Component ◽

Internal Gravity Waves ◽

Resonant Interaction ◽

Wave Interactions ◽

Incoming Wave ◽

Resonant Wave ◽

Background Density ◽

Stratified Shear Flow

Resonant interactions between internal gravity waves propagating in a stratified shear flow are considered for the case when the background density and shear flow vary slowly with respect to the waves. In Grimshaw (1988) triad resonances were considered, and interaction equations derived for the case when the resonance conditions are met only on certain space-time surfaces, being resonance sites. Here this analysis is extended to include higher-order resonances, with the aim of studying resonant wave interactions near a critical level. It is shown that a secondary resonant interaction between two incoming waves, in which two harmonic components of one incoming wave interact with a single harmonic component of another incoming wave, produces a reflected wave. This result is shown to agree with the study of Brown & Stewartson (1980, 1982a, b) who obtained this same result by a different approach.

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