On Surface Gravity Waves in Heterogeneous Shear Flows.
FLORIDA STATE UNIV TALLAHASSEE
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Two-dimensional surface waves in a stable stratified, inviscid and incompressible fluid, in which the mean flow varies only with depth, are studied. The vertical characteristic wavelength of these waves is assumed small compared to the characteristic scale-length of the fluid so that a geometric optics approximation yields a systematic expansion. Asymptotic results are obtained by the related W.K.B.J. method. In the absence of a critical level, at which the horizontal phase velocity relative to the mean flow vanishes, only discrete surface gravity wave mades exist. Each mode is reflected internally at a turning level as if a horizontal bottom exists. In contrast, continuous spectra of surface wave modes associated with the existence of critical levels are not affected by horizontal boundaries below their respective critical levels. Author
- Fluid Mechanics