Improved bounds on linear instability of barotropic zonal flow within the shallow water equations |
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| Authors: | AD Clark IH Herron |
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| Institution: | 1. Laboratory for Physical Sciences , University of Maryland , College Park , MD 20740 , USA;2. Department of Mathematical Sciences , Rensselaer Polytechnic Institute , Troy , NY 12180 , USA antwan@lps.umd.edu;4. Department of Mathematical Sciences , Rensselaer Polytechnic Institute , Troy , NY 12180 , USA |
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| Abstract: | Here we develop mathematical results to describe the location of linear instability of a parallel mean flow within the framework of the shallow water equations; growth estimates of near neutral modes (for disturbances subcritical with respect to gravity wave speed) in the cases of non-rotating and rotating shallow water. The bottom topography is taken to be one-dimensional and the isobaths are parallel to the mean flow. In the case of a rotating fluid, the isobaths and the mean flow are assumed to be zonal. The flow is front-like: there is a monotonic increase of mean flow velocity. Our results show that for barotropic flows the location of instabilities will be a semi-ellipse region in the complex wave velocity plane, that is based on the wave-number, Froude number, and depth of the fluid layer. We also explore the instability region for the case of spatially unbounded mean velocity profiles for non-rotating shallow water. |
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| Keywords: | Barotropic Instability Shallow water |
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