Frictional effect on stability of discontinuity interface in tangential velocity of a shallow-water flow |
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Authors: | Liangbing Jin Lê Thị Thái Yasuhide Fukumoto |
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Affiliation: | 1. Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang Province 321004, PR China;2. Graduate School of Mathematics, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan;3. Institute of Mathematics for Industry, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan |
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Abstract: | We examine a frictional effect on the linear stability of an interface of discontinuity in tangential velocity. The fluid is moving with uniform velocity U in a region but is at rest in the other, and the bottom surface is assumed to exert drag force, quadratic in velocity, on the thin fluid layer. In the absence of the drag, the instability of the Kelvin-Helmholtz type is suppressed for , with c being the propagating speed of the gravity wave. We find by asymptotic analyses for both small and large values of the drag strength that the drag, regardless of its strength, makes the flow unstable for the whole range of the Froude number . |
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Keywords: | Corresponding author. Kelvin-Helmholtz instability Shallow water Gravity waves Drag Dissipation induced instability |
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