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Energy Method for the Analysis of Stability of Shallow Water Flows

Author(s): M. S. Ghidaoui; A. A. Kolyshkin; M. Y. Lam

Linked Author(s): Mohamed S. Ghidaoui

Keywords: No Keywords

Abstract: A sufficient condition for linear stability of shallow flows is proposed in the present paper. The estimate is derived from the linearized energy equation under some simplifying assumptions and does not depend (in explicit form) on characteristics of base flow profile. It depends only on the Froude number of the flow. In order to analyze the accuracy of the proposed estimate linear stability characteristics of two base flow profiles (wake flow and mixing layer) are calculated. The critical value of the bed friction number obtained from the linearized energy equation is found to be exactly the same as the calculated value from the linear stability theory for both base flow velocity profiles. In the limit where there is no shear layer, the criterion governs the stability of gravity waves and recovers the classical condition which states that gravity waves are unstable when Froude number exceeds 2 if friction is represented by the Chezy equation. In addition, outside the shear layer, the criterion shows that the flow is stable if Froude number is less than 2. This analytical result agrees with previous linear stability calculations.


Year: 2009

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