Linear and weakly nonlinear analysis of shallow mixing layers with free surface is performed in the present paper. It is assumed that the resistance force is not constant in the transverse direction of the flow. Linear stability problem is solved numerically for different values of the parameters of the problem. Assuming that the bed friction number is slightly smaller than the critical value we derive an amplitude evolution equation for the most unstable mode. It is shown that the amplitude equation is the complex Schrödinger equation.


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    Title :

    Stability of shallow flows: A weakly nonlinear approach



    Conference:

    ICNPAA 2016 WORLD CONGRESS: 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences ; 2016 ; La Rochelle, France


    Published in:

    Publication date :

    2017-01-27


    Size :

    7 pages





    Type of media :

    Conference paper


    Type of material :

    Electronic Resource


    Language :

    English



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