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Dispersion relations for steady periodic water waves of fixed mean-depth with two rotational layers

  • * Corresponding author: Calin Iulian Martin

    * Corresponding author: Calin Iulian Martin 

C. I. Martin acknowledges the support of the Science Foundation Ireland (SFI)–research grant 13/CDA/2117 and the support of the Austrian Science Fund (FWF)–research grant P 30878-N32. A. Rodríguez-Sanjurjo acknowledges the support of the Science Foundation Ireland (SFI)–research grant 13/CDA/2117

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  • The aim of this paper is to obtain the dispersion relation for small-amplitude periodic travelling water waves propagating over a flat bed with a specified mean depth under the presence of a discontinuous piecewise constant vorticity. An analysis of the dispersion relation for a model with two rotational layers each having a non-zero constant vorticity is presented. Moreover, we present a stability result for the bifurcation inducing laminar flow solutions.

    Mathematics Subject Classification: Primary: 35Q31, 35Q35; Secondary: 74J15, 74J30, 76B15, 76E05.


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  • Figure 1.  Sketch of the graph of the polynomial providing the dispersion relation for two negative vorticities under the condition (44). The root x01 does not satisfy the non-stagnation condition while the root x02 verifies it if and only if (47) is assumed

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