Vladimir Kozlov, Nikolay Kuznetsov
The two-dimensional free-boundary problem of steady periodic waves with vorticity is considered for water of finite depth. We investigate how a flow with small-amplitude Stokes waves on the free surface bifurcates from a horizontal parallel shear flow in which counter-currents may be present. The bifurcation mechanism is described in terms of a dispersion equation; namely, wavelengths of Stokes waves bifurcate from the values defined by the roots of this equation. The latter generalizes that for irrotational waves and involves only quantities given on the horizontal free surface of the initial parallel shear flow. Sufficient conditions guaranteeing the existence of roots of the dispersion equation are obtained. Two particular vorticity distributions are considered in order to illustrate general results.
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http://arxiv.org/abs/1207.5181
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