Asymptotic expansions for steady periodic water waves in flows with constant vorticity |
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| Affiliation: | 1. Dpto. de Matemática Aplicada, Universidade de Santiago de Compostela, Campus Sur s/n, 15782 Santiago de Compostela, Spain;2. Dpto. de Estadística e Investigación Operativa, Universidade de Santiago de Compostela, Campus Sur s/n, 15782 Santiago de Compostela, Spain;1. Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, China;2. Faculty of Information Technology, Macau University of Science and Technology, Macau |
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| Abstract: | We provide high-order approximations to periodic travelling wave profiles, through a novel expansion which incorporates the variation of the total mechanical energy of the water wave. We show that these approximations are extended to any finite order. Moreover, we provide the velocity field and the pressure beneath the waves, in flows with constant vorticity over a flat bed. |
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| Keywords: | Travelling water waves Vorticity Velocity field Pressure |
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