A complex-analytic approach to kinetic energy properties of irrotational traveling water waves. (English) Zbl 1494.76012
Summary: Relying on conformal mappings we prove the logarithmic convexity of certain flow quantities associated with irrotational periodic travelling waves that propagate at the surface of water over a flat bed. These results enable us to quantify the observation that the kinetic energy and the time-period of the particle paths are larger near the surface and reduce with increasing depth.
MSC:
| 76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |
| 76M40 | Complex variables methods applied to problems in fluid mechanics |
Keywords:
irrotational periodic travelling wave; streamline time-period; total kinetic energy; conformal mapping; logarithmic convexityReferences:
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