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A theoretical remark about waves on a static water surface beneath a layer of moving air. (English) Zbl 0712.76024

Summary: I. H. Grundy and E. O. Tuck [J. Fluid Mech., 178, 441-457 (1987; Zbl 0633.76018)] treat the problem of large-amplitude waves on an air-water interface where the air is a steady nonuniform flow and the water is stationary. They computed both periodic nonlinear Stokes-like waves far downstream and a configuration of the water surface from the edge region of a hovercraft. However, there is no work that treats the existence of such Stokes-like waves theoretically. The present work aims to prove the existence of such solutions in the case where the cushion pressure is low, that is, the depression \(h_ 0\) at the upstream stagnation point from the mean water level is small.

MSC:

76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76B60 Atmospheric waves (MSC2010)
76T99 Multiphase and multicomponent flows
35Q30 Navier-Stokes equations

Citations:

Zbl 0633.76018
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