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A new limiting form for steady periodic gravity waves with surface tension on deep water

机译：A new limiting form for steady periodic gravity waves with surface tension on deep water

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摘要

The method developed by Longuet‐Higgins [J. Inst. Math. Appl.22, 261 (1978)] for the computation of pure gravity waves is extended to capillary‐gravity waves in deep water. Surface tension provides an additional term in the identities between the Fourier coefficients in Stokes’ expansion. This term is then reduced to a simple function of the slope of the local tangent to the profile of the free surface. A set of nonlinear algebraic equations is derived and solved by using the Newton’s method. A new family of limiting profiles of steady gravity waves with surface tension is found. ©1996 American Institute of Physics.

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