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- W2077593544 abstract "The method of multiple scales is used to examine the slow modulation of a harmonic wave moving over the surface of a two dimensional channel. The flow is assumed inviscid and incompressible, but the basic flow takes the form of an arbitrary shear. The appropriate nonlinear Schrödinger equation is derived with coefficients that depend, in a complicated way, on the shear. It is shown that this equation agrees with previous work for the case of no shear; it also agrees in the long wave limit with the appropriate short wave limit of the Korteweg-de Vries equation, the shear being arbitrary. Finally, it is remarked that the stability of Stokes waves over any shear can be examined by using the results derived here." @default.
- W2077593544 created "2016-06-24" @default.
- W2077593544 date "1976-01-27" @default.
- W2077593544 modified "2023-10-14" @default.
- W2077593544 title "On the modulation of water waves on shear flows" @default.
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- W2077593544 doi "https://doi.org/10.1098/rspa.1976.0015" @default.
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