Nonlinear Propagation of Wave-Packets on Fluid Interfaces.
Research rept. May-Jul 74,
VIRGINIA POLYTECHNIC INST AND STATE UNIV BLACKSBURG DEPT OF ENGINEERING SCIENCE AND MECHANICS
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The method of multiple scales is used to derive a nonlinear partial differential equation which describes the evolution of two-dimensional wave-packets on the interface of two semi-infinite, incompressible, inviscid fluids of arbitrary densities, taking into account the effect of the surface tension, this equation is used to show that the stability of uniform wavetrains depends on the wavelength, the surface tension, and the density ratio. The results show that gravity waves are unstable for all density ratios except unity, while capillary waves are stable unless the density ratio is below approximately 0.1716. Moreover, the presence of surface tension results in the stabilization of some waves which are otherwise unstable. Author
- Numerical Mathematics
- Fluid Mechanics