Nonlinear interfacial waves in streaming flows

Zakaria, Kadry

doi:10.1090/S0033-569X-09-01122-2

Author: Kadry Zakaria
Journal: Quart. Appl. Math. 67 (2009), 265-281
MSC (2000): Primary 34C15
DOI: https://doi.org/10.1090/S0033-569X-09-01122-2
Published electronically: March 19, 2009
MathSciNet review: 2514635
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Abstract: The nonlinear interfacial waves between viscous immiscible liquids have been analyzed, using the concepts of viscous potential flow and Kelvin-Helmholtz instability. The method of multiple scales is used for determining the evolution equations that are near and on the marginal state of the linear theory. We use the modulation concept in solving these equations to determine the stability criteria. Different numerical examples are considered that show the system is at greater risk of instability when the velocity of the stream is larger, whereas the effects of viscosity can be stabilizing or destabilizing.

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