Methods and Applications of Analysis
Volume 14 (2007)
An Asymptotic Analysis of Linear Interfacial Motion
Pages: 1 – 14
In this paper, we perform an asymptotic study on slightly viscous flows between two immiscible incompressible fluids. The motion is governed by linearized Navier-Stokes equations together with interfacial conditions. A second-order asymptotic expansion with respect to viscosity is obtained by using the method of multiple scales. In particular, viscous decay rate for the interfacial wave amplitude and viscous correction for the phase speed are explicitly identified.
Navier-Stokes equations; interfacial motion; asymptotic expansion; multiple scales
2010 Mathematics Subject Classification