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Linear Stability of Long Waves in Two-layer Channel Flow

Mark J. McCready
Organization: University of Notre Dame
Department: Department of Chemical Engineering
URL: http://www.nd.edu/~mjm
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This notebook solves the longwave stability problem for two-layer, pressure driven channel flow. Through this example, the method for using a regular perturbation technique to solve a differential eigenvalue problem, with boundary conditions, is demonstrated.

References: C. -S Yih (1967) "Instability due to viscosity stratification", J. Fluid Mech., 27 pp 337-352. S. G. Yiantsios and B. G. Higgins (1988) "Linear stability of plane Poiseullie flow of two-superposed fluids", Phys. Fluids, 31 pp 3225-3238.

The zeroth and first order terms for the wave velocity for a pressure driven channel flow are obtained from a long wave expansion. All of the necessary manipulations are shown for this direct perturbation solution method.

*Science > Physics > Fluid Mechanics

hydrodynamic stability, multifluid flow, gas-liquid flow, multiphase flow, interfacial waves
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longwave.nb (274.3 KB) - Mathematica notebook