Nonlinear wave modelling on the surface of a two-phase mixture

About the authors:

Barinov V. A, Associate Professor, Mathematical Modeling Department, Cand. Phys. and Math. Sci., Tyumen State University
Konstantin Yu. Basinsky, Cand. Sci. (Phys.-Math.), Associate Professor, Department of Fundamental Mathematics and Mechanics, University of Tyumen; k.y.basinskij@utmn.ru

Abstract:

The paper discusses a nonlinear boundary value problem of wave propagation on the free surface of a two-phase (disperse) mixture. To solve the problem, a method of time-variant frequency is applied, which was devised for the solution of nonlinear wave problems with dissipation. A solution has been found to a third order approximation using a small-amplitude parameter. Nonlinear wave frequency and near-surface Stokes flow rate have been defined. They are time functions depending on the wave length and elevation (as in the classical case) and on the dispersed phase concentration. Nonlinear paths of carrier and dispersed phase particles have been found. Basing on the obtained expression for the dispersed particles paths, the nonlinear effect has been described: in wave motion dispersed particles that are heavier than carrier phase particles float, while lighter particles sink.

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