This article is cited in 1 paper

Propagation of perturbations in a thin layer of a fluid with viscosity stratification

P. V. Kovtunenko<sup>ab

a</sup> Novosibirsk State University
^b Lavrentyev Institute of Hydrodynamics of Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: We consider a non-linear system of equations describing motion of a viscosity-layered fluid with a free surface in a long-wave approximation. In a semi-Lagrangian coordinate system we rewrite the governing equations in a integro-differencial form for which the necessary and sufficient hyperbolicity conditions are stated. An approximation for the integro-differential model in a form of finite-dimensional system of differential conservation laws with a right part is suggested. A modeling of propagation of nonlinear perturbations in a fluid with viscosity stratification was performed. In particular a problem about the evolution of a more viscous fluid column in a less viscous fluid during the passage of wave disturbances is considered.

Keywords: long waves, layered flows, viscous fluid, integro-differential equations.

UDC: 517.957+532.526

Received: 17.12.2014

DOI: 10.17377/PAM.2015.15.203

 English version: Journal of Mathematical Sciences, 2016, 215:4, 499–509