Oscillatory Motion of a Viscous Fluid in Contact with a Flat Layer of a Porous Medium


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Abstract

Analytical solutions are obtained for two problems of transverse internal waves in a viscous fluid contacting with a flat layer of a fixed porous medium. In the first problem, the waves are considered which are caused by the motion of an infinite flat plate located on the fluid surface and performing harmonic oscillations in its plane. In the second problem, the waves are caused by periodic shear stresses applied to the free surface of the fluid. To describe the fluid motion in the porous medium, the unsteady Brinkman equation is used, and the motion of the fluid outside the porous medium is described by the Navier–Stokes equation. Examples of numerical calculations of the fluid velocity and filtration velocity profiles are presented. The existence of fluid layers with counter-directed velocities is revealed.

About the authors

A. A. Kormilitsin

Evsev’ev Mordovian State Pedagogical Institute

Author for correspondence.
Email: aa.korm@yandex.ru
Russian Federation, Saransk

N. G. Taktarov

Evsev’ev Mordovian State Pedagogical Institute

Email: aa.korm@yandex.ru
Russian Federation, Saransk

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