NVESTIGATION OF THE STABILITY OF THE POTENTIAL FLUID FLOW IN A POROUS MEDIUM WITH VARIABLE TRANSVERSE DIFFUSION COEFFICIENT

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Abstract


We have considered the potential fluid flow in porous medium taking into account variable diffusion coefficient in the tube of radius . The flow is supposed to be cylindrically-symmetric. The velocity has two components: ⃗ =(,0,). The Euler equation has in the right hand side the term which determines Darcy force: ⃗ = −⃗, where - inverse Darcy coefficient. Continuity equation has the term which describes transverse diffusion of flowing fluid. We have established that for Euler equations system the equality 2/ ≡ 2/ is fulfilled identically. It means that Euler equations system is compatible and integrable. For (,) we have obtained Bessel equation, for (,) - the equation with diffusion coefficient (). We have investigated the solution of the equation for (,) with three types of diffusion coefficient (). We have established that in all cases the equation has unstable solution.

Yu P Rybakov

Peoples’ Friendship University of Russia

Email: soliton4@mail.ru
Department of Theoretical Physics and Mechanics

O D Sviridova

Peoples’ Friendship University of Russia

Email: oksanasviridova@yandex.ru
Department of Theoretical Physics and Mechanics

G N Shikin

Peoples’ Friendship University of Russia

Department of Theoretical Physics and Mechanics

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Copyright (c) 2014 Рыбаков Ю.П., Свиридова О.Д., Шикин Г.Н.

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