Physics – Fluid Dynamics
Scientific paper
2008-04-23
Physics
Fluid Dynamics
8 pages, 7 figures
Scientific paper
In this paper we address the problem which is mathematically reminiscent of the Anderson localization, although is related to a strongly dissipative dynamics. Specifically, we study thermal convection in a thin horizontal porous layer heated from below in the presence of a parametric disorder. Parameters are time-independent, but inhomogeneous in one of the horizontal directions. Under frozen parametric disorder, spatially localized flow patterns appear. We focus our study on their localization properties and the effect of an imposed longitudinal advection on these properties. Our interpretation of the results of the linear theory is underpinned by a numerical simulation for the nonlinear problem. For weak advection leading to upstream delocalization, the transition from a set of localized flow patches to an almost everywhere intense "global" flow occurs moderately below the instability threshold of the disorder-free system. The results presented are relevant for a broad variety of active media where pattern selection occurs.
Goldobin Denis S.
Shklyaeva Elizaveta V.
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