Localization and advectional spreading of convective currents under parametric disorder

Abstract

We address a problem which is mathematically reminiscent of the one of Anderson localization, although it is related to a strongly dissipative dynamics. Specifically, we study thermal convection in a horizontal porous layer heated from below in the presence of a parametric disorder; physical parameters of the layer are time-independent and randomly inhomogeneous in one of the horizontal directions. Under such a frozen parametric disorder, spatially localized flow patterns appear. We focus our study on their localization properties and the effect of an imposed advection along the layer on these properties. Our interpretation of the results of the linear theory is underpinned by numerical simulation for the nonlinear problem. Weak advection is found to lead to an upstream delocalization of localized current patterns. Due to this delocalization, the transition from a set of localized patterns to an almost everywhere intense "global" flow can be observed under conditions where the disorder-free system would be not far below the instability threshold. The results presented are derived for a physical system which is mathematically described by a modified Kuramoto-Sivashinsky equation and therefore they are expected to be relevant for a broad variety of dissipative media where pattern selection occurs.

19 pages, 8 figures

References in corpus (8)

• Destruction of Anderson localization by a weak nonlinearity
• Energy Spreading in Strongly Nonlinear Disordered Lattices
• Scaling properties of energy spreading in nonlinear Hamiltonian two-dimensional lattices
• Large-Scale Thermal Convection in a Horizontal Porous Layer
• Implications of Intermediate Mass Black Hole in globular cluster G1 on Dark Matter detection
• Diffusion of a passive scalar by convective flows under parametric disorder
• Advectional enhancement of eddy diffusivity under parametric disorder
• Re-localization due to finite response times in a nonlinear Anderson chain

Cited by in corpus (7)

• Large-Scale Thermal Convection in a Horizontal Porous Layer
• Diffusion of a passive scalar by convective flows under parametric disorder
• Advectional enhancement of eddy diffusivity under parametric disorder
• High-Order Schemes of Exponential Time Differencing for Stiff Systems with Nondiagonal Linear Part
• Two scenarios of advective washing-out of localized convective patterns under frozen parametric disorder
• Noise Can Reduce Disorder in Chaotic Dynamics
• Stochastic parametric excitation of convective heat transfer