Diffusion of a passive scalar by convective flows under parametric disorder

TL;DR

This paper investigates how convective flows in a porous layer with random inhomogeneities influence the transport of a passive scalar, revealing localization effects and transitions to global flow regimes through numerical and analytical methods.

Contribution

It introduces a combined numerical and analytical study of scalar transport in disordered convective flows, highlighting localization phenomena and flow transition mechanisms.

Findings

Localized flow patterns occur below the instability threshold due to disorder.

Effective diffusivity indicates a transition from localized to global flow.

Numerical results align well with analytical predictions for small diffusivity.

Abstract

We study transport of a weakly diffusive pollutant (a passive scalar) by thermoconvective flow in a fluid-saturated horizontal porous layer heated from below under frozen parametric disorder. In the presence of disorder (random frozen inhomogeneities of the heating or of macroscopic properties of the porous matrix), spatially localized flow patterns appear below the convective instability threshold of the system without disorder. Thermoconvective flows crucially effect the transport of a pollutant along the layer, especially when its molecular diffusion is weak. The effective (or eddy) diffusivity also allows to observe the transition from a set of localized currents to an almost everywhere intense "global" flow. We present results of numerical calculation of the effective diffusivity and discuss them in the context of localization of fluid currents and the transition to a "global" flow. Our numerical findings are in a good agreement with the analytical theory we develop for the limit of a small molecular diffusivity and sparse domains of localized currents. Though the results are obtained for a specific physical system, they are relevant for a broad variety of fluid dynamical systems.