Dissolution instability and roughening transition

TL;DR

This paper presents a theoretical study of dissolution pattern formation over dissolving beds, linking instability to flow turbulence transition and bed roughness, with implications for natural pattern selection.

Contribution

It introduces a turbulence-based model that explains dissolution instability and pattern wavelength selection related to bed roughness and flow transition.

Findings

Dissolution instability is linked to a turbulence transition anomaly.

Pattern amplitude may be selected by bed roughness effects.

Most unstable wavelength scales with viscous sublayer thickness.

Abstract

We theoretically investigate the pattern formation observed when a fluid flows over a solid substrate that can dissolve or melt. We use a turbulent mixing description that includes the effect of the bed roughness. We show that the dissolution instability at the origin of the pattern is associated with an anomaly at the transition from a laminar to a turbulent hydrodynamic response with respect to the bed elevation. This anomaly, and therefore the instability, disappears when the bed becomes hydrodynamically rough, above a threshold roughness-based Reynolds number. This suggests a possible mechanism for the selection of the pattern amplitude. The most unstable wavelength scales as observed in nature on the thickness of the viscous sublayer, with a multiplicative factor that depends on the dimensionless parameters of the problem.