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Dissolution instability and roughening transition

Published online by Cambridge University Press:  26 October 2017

Philippe Claudin*
Affiliation:
Physique et Mécanique des Milieux Hétérogènes, UMR 7636 ESPCI – CNRS – Univ. Paris-Diderot – Univ. P. M. Curie, 10 rue Vauquelin, 75005 Paris, France
Orencio Durán
Affiliation:
Department of Ocean Engineering, Texas A & M University, College Station, TX 77843-3136, USA
Bruno Andreotti
Affiliation:
Laboratoire de Physique Statistique, UMR 8550 Ecole Normale Supérieure – CNRS – Univ. Paris-Diderot – Univ. P. M. Curie, 24 rue Lhomond, 75005 Paris, France
*
Email address for correspondence: philippe.claudin@espci.fr

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.

Type
Rapids
Copyright
© 2017 Cambridge University Press 

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