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An asymptotic approach to the crenulation instability

Published online by Cambridge University Press:  09 August 2017

Carlo Camporeale Open the ORCID record for Carlo Camporeale [Opens in a new window]
Carlo Camporeale*
Affiliation:
Department of Environment, Land and Infrastructure Engineering, Politecnico di Torino, Torino 10129, Italy
*
†Email address for correspondence: carlo.camporeale@polito.it
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Abstract

A novel linear stability analysis for the pattern formation of ripple-like corrugations, over the surface of stalactites due to calcite-laden falling films, is presented by using a modified version of the gradient expansion technique. A fully analytical theory combining thin film hydrodynamics, Kármán–Pohlhausen solution of the advection–diffusion equation for calcium concentration and an evolution equation for the shape of the liquid–solid interface is developed. Analytical formulas for the selected wavelength and the corresponding phase velocity are provided, which match previous numerical solutions. The obtained easy-to-use mathematical results have a potential for developing a novel set of paleo-reconstruction proxies based on the link between morphological patterns and paleo-flows.

JFM classification

Instability: Absolute/convective instability Phase change: Morphological instability Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 826 , 10 September 2017 , pp. 636 - 652
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Copyright
© 2017 Cambridge University Press 

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