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The hydrodynamic genesis of linear karren patterns

Published online by Cambridge University Press:  26 February 2021

M.B. Bertagni Open the ORCID record for M.B. Bertagni [Opens in a new window]  and
C. Camporeale Open the ORCID record for C. Camporeale [Opens in a new window]
M.B. Bertagni*
Affiliation:
The High Meadows Environmental Institute, Princeton University, Princeton, NJ08544, USA
C. Camporeale
Affiliation:
Department of Land, Infrastructure and Environmental Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10124Torino, Italy
*
†Email address for correspondence: matteobb@princeton.edu
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Abstract

In karst and alpine areas, the interactions between water and rocks give rise to a large variety of marvellous patterns. In this work, we provide a hydrodynamic model for the formation of dissolutional patterns made of parallel longitudinal channels, commonly referred to as linear karren forms. The model addresses a laminar film of water flowing on a rock that is dissolving. The results show that a transverse instability of the water–rock system leads to a longitudinal channelization responsible for the pattern formation. The instability arises because of a positive feedback within the channels between the higher water flow and the enhanced chemical dissolution. The spatial scales predicted by the linear stability analysis span different orders of magnitude depending on the Reynolds number. This may explain why similar patterns of different sizes are observed on natural rocks. Results also show that the rock solubility affects just the temporal scale of the instability and the rock inclination plays a minor role in the pattern formation. It is eventually discussed how rain is not strictly necessary for the appearance of linear karren patterns, but it may affect some of their features.

JFM classification

Interfacial Flows (free surface): Thin films Nonlinear Dynamical Systems: Pattern formation Phase change: Morphological instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 913 , 25 April 2021 , A34
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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