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Hydrodynamic-driven morphogenesis of karst draperies: spatio-temporal analysis of the two-dimensional impulse response

Published online by Cambridge University Press:  22 January 2021

Pier Giuseppe Ledda Open the ORCID record for Pier Giuseppe Ledda [Opens in a new window] ,
Gioele Balestra Open the ORCID record for Gioele Balestra [Opens in a new window] ,
Gaétan Lerisson ,
Benoit Scheid Open the ORCID record for Benoit Scheid [Opens in a new window] ,
Matthieu Wyart  and
François Gallaire Open the ORCID record for François Gallaire [Opens in a new window]
Pier Giuseppe Ledda*
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, École Polytechnique Fédérale de Lausanne, LausanneCH-1015, Switzerland
Gioele Balestra
Affiliation:
iPrint Institute, HEIA-FR, HES-SO University of Applied Sciences and Arts Western Switzerland, FribourgCH-1700, Switzerland
Gaétan Lerisson
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, École Polytechnique Fédérale de Lausanne, LausanneCH-1015, Switzerland
Benoit Scheid
Affiliation:
TIPs, Université Libre de Bruxelles, Avenue F.D. Roosevelt 50, 1050Bruxelles, Belgium
Matthieu Wyart
Affiliation:
Physics of Complex Systems Laboratory, École Polytechnique Fédérale de Lausanne, LausanneCH-1015, Switzerland
François Gallaire
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, École Polytechnique Fédérale de Lausanne, LausanneCH-1015, Switzerland
*
†Email address for correspondence: [email protected]
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Abstract

We study the role of hydrodynamic instabilities in the morphogenesis of some typical karst draperies structures encountered in limestone caves. The problem is tackled using the long wave approximation for the fluid film that flows under an inclined substrate, in the presence of substrate variations that grow according to a deposition law. We numerically study the linear and nonlinear evolution of a localized initial perturbation both in the fluid film and on the substrate, i.e. the Green function. A novel approach for the spatio-temporal analysis of two-dimensional signals resulting from linear simulations is introduced, based on the concepts of the Riesz transform and the monogenic signal, the multidimensional complex continuation of a real signal. This method allows for a deeper understanding of the pattern formation. The linear evolution of an initial localized perturbation in the presence of deposition is studied. The deposition linearly selects substrate structures aligned along the streamwise direction, as the spatio-temporal response is advected away. Furthermore, the growth of the initial defect produces a quasi-steady region also characterized by streamwise structures both on the substrate and the fluid film, which is in good agreement with the Green function for a steady defect on the substrate, in the absence of deposition.

JFM classification

Interfacial Flows (free surface): Thin films Instability: Absolute/convective instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 910 , 10 March 2021 , A53
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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