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Shear-induced instabilities of flows through submerged vegetation

Published online by Cambridge University Press:  23 March 2020

Clint Y. H. Wong Open the ORCID record for Clint Y. H. Wong [Opens in a new window] ,
Philippe H. Trinh Open the ORCID record for Philippe H. Trinh [Opens in a new window]  and
S. Jonathan Chapman Open the ORCID record for S. Jonathan Chapman [Opens in a new window]
Clint Y. H. Wong*
Affiliation:
Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, OxfordOX2 6GG, UK
Philippe H. Trinh
Affiliation:
Department of Mathematical Sciences, University of Bath, BathBA2 7AY, UK
S. Jonathan Chapman
Affiliation:
Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, OxfordOX2 6GG, UK
*
†Email address for correspondence: clint.wong@maths.ox.ac.uk
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Abstract

We consider the instabilities of flows through a submerged canopy and show how the full governing equations of the fluid–structure interactions can be reduced to a compact framework that captures many key features of vegetative flow. First, by modelling the canopy as a collection of homogeneous elastic beams, we predict the steady configuration of the plants in response to a unidirectional flow. This treatment couples the beam equations in the canopy to the fluid momentum equations. Subsequently, a linear stability analysis suggests new insights into the development of instabilities at the surface of the vegetative region. In particular, we show that shear at the top of the canopy is a dominant factor in determining the onset of instabilities known as monami. Based on numerical and asymptotic analysis of the quadratic eigenvalue problem, the system is shown to be stable if the canopy is sufficiently sparse.

JFM classification

Geophysical and Geological Flows: Coastal engineering Wakes/Jets: Shear layers Instability: Absolute/convective instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 891 , 25 May 2020 , A17
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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