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Deep-water sediment wave formation: linear stability analysis of coupled flow/bed interaction

Published online by Cambridge University Press:  18 May 2011

L. LESSHAFFT ,
B. HALL ,
E. MEIBURG  and
B. KNELLER
L. LESSHAFFT
Affiliation:
Laboratoire d'Hydrodynamique, CNRS – École Polytechnique, 91128 Palaiseau, France Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA
B. HALL
Affiliation:
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA
E. MEIBURG*
Affiliation:
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA
B. KNELLER
Affiliation:
Department of Geology and Petroleum Geology, University of Aberdeen, Aberdeen AB24 3FX, UK
*
†Email address for correspondence: meiburg@engineering.ucsb.edu
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Abstract

A linear stability analysis is carried out for the interaction of an erodible sediment bed with a sediment-laden, stratified flow above the bed, such as a turbidity or bottom current. The fluid motion is described by the full, two-dimensional Navier–Stokes equations in the Boussinesq approximation, while erosion is modelled as a diffusive flux of particles from the bed into the fluid. The stability analysis shows the existence of both Tollmien–Schlichting and internal wave modes in the stratified boundary layer. For the internal wave mode, the stratified boundary layer acts as a wave duct, whose height can be determined analytically from the Brunt–Väisälä frequency criterion. Consistent with this criterion, distinct unstable perturbation wavenumber regimes exist for the internal wave mode, which are associated with different numbers of pressure extrema in the wall-normal direction. For representative turbidity current parameters, the analysis predicts unstable wavelengths that are consistent with field observations. As a key condition for instability to occur, the base flow velocity boundary layer needs to be thinner than the corresponding concentration boundary layer. For most of the unstable wavenumber ranges, the phase relations between the sediment bed deformation and the associated wall shear stress and concentration perturbations are such that the sediment waves migrate in the upstream direction, which again is consistent with field observations.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Sediment transport

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Type
Papers
Information
Journal of Fluid Mechanics , Volume 680 , 10 August 2011 , pp. 435 - 458
Copyright
Copyright © Cambridge University Press 2011

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