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

Lutz Lesshafft, Brendon Hall, Eckart Meiburg, Benjamin Charles Kneller

Research output: Contribution to journalArticle

9 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)435-458
Number of pages24
JournalJournal of Fluid Mechanics
Volume680
Early online date18 May 2011
DOIs
Publication statusPublished - Aug 2011

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Linear stability analysis
deep water
internal waves
beds
boundary layers
Sediments
sediments
Boundary layers
turbidity
Water
Turbidity
interactions
base flow
stratified flow
Boussinesq approximation
perturbation
fluids
range (extremes)
ducts
Fluids

Keywords

  • internal waves
  • sediment transport
  • geophysical and geological flows

Cite this

Deep-water sediment wave formation : linear stability analysis of coupled flow/bed interaction. / Lesshafft, Lutz; Hall, Brendon; Meiburg, Eckart; Kneller, Benjamin Charles.

In: Journal of Fluid Mechanics, Vol. 680, 08.2011, p. 435-458.

Research output: Contribution to journalArticle

Lesshafft, Lutz ; Hall, Brendon ; Meiburg, Eckart ; Kneller, Benjamin Charles. / Deep-water sediment wave formation : linear stability analysis of coupled flow/bed interaction. In: Journal of Fluid Mechanics. 2011 ; Vol. 680. pp. 435-458.
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AB - 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.

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