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

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-Väisäläf r e q u e n c y 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.

TURBINS: An immersed boundary, Navier–Stokes code for the simulation of gravity and turbidity currents interacting with complex topographies

“…It will allow us to explore the complex nonlinear interactions between density-driven flows and such topographical seafloor features as channels, gullies, sediment waves, levees and basins. Specifically, it will enable us to extend recent linear stability analysis investigations of emerging seafloor topography [16,30] into the nonlinear regime. This will help our understanding of the processes governing the formation of large-scale sediment deposits in the deep oceans, which in turn is highly relevant with regard to hydrocarbon exploration.…”

Turbidity currents interacting with three-dimensional seafloor topography

“…Luthi 1981;Bonnecaze, Huppert & Lister 1993;Gladstone, Phillips & Sparks 1998;de Rooij & Dalziel 2001). Currents over flat substrates are also amenable to simplified theoretical approaches, such as box models, shallow-water models and linear stability analyses (Rottman & Simpson 1983;Bonnecaze et al 1993;Dade & Huppert 1995;Hallworth, Hogg & Huppert 1998;Hall, Meiburg & Kneller 2008;Lesshafft et al 2011). In recent years, fully three-dimensional numerical simulations of turbidity currents propagating over flat beds have become feasible as well (e.g.…”

Three‐dimensional seismic analysis of sediment waves and related geomorphological features on a carbonate shelf exposed to large amplitude internal waves, Browse Basin region, Australia

“…Malinverno et al ., ; Wynn et al ., ), or if the turbidite deposits were reworked by other bottom currents in the channels (e.g. Shepard et al ., ), because both processes would result in bedforms of comparable dimensions (Lesshafft et al ., ). The sediment waves on channel B (Fig.…”