Channel formation by turbidity currents: Navier–Stokes-based linear stability analysis

Abstract

The linear stability of an erodible sediment bed beneath a turbidity current is analysed, in order to identify potential mechanisms responsible for the formation of longitudinal gullies and channels. On the basis of the three-dimensional Navier–Stokes equations, the stability analysis accounts for the coupled interaction of the three-dimensional fluid and particle motion inside the current with the erodible bed below it. For instability to occur, the suspended sediment concentration of the base flow needs to decay away from the sediment bed more slowly than does the shear stress inside the current. Under such conditions, an upward protrusion of the sediment bed will find itself in an environment where erosion decays more quickly than sedimentation, and so it will keep increasing. Conversely, a local valley in the sediment bed will see erosion increase more strongly than sedimentation, which again will amplify the initial perturbation.The destabilizing effect of the base flow is modulated by the stabilizing perturbation of the suspended sediment concentration and by the shear stress due to a secondary flow structure in the form of counter-rotating streamwise vortices. These streamwise vortices are stabilizing for small Reynolds and Péclet numbers and destabilizing for large values.For a representative current height of O(10–100m), the linear stability analysis provides the most amplified wavelength in the range of 250–2500m, which is consistent with field observations reported in the literature. In contrast to previous analyses based on depth-averaged equations, the instability mechanism identified here does not require any assumptions about sub- or supercritical flow, nor does it require the presence of a slope or a slope break.

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

“…Flow equations The model for the interaction of a turbidity current, or correspondingly, a bottom current, with an erodible bed follows the approach introduced by Hall, Meiburg & Kneller (2008), who described a linear instability mechanism for the formation of submarine channels. The two-dimensional Navier-Stokes equations are written in the Boussinesq approximation, which presumes moderate density differences (<O(10)%) between particle-laden and clear fluid.…”

“…It is assumed that sediment in the turbidity current is predominantly transported as suspended load, due to high wall shear, whereas the effects of bedload are not accounted for in the present model. Following Hall et al (2008), the interface elevation is taken to evolve according to…”

“…Non-dimensionalisation and choice of parameters The governing equations are rendered dimensionless with respect to a diffusive length scale l = D/w s , the outer flow velocity u ∞ and the fluid density ρ f . The concentration c already represents a non-dimensional volume fraction, and, in contrast to Hall et al (2008), is not renormalized in the present framework.…”

“…Parameter values identical to those used in Hall et al (2008) are considered as a standard configuration in the present analysis. These values were estimated from experimental literature: Fildani et al (2006) describe characteristic property values of flow-stripped turbidity currents with u ∞ =5ms −1 .…”

“…In contrast to previous studies that focused on bedload transport, the present analysis aims to elucidate the role of suspended sediment in generating density variations which, in turn, can support the existence of internal waves. The analytical approach corresponds to the one taken by Hall et al (2008) for investigating the formation of streamwise channels and gullies. While the base flow profiles employed here pertain to turbidity currents, corresponding profiles for bottom currents could easily be substituted.…”