Submarine channel and sediment wave formation by turbidity currents: Navier-Stokes based linear stability analysis

Turbidity currents are a primary sediment transport mechanism on the continental shelf and down the continental slope. They play an important role in the evolution of seafloor morphology. Two linear stability analyses have been performed that investigate the ability of turbidity currents to generate two types of deep water bedforms: longitudinal submarine channels and transverse sediment waves. Based on the 2 & 3D Boussinesq Navier-Stokes equations, the models account for the coupled interaction of the fluid and particle motion inside the current with the erodible bed below. In both cases, for instability to occur, the suspended sediment concentration of the base flow needs to decay more slowly away from the sediment bed 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, so that it will keep growing.;For the case of submarine channels, 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 numbers, and destabilizing for large values. For a representative current height of O(10-100m), the linear stability analysis provides a most amplified wavelength in the range of 250-2,500 m, which is consistent with field observations reported in the literature.;The sediment wave analysis shows that base flow provides the destablizing effect and a phase shift exists between perturbations of the bed, sediment concentration and shear. This results in the shear perturbation reaching a maximum on the downstream flank of the sediment wave, causing the resulting bedform to migrate upstream. For subcritical flow (Fr < 1) multiple unstable modes appear. It is shown that these unstable modes correspond to stationary internal lee waves, which have previously been argued to play a role in the formation of sediment waves. The analysis predicts a most amplified wavelength of six times the current height, which is consistent with the literature.