The linear stability of an erodible sediment bed beneath a turbidity current is analyzed based on the Navier-Stokes equations, in order to identify potential mechanisms responsible for the formation of longitudinal gullies and channels. The analysis shows that 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.

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 Peclet 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 250-2,500m, 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.