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# [HCG27-04] Cyclic steps formed by long-runout turbidity currents

Keywords:cyclic steps, turbidity currents, submarine bedform

Integrating the Reynolds-averaged Navier-Stokes equations and continuity equation over the high concentrated lower layer, we obtain the boundary layer approximated (layer-averaged) momentum and continuity equations. In the integration, it is possible to simplify the governing equations by ignoring the entertainment from the top of the high concentrated lower layer with the assumption that the Reynolds stress becomes almost zero and the shear stress almost vanishes there. In addition to the momentum equations and continuity equation, we employ the diffusion/dispersion equation of suspended sediment, and the continuity equation of sediment (Exner equation).

The unknown variables in the problem are four: the velocity, the layer thickness, the layer-averaged suspended sediment concentration, and the bed elevation. The governing equations are the layer-averaged momentum and continuity equations, the layer-averaged diffusion/dispersion equation of suspended sediment, and the continuity equation of sediment (Exner equation). The boundary conditions for this problem are that the momentum has to be continuous before and after each hydraulic jump. More specifically, the velocity and the layer thickness have to satisfy the jump condition before and after each jump. In addition, the suspended sediment concentration has to be continuous at the jump.

We solve the problem numerically, and obtain the wavelengths of steps. The wavelength of a long-run out turbidity current is determined by the thickness of the high-concentration layer near the bottom. It is shown that the wavelengths obtained in the analysis agree relatively well with the observation.