Cyclic steps and roll waves in shallow water flow over an erodible bed

  title={Cyclic steps and roll waves in shallow water flow over an erodible bed},
  author={Neil J. Balmforth and Ali Vakil},
  journal={Journal of Fluid Mechanics},
  pages={35 - 62}
Abstract The St Venant equations in conjunction with a phenomenological law for erosion are used to explore the nonlinear dynamics of cyclic steps – linearly unstable bedform patterns which emerge when uniform flow over an erodible bed becomes supercritical. The instability saturates by blocking the overlying flow and creating hydraulic jumps just downstream of the steepest part of the steps. Near onset, steadily migrating, nonlinear step patterns are constructed and shown to suffer a short… 
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