Free-surface flow of hyperconcentrations

A mixture of fluid and solid particles with high sediment concentration (hyperconcentration) is described by a non-Newtonian rheological model incorporating the yield stress, a linear (viscous) stress, and a quadratic (turbulent-dispersive) term. Unsteady flow of hyperconcentration down an inclined plane is studied: first the set of equations governing the flow are derived, then velocity profiles for steady uniform motion are illustrated. The solution for unsteady state flow is obtained in term of permanent waves; their speed is derived and the possible surface profiles are illustrated as functions of a dimensionless parameter describing the relative importance of the linear and quadratic term. When the viscous stress overwhelms the turbulent-dispersive one, earlier relations for a Bingham fluid are recovered. It is shown that more types of gravity currents are possible than in a Newtonian fluid; these include some cases of permanent waves propagating up a slope.