Quasi-exact solution of the Riemann problem for generalised dam-break over a mobile initially flat bed

Abstract

This paper investigates dam-break problems with flows on one or two sides of zero or nonzero velocities over a mobile initially flat bed, and quasi-exact solutions are presented by solving the Riemann problems using the simple wave theory. The flow structures after dam collapse for nonzero velocities are much richer than those for zero velocities on both sides, although they are also a combination of waves of different characteristic families, which are consistent with Lax [CBMS-Regional Conference Series in Applied Mathematics, SIAM, 1973]. The wave can be a rarefaction, a shock, or a combination of a rarefaction and a semi-characteristic shock. The semi-characteristic shock is related to the morphodynamic characteristics. The relationship between morphodynamic and hydrodynamic characteristics is illustrated, along with types of waves (shock, rarefaction or a combination of these), and sediment convergence and type of characteristic. It is shown that the types of waves that may occur in the Riemann solution, and, in some cases, their possible approximate locations, can be determined prior to the construction of the Riemann solution itself. The Riemann solution presented here can be used to study shock–shock interactions.