The effect of suspended sediment on the modification of individual dunes in unsteady channel flow is analyzed. The model is an extension of that developed by Fredsøe (1979), in which the change of the dune dimensions was analyzed assuming that the transport of sediment mainly occurs as bed load. By including suspended sediment, it is possible to describe dune behaviour at high sediment transport rates, for which the dunes are washed out, so the bed at sufficiently high bed shear stress becomes plane. The model is compared with laboratory experiments and the agreement is reasonable. The effect of temperature variations on dune dimensions is incorporated in the analysis.

The experimental results of Saffman & Taylor (1958) and Pitts (1980) on fingering in a Hele Shaw cell are modelled by two-dimensional potential flow with surface-tension effects included at the interface. Using free streamline techniques, the shape of the free surface is expressed as the solution of a nonlinear integro-differential equation. The equation is solved numerically and the solutions are compared with experimental results. The shapes of the profiles are very well predicted, but the dependence of finger width on surface tension is not quantitatively accurate, although the qualitative behaviour is correct. A conflict between the numerics and a formal singular perturbation analysis is noted but not resolved. The stability of the steady finger to small disturbances is also examined. Linearized stability analysis indicates that the two-dimensional fingers are not stabilized by the surface-tension effect, which disagrees with the experimental observations. A possible reason for the discrepancy between theory and experiment is suggested.