Time dependent gravity-capillary flows past an obstacle

The evolution of free surface gravity-capillary flows past a submerged obstacle in a shallow water channel is studied. For weakly nonlinear waves, the problem is formulated as a forced fifth-order Korteweg-de Vries (KdV) equation for the free-surface profile. Solutions to the initial value problem for this equation are computed numerically. It is found that there is a wealth of steady and unsteady behaviors, and several regimes are identified by varying the Froude and Bond numbers. This generalizes previous calculations in the absence of surface tension. (C) 1999 Elsevier Science B.V. All rights reserved.