Manchester Applied Mathematics and Numerical Analysis Seminars Winter 1998

December 16, 1998, 4.00 pm

Lecture Theatre D13 Material Science

Time dependent gravity-capillary flows past an obstacle

Prof. Jean-Marc Vanden-Broeck, School of Mathematics, UEA

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 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 abscence of surface tension. Results on the interaction of gravity capillary solitary waves will also be presented.

For further info contact either Matthias Heil (mheil@ma.man.ac.uk), Mark Muldoon (M.Muldoon@umist.ac.uk)or the seminar secretary (Tel. 0161 275 5800).