Instability of gravity flows on a slope

A Hamiltonian version of contour dynamics is formulated for the model of a potential slope flow of homogeneous incompressible fluid. The particle-like solutions that play the role of structural elements in the disintegration of strongly perturbed slope flows are studied in terms of this approach. Investigation of the solution instability mechanism has shown that two collapse scenarios are realized, depending on the slope steepness. The singularity for the surface shape develops according to the law (t - t (0))(-1/3) on a vertical slope and slightly more slowly, according to the law (t - t (0))(-2/7), where t (0) is the collapse time, on a nonvertical slope. A sufficient collapse criterion that allows this effect to be judged from the first three integrals of motion has been established.