HIGH-JACOBIAN APPROXIMATION IN THE FREE-SURFACE DYNAMICS OF AN IDEAL FLUID

Using a combination of the canonical formalism for free-surface hydrod ynamics and conformal mapping to a horizontal strip we obtain a simple system of pseudo-differential equations for the surface shape and hyd rodynamic velocity potential, The system is well-suited for numerical simulation. It can be effectively studied in the case when the Jacobia n of the conformal mapping takes very high values in the vicinity of s ome point on the surface. At first order in an expansion in inverse po wers of the Jacobian one can reduce the whole system of equations to a single equation which coincides with the well-known Laplacian Growth Equation (LGE). In the framework of this model one can construct remar kable special solutions of the system describing such physical phenome na as formation of finger-type configurations or changing of the surfa ce topology generation of separate droplets.