Dynamics of strongly nonlinear fingers and bubbles of the free surface of an ideal fluid

An analytical model is presented for the dynamics of fingers and bubbles of the free surface of an ideal fluid. A time-dependent conformal mapping similar to Zakharov–Dyachenko’s N-finger solution is used to describe the growth of fingers and bubbles. The time evolution of the conformal mapping is determined using a variational principle for the free surface dynamics of an ideal fluid. In the limit of strong nonlinearity, the dynamics reduces to simple integrable Hamiltonian systems. Exact solutions of these Hamiltonian systems are given in closed form.