Nonlinear Dynamics and Chaos in Parametrically Excited Surface Waves

Surface waves in a closed container subject to vertical oscillation are studied. Nonlinear dynamical equations of two nearly degenerate subharmonic modes responding to the external forcing are derived, using the averaged Lagrangian method for slowly varying amplitudes. Stability and bifurcation diagrams are shown for the system with linear damping. Period-doubling bifurcation and chaotic solutions with one positive Lyapunov characteristic exponent are obtained numerically. It is shown that some of the period-doubling bifurcations are related to the symmetry of the dynamical system.