Nonlinear wave dynamics in Faraday instabilities

Nonlinear wave dynamics in parametrically driven surface waves are studied in numerical simulations of the two-dimensional Navier-Stokes equation, with an emphasis on the evolution and interaction between different wave number modes. The dynamics are found to be closely correlated with the single-mode nonlinear saturated wave amplitudes. Modulating behavior of primary wave modes in a particular parameter range and in time scales much longer than the underlining wave periods is observed.