Grid states and nonlinear selection in parametrically excited surface waves

Interacting surface waves, parametrically excited by two commensurate frequencies (Faraday waves), yield a rich family of nonlinear states, which result from a variety of three-wave resonant interactions. By perturbing the system with a third frequency, we selectively favor different nonlinear wave interactions. Where quadratic nonlinearities are dominant, the only observed patterns correspond to "grid" states. Grid states are superlattices in which two corotated sets of critical wave vectors are spanned by a sublattice whose basis states are linearly stable modes. Specific driving phase combinations govern the selection of different grid states.