VISCOUS EFFECTS ON CROSS-WAVES, BIFURCATIONS, AND COUPLING BETWEEN MODES.

Some recent theoretical and experimental results on cross-waves are summarized: A nonlinear Schroedinger equation for the evolution of viscous cross-waves is presented. From the analysis, a few simple expressions are presented which determine the relative contribution of the free surface, sidewall, and bottom damping. A bifurcation analysis shows a transition to hysteretic behaviour. A similarity scaling, relevant to large forcing amplitude, indicates that bifurcations occur along lines in left bracket ( omega //0 - omega )/ omega //0, epsilon **2 right bracket , where omega //0 is the cut-off frequency, omega is the forcing frequency, and epsilon is the forcing amplitude. Finally, the equations for coupling between two unstable modes are presented. Many of the theoretical results are compared with recent experiments.