Joe Hammack , Diane Henderson , Harvey Segur
Experiments are conducted to generate wavefields in deep water with two-dimensional surface patterns for which two parameters are systematically varied: (i) the aspect ratio of the cells comprising the surface patterns and (ii) a measure of nonlinearity of the input wavefield. The goal of these experiments is to determine whether these patterns persist, what their main features are, whether standard models of waves describe these features, and whether there are parameter regimes in which the patterns are stable. We find that in some parameter regimes, surface patterns in deep water do persist with little change of form during the time of the experiment. In other parameter regimes, particularly for large{amplitude experiments, the patterns evolve more significantly. We characterize the patterns and their evolutions with a list of observed features. Some of these are that (i) unlike persistent two-dimensional surface patterns in shallow water, which comprise sixsided cells, surface patterns in deep water comprise primarily four-sided cells; (ii) crests parallel to the wavemaker may be at or have a dip; (iii) for some experiments with large nonlinearity, cells appear to pinch in half; (iv) modulations may develop in the direction of propagation; (v) the nodal line-region may develop a time-varying width; (vi) oscillations may develop in the nodal line region; (vii) small-scale waves may grow on the larger pattern, and (viii) a connecting leg between cells may develop. To describe the patterns and these features, we consider two models: (a) the standard nonlinear Schrodinger equation and (b) coupled nonlinear Schrodinger equations for two interacting wavetrains. Exact solutions of these models provide qualitative explanations for (i)-(iii) listed above. Qualitative stability considerations of the exact solutions provide alternative explanations for features (ii) and (iii) above and explanations for (iv)-(viii).