Dr. Diane Henderson
William G. Pritchard Fluid Mechanics Laboratory
Department of Mathematics
Penn State

Experiments are conducted to generate wavefields in deep-water with two-dimensional surface patterns. The goals are to determine whether these patterns persist, what their main features are, whether standard models of deep-water waves describe these features, and whether there are parameter regimes in which the patterns are stable. We observe that indeed, the patterns do persist within the length of the wavetank despite classic stability analyses that would suggest otherwise. The stability analysis for a one-dimensional, Stokes wave (the Benjamin-Feir instability) is revisited by taking into account nonzero damping. We find that nonzero damping stabilizes this instability so that perturbations grow to a bounded value and stop growing, allowing the carrier wave to persist with little change of form. The direction this work is to determine the useful consequences of patterns of waves that can propagate for long distances with little change of form in the study and description of deep-water waves.

(joint work with Joe Hammack, Dana Pheiff, Harvey Segur, Katherine Socha)