Experimental evidence of stable wave patterns on deep water

Recent predictions from competing theoretical models have disagreed about the stability/instability of bi-periodic patterns of surface waves on deep water. We present laboratory experiments to address this controversy. Growth rates of modulational perturbations are compared to predictions from: (i) inviscid coupled nonlinear Schrödinger (NLS) equations, according to which the patterns are unstable and (ii) dissipative coupled NLS equations, according to which they are linearly stable. For bi-periodic wave patterns of small amplitude and nearly permanent form, we find that the dissipative model predicts the experimental observations more accurately. Hence, our experiments support the claim that these bi-periodic wave patterns are linearly stable in the presence of damping. For bi-periodic wave patterns of large enough amplitude or subject to large enough perturbations, both models fail to predict accurately the observed behaviour, which includes frequency downshifting.