Experimental investigation on the evolution of the modulation instability with dissipation

Abstract

AbstractAn experimental investigation focusing on the effect of dissipation on the evolution of the Benjamin–Feir instability is reported. A series of wave trains with added sidebands, and varying initial steepness, perturbed amplitudes and frequencies, are physically generated in a long wave flume. The experimental results directly confirm the stabilization theory of Segur et al. (J. Fluid Mech., vol. 539, 2005, pp. 229–271), i.e. dissipation can stabilize the Benjamin–Feir instability. Furthermore, the experiments reveal that the effect of dissipation on modulational instability depends strongly on the perturbation frequency. It is found that the effect of dissipation on the growth rates of the sidebands for the waves with higher perturbation frequencies is more evident than on those of waves with lower perturbation frequencies. In addition, numerical simulations based on Dysthe’s equation with a linear damping term included, which is estimated from the experimental data, can predict the experimental results well if the momentum integral of the wave trains is conserved during evolution.