Excitation of rogue waves in a variable medium: An experimental study on the interaction of water waves and currents

Abstract

We show experimentally that a stable wave propagating into a region characterized by an opposite current may become modulationally unstable. Experiments have been performed in two independent wave tank facilities; both of them are equipped with a wavemaker and a pump for generating a current propagating in the opposite direction with respect to the waves. The experimental results support a recent conjecture based on a current-modified nonlinear Schrödinger equation which establishes that rogue waves can be triggered by a nonhomogeneous current characterized by a negative horizontal velocity gradient.

An analytical model of the evolution of a Stokes wave and its two Benjamin–Feir sidebands on nonuniform unidirectional current

“…Our simulations confirm that initially stable waves in experiments of Toffoli et al (2013) undergo a modulationally unstable process and wave amplification in the presence of adverse current. Maximum amplification reasonably corresponds to results of experiments at the Tokyo University Tank for moderate strength of current.…”

“…Both nonlinear instability and refractive focusing have been identified as mechanisms for extreme-wave generation and these processes are generally concomitant in oceans and potentially act together to create giant waves. Toffoli et al (2013) showed experimentally that an initially stable surface wave can become modulationally unstable and even produce freak or giant waves when meeting negative horizontal current. Onorato et al (2011) suggested an equation for predicting the maximum amplitude A max during the wave evolution of currents in deep water.…”

“…They mentioned that theoretical values of amplification (Onorato et al, 2011;Toffoli et al, 2013) are essentially overestimated, probably owing to the effects of finite depth and wave breaking.…”

“…Section 3 is devoted to stationary nondissipative solutions for adverse and following nonuniform currents and various initial steepness of the surface wave train. We calculate the maximum amplitude amplification in dependence from relative strength of opposing current and compared it with available experimental and theoretical results (Toffoli et al, 2013;Ma et al, 2013). The interaction of steep surface waves with strong adverse current under wave-blocking conditions including wave breaking effects is presented in Sect.…”

“…The boundary conditions for the unperturbed waves were taken from experiments conducted by Toffoli et al (2013) and Ma et al (2013). Results of the calculations are presented in Fig.…”