An experimental and numerical study on breather solutions for surface waves in the intermediate water depth

Abstract

A series of laboratory experiments related to Kuznetsov-Ma breather solution have been performed in a seakeeping wave tank with different initial wave steepness and intermediate water depths. Analysis of the experimental results reveals that the maximum wave height in Kuznetsov-Ma breather solution is normally accompanied with a large crest amplitude, which can be largely reduced with the decreasing water depth due to the slower modulational process and the limited length of wave tank, regardless of the initial nonlinearity. The laboratory observations can be accurately simulated by the high-order spectral model (HOS) if the initial Benjamin-Feir index is not very large as a result of weak nonlinearity and/or decreased water depth. Numerical studies also indicate that in the evolutionary process the amplitude of carrier wave will decrease sharply and a peak frequency downshifting can be detected. If the evolutionary time scale is long enough, the spectrum will eventually evolve into a continuous one with the energy relocated in the lower wave frequency part. For Peregrine breather solution that is a particular case of Kuznetsov-Ma solution, it is found that in some cases a specific phase shift of the initial condition can lead to a longer distance for the wave group to travel to achieve the first maximum amplitude and a larger amplification factor than that predicted by the theoretical solution.