Abstract:

According to the nonlinearity of freak waves and the sideband instability existing in the evolution of slowly-modulated periodic wave trains, the modified four-order nonlinear Schrodinger equation is employed to investigate the generation of freak waves and the variation of the corresponding complex wave-envelope spectra in the condition of sideband disturbances. Then, with the sideband instability being satisfied, the influences of the disturbance fre- quency bandwidth, the initial disturbance amplitude, the wave steepness and the nonlinear order on the develop- ment of sideband instability and on the occurrence of freak waves are analyzed. The results show that the occurrence of freak waves is due to the local exponential growth of the wave train because the carrier wave energy rapidly transfers to the neighbourly-unstable sideband components. Thus, energy transfer is a main reason for the occurrence of freak waves in the condition of sideband disturbances. It is also indicated that narrow frequency bandwidth, high disturbance amplitude, large wave steepness and strong nonlinearity all contribute favorably to the development of sideband instability and to the occurrence of freak waves.

Key words: freak wave, nonlinear Schrodinger equation, sideband instability, nonlinear mechanism