Steepness effect on modulation instability of the nonlinear wave train

Abstract

The long-term evolution of a nonlinear wave train in deep water with varied initial wave steepness between 0.1 and 0.3 was experimentally investigated in a super wave flume (300m long, 5m wide, and 5.2m deep). The initial wave train was the combination of one carrier wave and a pair of imposed sideband components which is the most unstable mode, referred to as sideband instability theory. Sixty-six wave gauges were installed downstream along the wave flume to simultaneously measure the evolution of a wave train. Increasing modulation of the wave train was observed due to sideband instability until a critical value which either wave breaking is initiated or maximum modulation is reached. The near recurrence of the initial state of the wave train is exhibited for the nonbreaking case. An effective frequency downshift of the wave spectrum accompanied with wave breaking is observed as the initial wave steepness is larger than 0.11. At postbreaking, the wave train reveals periodic modulation and demodulation, meanwhile, the related wave spectrum shows a down and upshift, respectively. Present results support the hypothesis that the frequency downshift induced by wave breaking is not permanent.