Three-dimensional deep-water waves. Part 1. Experimental measurement of skew and symmetric wave patterns

Abstract

The three-dimensional structures of symmetric and skew wave patterns in deep water observed in a tow tank and a wide basin are described. These symmetric waves are the result of three-dimensional subharmonic bifurcation of two-dimensional wave-trains with steepness a0k0 ≥ 0·25, where a0, and k0, are the wave amplitude and wave-number respectively. The wave profiles, local surface slopes and amplitude spectra at various cross-sections of the crescent-shaped symmetric waves are presented and discussed.The skew waves are another type of three-dimensional bifurcation from a uniform wavetrain, and occur most clearly when 0·16 [siml ] a0k0 [siml ] 0·18. These skew wave patterns are found to interact between two sets of themselves propagating from different directions, and to be subject to the Benjamin–Feir type modulations. The interactions cause compact three-dimensional wave packets. Agreement between experiment and theory is found for the case of symmetric wave patterns. The bifurcation of uniform Stokes waves into symmetric wave patterns provide a new physical process for directional energy spreading.