Shallow-water nonlinear wave instabilities and energy transfer

There are essentially two types of three-dimensional instabilities of nonlinear surface gravity waves (Types I and II). Their relative importance depend on their wave steepness as well as on the water depth on which waves travel. In shallow water, Type II instability is one-order stronger than Type I instability and has the strongest instability in the directions away from the main wave propagation direction. The current theories about nonlinear wave-wave interactions in shallow water include three types: The first is unidirectional (Freilich and Guza, 1984). The second is three dimensional in general and strongest in the primary wave direction, but is suppressed in very shallow water(Hasselman, 1962). The third is also 3-dimensional but is enhanced in shallow water (McLean, 1982, Su a al., 1982b Liu and Huang, 1996). This paper shall discuss the physical meaning and the relationship among the above nonlinear wave instabilities and the nonlinear wave-wave interactions.