Unexpected Waves

Extreme, or “rogue,” waves are those in the tail of the probability distribution and are a matter of great concern and considerable research. They may be partly associated with non-Gaussian behavior caused by resonant nonlinear interactions. Here it is shown that even in a Gaussian sea, “unexpected” waves, in the sense of, for example, waves twice as large as any in the preceding 30 periods, occur with sufficient frequency to be of interest and importance. The return period of unexpected waves is quantified as a function of the height multiplier and prior quiescent interval for various spectral shapes, and it is shown how the return period is modified if allowance is made for nonlinear changes in wave shape and/or a buildup of one or more waves prior to the unexpected wave. The return period of “two-sided” unexpected waves, with subsequent as well as prior quiescence, is also evaluated.