16 research outputs found
Freak Waves in Random Oceanic Sea States
Freak waves are very large, rare events in a random ocean wave train. Here we
study the numerical generation of freak waves in a random sea state
characterized by the JONSWAP power spectrum. We assume, to cubic order in
nonlinearity, that the wave dynamics are governed by the nonlinear Schroedinger
(NLS) equation. We identify two parameters in the power spectrum that control
the nonlinear dynamics: the Phillips parameter and the enhancement
coefficient . We discuss how freak waves in a random sea state are more
likely to occur for large values of and . Our results are
supported by extensive numerical simulations of the NLS equation with random
initial conditions. Comparison with linear simulations are also reported.Comment: 7 pages, 6 figures, to be published in Phys. Rev. Let
Linear and Nonlinear Rogue Wave Statistics in the Presence of Random Currents
We review recent progress in modeling the probability distribution of wave
heights in the deep ocean as a function of a small number of parameters
describing the local sea state. Both linear and nonlinear mechanisms of rogue
wave formation are considered. First, we show that when the average wave
steepness is small and nonlinear wave effects are subleading, the wave height
distribution is well explained by a single "freak index" parameter, which
describes the strength of (linear) wave scattering by random currents relative
to the angular spread of the incoming random sea. When the average steepness is
large, the wave height distribution takes a very similar functional form, but
the key variables determining the probability distribution are the steepness,
and the angular and frequency spread of the incoming waves. Finally, even
greater probability of extreme wave formation is predicted when linear and
nonlinear effects are acting together.Comment: 25 pages, 12 figure
Nonlinear wave interaction in coastal and open seas -- deterministic and stochastic theory
We review the theory of wave interaction in finite and infinite depth. Both of these strands of water-wave research begin with the deterministic governing equations for water waves, from which simplified equations can be derived to model situations of interest, such as the mild slope and modified mild slope equations, the Zakharov equation, or the nonlinear Schr\"odinger equation. These deterministic equations yield accompanying stochastic equations for averaged quantities of the sea-state, like the spectrum or bispectrum. We discuss several of these in depth, touching on recent results about the stability of open ocean spectra to inhomogeneous disturbances, as well as new stochastic equations for the nearshore