Twenty-First Symposium on Naval Hydrodynamics (1997) / Chapter Skim
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Freak Waves-A Three-Dimensional Wave Simulation
Freak Waves-A Three-Dimensional Wave Simulation
Pages 550-560
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From page 550... ...
However, existing models for weakly nonlinear, slowly modulated surface gravity waves, i.e. the third order nonlinear Schrodinger equation and the fourth order modified nonlinear Schrodinger equation, do not have sufficient resolution in bandwidth.
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From page 551... ...
We seek to explain the occurrence of freak waves in the absence of ocean currents or non-uniform bottom topography by nonlinear self modulation of a wave train. Even though the wind is essential to produce the wave spectrum, it can be neglected over the relatively short scales characteristic for a freak wave event.
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From page 552... ...
Even though the waves in figure 1 are not on deep water, we limit the present discussion to waves on deep water. In section 2 we first review the NLS and MNLS equations, and then summarize a new modified nonlinear Schrodinger equation for broader bandwidths by requiring ~ /\k~/k = O(e 2 ~ while keepin~ the same accuracy in nonlinearity (Trulsen & Dys .
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From page 553... ...
We believe that three-dimensional wave modulation is important and plan to use the BMNLS equation to carry out fully three-dimensional computations of a spectrum that is statistically stationary and homogeneous, similar to the energetic part of a realistic ocean wave spectrum. Our interests include the occurrence, parametric dependence and dynamics of freak waves.
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From page 554... ...
(26) For numerical solution of the governing equations it is convenient to transform into a moving coordinate system to eliminate the leading order advec¢18' tion with the group velocity of the central wavenumber cg = 2.
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From page 555... ...
The higherorder modified nonlinear Schrodinger equations have primary instability regions that are bounded, and they have the most unstable perturbations located at isolated points near the origin. The BMNLS equation confines the instability region even better than the MNLS equation.
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From page 556... ...
However, the required bandwidth is wider than the constraints imposed by the existing fourth order modified nonlinear Schrodinger equation of Dysthe (1979~. We have derived a new modified nonlinear Schrodinger equation valid for broader bandwidths, which is more appropriate for a realistic ocean wave spectrum.
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From page 557... ...
. Slow evolution of nonlinear deep water waves in two horizontal directions: A numerical study.
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From page 558... ...
(1992~. Freak waves in unidirectional wave trains and their properties.
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From page 559... ...
The present modification for a relaxed narrow bandwidth constraint is very much welcome and contributes to further understanding of nonlinear wave processes in deep waters. The offshore industry is at present very interested in obtaining detailed knowledge about wave processes in steep waves as these contribute to transient higher order loading of slender structures (Stansberg and Gudmestad, 1996~.
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From page 560... ...
(1979~. "Note on a modification of the nonlinear Schrodinger equation for application to deep water wave," Proc.
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