Wave models in WAFO

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Wave models - from Chapter 2 in the Tutorial

Gaussian and non-Gaussian wave models and their power spectra

WAFO handles symmetric and asymmetric wave and load processes in time and space (one- and two-dimensional). The basic model are always Gaussian but non-Gaussian asymmetric waves can be handled by a simple transformation of a Gaussian wave to give the correct intensity of crossings of different levels. The transformation can be estimated from data or taken from a standard family of transformations. In WAFO one can estimate the spectrum or correlation and also find a transformation to make the model (marginally) Gaussian if it is not so from the beginning. Several standard wave spectra are provided for exact analysis and computation and comparison with empirical data.The toolbox also provides efficient algorithms for simulation of waves (in time as well as in space) for waves with specified directional spectra. It is also possible to construct a wave movie.  Encountered wave spectrum for a moving ship can easily be handled.

A record of asymmetric waves on shallow water.
Level crossing intensity for sea waves on shallow water (solid line) compared to crossing intensity (dashed line) for a Gaussian wave with the same significant wave height. A transformation of wave data can be estimated by WAFO that transforms a true Gaussian wave process to a non-Gaussian process that has the same crossings intensity as the observed waves. This transformation can be either a parametric function, like a Hermite polynomial transformation based on skewness and kurtosis, suggested by Winterstein, an exponential transformation suggested by Ochi, or a smoothed non-parametric transformation suggested by Rychlik. 
Estimated spectrum for shallow wave data with different degrees of smoothing. 
A catalogue of standard spectra from WAFO:
  • Wallop
  • Bimodal Ochi-Hubble
  • Bimodal (swell+wind) Torsethaugen
  • Pierson-Moskowitz
  • McCormick
  • JONSWAP for finite water depth 
A JONSWAP directional spectrum with directional spreading proportional to cos^2 s, together with the encountered directional spectrum for a ship heading the waves with spead 10 m/s.
A JONSWAP frequency spectrum compared with encountered frequency spectrum for heading sea speed 10 m/s. 


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