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Wave crest statistics calculated using a fully nonlinear spectral response surface method

This study presents a fully nonlinear spectral response surface method for calculating wave crest statistics, based on a wave model by Bateman et al. (2001) and profiling and kinematics models by Tromans and Vanderschuren (1995). The method discretizes the spectrum into components and determines the probability distribution of each component. The response function is then calculated based on these components, with the maximum crest elevation as the focus. The most probable event is identified as the point closest to the origin on the response surface. The method also includes linear and second-order response functions, as well as a fully nonlinear correction to a linear optimization.

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Wave crest statistics calculated using a fully nonlinear spectral response surface method

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  1. Wave crest statistics calculated using a fully nonlinear spectral response surface method R. Gibson, C. Swan, P.Tromans and L.Vanderschuren Imperial College London

  2. Short-Term Statistics Spectral Response Surface Method Fully nonlinear wave-model of Bateman et al. (2001). Long-Term Statistics Tromans and Vanderschurn (1995) Fully nonlinear SRS method Profile and Kinematics Modelled using a fully nonlinear wave-model Profile and Kinematics Introduction

  3. Spectrum is discretised into a number of components. The variance of each component determines its probability distribution. Response function is given as a function of these components: in this case maximum crest elevation. Each point in the domain One realisation of the possible values of each component. One value of the response function. Spectral Response Surface Method

  4. Spectral Response Surface Method Point closest to the origin represent the most probable event. The point on the response surface with the greatest response is identified.

  5. Spectral Response Surface Method Linear and second-order response function

  6. Fully-nonlinear Correction to a Linear Optimisation Unidirectional Sea-States Desired probability of exceedence is determined. Fully-nonlinear increase in crest elevation is modelled.

  7. Fully-nonlinear Optimisation Unidirectional Sea-States

  8. A ‘New’ Method Desired event is pre-determined. Interactions that cause the event modelled. Probability of exceedence of the event calculated. Unidirectional Sea-States

  9. Comparison with fully-nonlinear time-domain simulations Unidirectional Sea-States

  10. Directional Sea-States

  11. Directional Sea-States

  12. Fully nonlinear unidirectional 105 Fully nonlinear directional 106 Fully nonlinear Gaussian 105 Short-Term Statistics of the Draupner Event

  13. Tromans and Vanderschuren (1995) Storms as independent events: Hmost probable. Long-term statistics of storms modelled using an Error function fit to Hmost probable. Short-term statistics conditional on Hmost probable. Transfer function from linear to fully-nonlinear crest elevations: Long-Term Statistics of the Draupner Event

  14. Results Linear 3000 years Second-order 300 years Fully-nonlinear 800 years Long-Term Statistics of the Draupner Event

  15. Method Spectrum determined from the time-trace. Initial conditions: Profile using Zakharov’s equation. Potential using double-Fourier method of Baldock and Swan (1994). Evolution of the Draupner Event

  16. Surface Profile Evolution of the Draupner Event

  17. Evolution of the Draupner Event Sea-State

  18. Water Particle Kinematics Evolution of the Draupner Event

  19. Spectral Response Surface method can successfully predict the statistics of crest elevation. Crest elevations in directional JONSWAP sea-states lower than the second-order prediction. Crest elevations in directional Gaussian sea-states significantly higher than the second-order prediction. Return period of the Draupner wave based on fully-nonlinear SRS method 800 years. Largest horizontal velocity associated with the event 8.4m/s. Conclusions

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