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Page 1: · PDF filecp[]=!? 8 gjjojob>=@?¢b io=@e gpeh=@xu?y_

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18th IWWFB Le Croisic (France) 6-9 April 2003

Question by : M. Tulin

1. Since Mirhauq (Trondheim) has shown that extreme waves in the North Sea are not symmetric (steep front faces), how can you claim to model them as Stokes Waves?

2. Isn’t it true that the maximum orbital velocity (and therefore the design condition) is simply the wave phase speed augmented by a factor depending on the breaking jet strength?

3. You say: “Despite numerous studies, proper knowledge of kinematics of steep ocean waves above mean level is still lacking”. How can this be true when there exist several published studies of fully nonlinear wave propagation, including wave grouping and breaking, and these allow detailed knowledge of kinematical and velocity fields?

Author’s reply: We are very thankful for these valuable comments and questions.

1. Regarding question 1 we do not claim that steady Stokes waves is a proper model for irregular waves at sea. Our angle of attack is this: with the purpose of having a theoretical reference of a slowly varying wave field, that is weakly nonlinear and narrow banded, we identify a local wave period and a local wave length. This can be justified mathematically. Moreover, accurate laboratory measurements confirm the weakly nonlinear dispersion relation, both for small, moderate and even large waves. The weakly nonlinear reference velocity, /g kε ,see the paper, is then used in all the measurements. The collapse of the velocity recordings, put on nondimensional form, is a surprising result of the investigation. They are useful for simple predictions of wave induced fluid velocities.

2. It may be true that the maximal velocity in ocean waves at sea is the wave speed. In our laboratories we have been able to measure fluid velocities up to 75% of the estimated wave speed. LDA experiments by Baldoch, Swan & Taylor showed velocities up to 40% of the wave speed, and by Kim et al. up to 64% of C. References are given in the paper.

3. You are right in referring to the many publications on fully nonlinear wave computations, with lots of documentation of the wave induced velocities, from a theoretical point of view. Our main contribution precisely consists in 122 different PIV measurements of large wave events giving an experimental confirmation and supplement to the existing knowledge. Such a documentation has repeatedly been suggested by experts in the ocean engineering community.

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