Various experimental wave statistics emerging from a single energy spectrum

As it strongly impacts the design of offshore structures, the accurate control of experimental wave fields is of great interest for the ocean engineering community. A significant majority of sea keeping tests are based on the stochastic approach. Long duration runs of irregular design sea states are generated at model scale in numerical or experimental wavetanks. The run duration is carefully chosen to observe the emergence of extreme events. The quality of the wavefield at the domain area of interest is assessed thanks to i) the wave energy spectrum and ii) the crest height distribution. The accurate reproduction of those two quantities stands a difficult process. Numerous complex phenomena such as wave breaking or Benjamin Feir (modulational) instabilities strongly impact the wave field. The shapes of i) the wave spectrum and ii) the tail of crest height distributions significantly evolve along the tank depending i) the wave steepness, ii) the spectral width, iii) the water depth and iv) the directional spreading (for directional sea states) [1, 2, 3].

The vast majority of the work in this area has focused on reproducing realistic wave energy spectra at the location of interest, assuming the indirect control of wave statistics. The present study intends to question such a characterization of a sea state. We address the problem within the framework of long crested irregular deep water waves generated in an experimental wave tank. In this respect, using the Ecole Centrale de Nantes (ECN) towing tank (140m*5m*3m), a narrow banded sea state has been generated at several locations of a long domain. The shape of the spectrum is accurately controlled thanks to a procedure based on wavemaker motion iterative correction [4]. For such nonlinear wave conditions the statistics along the wave propagation in the tank are known to be enhanced by significant spatial dynamics [1, 3]. As a result, configurations characterized by strictly identical wave spectra lead to the emergence of strongly different crest distributions. The data yielded by the study provide convincing evidence that the characterization of the wave field using the sole energy spectrum is insufficient. Particular attention must be given to the spatial dynamics of the wave field in order to control the wave statistics.

[1] Janssen, P. A. (2003). Nonlinear four-wave interactions and freak waves. Journal of Physical Oceanography, 33(4), 863-884.

[2] Shemer, L., Sergeeva, A., & Liberzon, D. (2010). Effect of the initial spectrum on the spatial evolution of statistics of unidirectional nonlinear random waves. Journal of Geophysical Research: Oceans, 115(C12).

[3] Onorato, M., Cavaleri, L., Fouques, S., Gramstad, O., Janssen, P. A., Monbaliu, J., ... & Trulsen, K. (2009). Statistical properties of mechanically generated surface gravity waves: a laboratory experiment in a three-dimensional wave basin.

[4] Canard, M., Ducrozet, G., & Bouscasse, B. (2020, August). Generation of 3-hr Long-Crested Waves of Extreme Sea States With HOS-NWT Solver. In International Conference on Offshore Mechanics and Arctic Engineering (Vol. 84386, p. V06BT06A064). American Society of Mechanical Engineers.