On the equivalence of unidirectional rogue waves detected in periodic simulations and reproduced in numerical wave tanks

Abstract

This paper deals with the reproduction of unidirectional extreme events in a numerical wave basin. From a rogue wave measurement at a given location, experiments or numerical simulations are conducted with the same wave profiles using reproduction procedures. Although it is recognized that many different physical mechanisms may be at play in freak wave formation, reproduction procedures generally use frequency focusing to generate these high waves. This paper intends to assess the validity of this approach. In particular, it will focus on the relationship between an accurate reproduction of the free surface elevation and the accuracy of the corresponding wave kinematics inside the fluid domain. A highly nonlinear model is used to compute

Time-reversal of nonlinear waves: Applicability and limitations

“…This is based on the free surface elevation recorded by the wave gauge after application of TR, namely η T R (t). In the context of the reproduction of extreme waves in wave basins, it has been shown in [40] that the most important parameter to ensure the correct kinematics inside the fluid domain, also essential for example to study wave-structure interactions, is the wave amplitude. Consequently, the chosen accuracy parameter is defined by…”

Experimental reconstruction of extreme sea waves by time reversal principle

“…This is known to be complex and highly influenced by the wave nonlinearities for extreme waves (Yasuda et al 1994;Grue & Jensen 2006;Alberello et al 2018). However, it is expected that once the free-surface profile is accurately reproduced, the induced kinematics would naturally follow (Ducrozet et al 2016a). This particular point will be the subject of further investigations.…”

“…Despite the slight inaccuracies, the TR principle seems to be the simplest procedure for reconstructing highly nonlinear and steep waves in a wave flume compared to existing procedures (Tromans et al 1991;Chaplin 1996;Clauss & Schmittner 2007;Schmittner et al 2009;Fernandez et al 2014;Ducrozet et al 2016a), since it provides a similar level of accuracy and high robustness, independently of the physical complexities that are at play in the ocean environment.…”

“…The levels of accuracy are indeed satisfying in the range k p x M 50. The TR procedure, which is a straightforward process to set up experimentally compared to existing ones based on dispersive focusing, such as the New Wave theory (Tromans et al 1991;Chaplin 1996;Clauss & Schmittner 2007;Schmittner et al 2009;Fernandez et al 2014;Ducrozet et al 2016a), consequently manages to accurately reproduce highly nonlinear extreme events such as the New Year wave in a straightforward way. The presence of wave breaking during the first experiment or during the refocusing did not lead to a failure of the complete procedure, demonstrating its robustness.…”

“…As a consequence, it appears to be tempting to test its validity in the reproduction of measured ocean extreme waves in a laboratory environment. The reconstruction of rogue waves using the dispersive focusing mechanism, also known as New Wave theory, has been demonstrated to be fairly challenging in practice (Tromans, Anaturk & Hagemeier 1991;Chaplin 1996;Clauss & Schmittner 2007;Schmittner, Kosleck & Hennig 2009;Fernandez et al 2014;Ducrozet, Bonnefoy & Ferrant 2016a;Alberello et al 2018) and any development of a simple and efficient procedure is of major significance for the nonlinear and experimental water-wave physics and ocean engineering communities.…”