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

• A new reproduction procedure dedicated to extreme waves is presented.
• Reproduced rogue waves are embedded in an irregular sea state.
• The wavemaker motion is deduced using non-linear phase velocity.
• Highly nonlinear models are used for the computation of wave fields.
• The accurate reproduction of wave elevation and kinematics induced is demonstrated.

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 the occurrence of unidirectional freak waves in large periodic domain, which are reproduced in a 2-D numerical wave tank and compared. The study presents an advanced reproduction procedure that deals with rogue waves embedded in an irregular sea state. It shows that, using the appropriate reproduction procedure, it is possible to accurately reproduce free surface elevation as well as kinematics induced by this extreme event.