Account of Occasional Wave Breaking in Numerical Simulations of Irregular Water Waves in the Focus of the Rogue Wave Pro
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Account of Occasional Wave Breaking in Numerical Simulations of Irregular Water Waves in the Focus of the Rogue Wave Problem Alexey Slunyaev1,2,3
· Anna Kokorina1,2
Received: 31 January 2019 / Accepted: 30 July 2019 © Springer Nature Switzerland AG 2019
Abstract The issue of accounting of the wave breaking phenomenon in direct numerical simulations of oceanic waves is discussed. It is emphasized that this problem is crucial for the deterministic description of waves, and also for the dynamical calculation of extreme wave statistical characteristics, such as rogue wave height probability, asymmetry, etc. The conditions for accurate simulations of irregular steep waves within the High Order Spectral Method for the potential Euler equations are identified. Such non-dissipative simulations are considered as the reference when comparing with the simulations of occasionally breaking waves which use two kinds of wave breaking regularization. It is shown that the perturbations caused by the wave breaking attenuation may be noticeable within 20 min of the performed simulation of the wave evolution. Keywords Sea waves direct numerical simulation · Wave breaking regularization · Wave statistics · High Order Spectral Method
1 Introduction The direct numerical simulation of hydrodynamic equations has become recently an accessible alternative to the simulation of kinetic equations for oceanic waves. In addition to the open possibility of a direct comparison between results of the dynamic and kinetic approaches (e.g., [1]), the direct numerical simulations are a promising means to solve new challenging problems, such as a reproduction of the rogue wave
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Alexey Slunyaev [email protected] Anna Kokorina [email protected]
1
Institute of Applied Physics, Box-120, 46 Ulyanova Street, Nizhny Novgorod 603950, Russia
2
Nizhny Novgorod State Technical University n.a. R.E. Alekseev, Nizhny Novgorod, Russia
3
National Research University – Higher School of Economics, Nizhny Novgorod, Russia
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A. Slunyaev, A. Kokorina
phenomenon [15]. In contrast to the kinetic equations, the dynamic equations do not employ the assumption of independent wave phases, which is obviously violated in rough sea conditions. Besides, the degree of idealization of the simulated equations may be chosen appropriately to meet the requirements on capturing significant physical effects as well as on the acceptable computation speed. Today simulations of the sea surface areas of O(102 ) km within the 3D potential Euler equations which account for strongly nonlinear effects may be performed with the speed greater than the waves evolve in the real sea [16]. Consequently, besides the ability of accumulating the statistical data, the direct numerical simulation is considered as a tool of an operational short-term wave forecast for the needs of navigation [16, 25, 26]. One may look forward to the forthcoming future when even faster approaches for the simulation of the hydrodynamic equations (maybe with reasonable simplifying assumptions) w
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