Extreme waves at the sea surface can have severe impacts to ships, offshore platforms and coastal structures. One of the theoretical mechanisms leading to extreme waves is the instability of deep-water wave trains subject to initially small perturbations, which then grow exponentially. Benjamin and Feir (1967) first showed that weakly nonlinear deep-water waves can be unstable to modulational perturbations. Under certain conditions, wave breaking will occur. McLean (1982) classified the so-called Benjamin-Feir wave instability as Class I instability, which is generally strongest in the case of a plane wave train subject to two-dimensional (2D) perturbations. Tulin and Waseda (1999) conducted a massive study of seeded experiments of wave train evolutions, where the modulation naturally evolved from background noise in the experiments. They observed an overall decrease of the carrier waves with an increase of the lower sideband wave amplitudes. Madsen et al. (2002) reproduced the experiments in Tulin and Waseda (1999) numerically using a Boussinesq model and demonstrated accurate modeling of the frequency downshift and nonlinear shoaling of regular waves up to the point of breaking. Another type of wave instability of our interest leads to predominantly three-dimensional (3D) crescent waves, also known as Class II instability according to McLean (1982). Numerical simulations of crescent waves using a boundary-element model were performed by Xue et al. (2001), in which their investigation was limited to relatively small domains and short time scales. Fuhrman et al. (2004) studied crescent waves with a high-order Boussinesq model at somewhat larger spatial and temporal scales, providing new insight into the physical processes involved.To the authors’ knowledge, seemingly all of the numerical studies on Class I and Class II wave instabilities to date have been limited to models founded on potential flow theory, thus they could only properly investigate the process from initial growth of the perturbations to the initial breaking point. The present study will conduct CFD simulations to investigate the phenomena of both Class I and Class II deep-water wave instabilities in a detailed manner. The experiments of Tulin and Waseda (1999) for Class I wave instability in 2D with steep incident waves will be reproduced. The simulation of 3D crescent waves will be generating the common phase-locked (L2) patterns. The open-source CFD wave generation toolbox waves2foam (Jacobsen et al. 2012) developed in the OpenFOAM v1912 framework will be used to conduct simulations. As the wave instabilities will involve turbulence after initial breaking, a model solving Reynolds-averaged Navier-Stokes (RANS) equations coupled with turbulence closure in terms of the anisotropic Reynolds stress model (the stress-omega&nbsp;model of Wilcox 2006) will be applied. The physical process of wave instabilities will be analyzed through spatial Fourier transform. Wave forms evolutions, Fourier amplitudes, and the turbulence beneath the broken waves will be investigated. Since the CFD model is able to simulate the breaking process, the long time evolution of deep-water wave instabilities can be studied in a detailed and proper manner, thus extending previous investigations based on nonlinear potential flow theories.ReferencesBenjamin, T. B., &amp; Feir, J. E. (1967). The disintegration of wave trains on deep water.&nbsp;J. Fluid mech,&nbsp;27(3), 417-430.Fuhrman, D. R., Madsen, P. A., &amp; Bingham, H. B. (2004). A numerical study of crescent waves.&nbsp;Journal of Fluid Mechanics,&nbsp;513, 309.Jacobsen, N. G., Fuhrman, D. R., &amp; Fredsøe, J. (2012). A wave generation toolbox for the open‐source CFD library: OpenFoam®.&nbsp;International Journal for numerical methods in fluids,&nbsp;70(9), 1073-1088.McLean, J. W. (1982). Instabilities of finite-amplitude water waves.&nbsp;Journal of Fluid Mechanics,&nbsp;114, 315-330.Tulin, M. P., &amp; Waseda, T. (1999). Laboratory observations of wave group evolution, including breaking effects.&nbsp;Journal of Fluid Mechanics,&nbsp;378, 197-232.Xue, M., Xü, H., Liu, Y., &amp; Yue, D. K. (2001). Computations of fully nonlinear three-dimensional wave-wave and wave-body interactions. Part 1. Dynamics of steep three-dimensional waves. Journal of Fluid Mechanics, 438, 11.

CFD Simulation of Nonlinear Deep-Water Wave Instabilities_x000B_Involving Wave Breaking

Paper Proceedings: https://asmedigitalcollection.asme.org/OMAE/OMAE2021/volume/85116

OMAE 2021

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