A hybrid model for simulating rogue waves in random seas on a large temporal and spatial scale

A hybrid model for simulating rogue waves in random seas on a large temporal and spatial scale is proposed in this paper. It is formed by combining the derived fifth order Enhanced Nonlinear Schrödinger Equation based on Fourier transform, the Enhanced Spectral Boundary Integral (ESBI) method and its simplified version. The numerical techniques and algorithm for coupling three models on time scale are suggested. Using the algorithm, the switch between the three models during the computation is triggered automatically according to wave nonlinearities. Numerical tests are carried out and the results indicate that this hybrid model could simulate rogue waves both accurately and efficiently. In some cases discussed, the hybrid model is more than 10 times faster than just using the ESBI method, and it is also much faster than other methods reported in the literature

Deterministic numerical modelling of three-dimensional rogue waves on large scale with presence of wind

Oceanic rogue waves are a subject of great interest and can cause devastating consequences. Rogue waves are abnormal in that they stand out from the waves that surround them. Rogue waves are often observed accompanied by high wind in reality, and some earlier studies have demonstrated that the energy input due to the wind can enhance the dynamics of the rogue waves, which further causes huge concern about the safety of the human’s oceanic activities. Thus it is important, to better understand the mechanisms between the wind-wave interactions and to study the rogue waves with the presence of wind, especially on a three-dimensional large scale. In this study, numerical simulations are performed by using the Enhanced Spectral Boundary Integral (ESBI) method based on the fully nonlinear potential theory, in order to investigate the effects of wind on the rogue waves. The wind effects are introduced by imposing a wind-driven pressure on the free surface, which is empirically formulated based on intensive numerical investigation using multiple-phase Navier-Stokes solver. The results of the simulation confirm that the presented ESBI can produce satisfactory results on the formation of rogue waves under the action of wind. It provides a foresight of modelling rogue waves with presence of wind on a large scale in a phase-resolved fashion, which may motivate relevant studies in the futur

On quantitative errors of two simplified unsteady models for simulating unidirectional nonlinear random waves on large scale in deep sea

To investigate nonlinear random wave dynamics or statistics, direct phase-resolved numerical simulation of nonlinear random waves in deep sea on large-spatial and long-temporal scales are often performed by using simplified numerical models, such as those based on the Nonlinear Schrödinger Equation (NLSE). They are efficient and can give sufficiently acceptable results in many cases but they are derived by assuming narrow bandwidth and small steepness. So far, there has been no formula to precisely predict the quantitative errors of such simplified models. This paper will present such formulas for estimating the errors of enhanced NLSE based on the Fourier transform and quasi spectral boundary integral method when they are applied to simulate ocean waves on large-spatial and long-temporal scales (about 128 peak wavelengths and 1000 peak periods). These formulas are derived by fitting the errors of the simplified models, which are estimated by comparing their wave elevations with these obtained by using a fully nonlinear model for simulating the cases with initial conditions defined by two commonly used ocean wave spectra with a wide range of parameters. Based on them, the suitable regions for the simplified models to be used are shown

An Enhanced Spectral Boundary Integral Method for Modeling Highly Nonlinear Water Waves in Variable Depth

This paper presents a new numerical model based on the highly nonlinear potential flow theory for simulating the propagation of water waves in variable depth. A new set of equations for estimating the surface vertical velocity is derived based on the boundary integral equation considering the water depth variability. A successive approximation scheme is also proposed in this study for calculating the surface vertical velocity. With the usage of Fast Fourier Transform, the model can be efficiently used for simulating highly nonlinear water waves on large spatiotemporal scale in a phase-resolving approach. The new model is comprehensively verified and validated through simulating a variety of nonlinear wave phenomenon including free propagating solitary wave, wave transformations over submerged bar, Bragg reflection over undulating bars, nonlinear evolution of Peregrine breather, obliquely propagating uniform waves and extreme waves in crossing random seas. Good agreements are achieved between the numerical simulations and laboratory measurements, indicating that the new model is sufficiently accurate. A discussion is presented on the accuracy and efficiency of the present model, which is compared with the Higher-Order Spectral method. The results show that the present model can be significantly more efficient at the same level of accuracy. It is suggested that the new model developed in the paper can be reliably used to simulate the nonlinear evolution of ocean waves in phase-resolving approach to shed light on the dynamics of nonlinear wave phenomenon taking place on a large spatiotemporal scale, which may be computationally expensive by using other existing methods

A hybrid model for large scale simulation of unsteady nonlinear waves

A hybrid model for simulating rogue waves in random seas on a large time and space scale is proposed in this thesis. It is formed by combining the derived fifth order Enhanced Nonlinear Schrödinger Equation based on Fourier transform (ENLSE-5F), the fully nonlinear Enhanced Spectral Boundary Integral (ESBI) method and its simplified version. The numerical techniques and algorithm for coupling three models on time scale are provided. Using them, and the switch between the three models during the computation is triggered automatically according to wave nonlinearities. Numerical tests are carried out and the results indicate that this hybrid model could simulate rogue waves both accurately and efficiently. In some cases showed, the hybrid model is more than 10 times faster than just using the ESBI method

Ocean swell within the kinetic equation for water waves

Effects of wave-wave interactions on ocean swell are studied. Results of extensive simulations of swell evolution within the duration-limited setup for the kinetic Hasselmann equation at long times up to $10^6$ seconds are presented. Basic solutions of the theory of weak turbulence, the so-called Kolmogorov-Zakharov solutions, are shown to be relevant to the results of the simulations. Features of self-similarity of wave spectra are detailed and their impact on methods of ocean swell monitoring are discussed. Essential drop of wave energy (wave height) due to wave-wave interactions is found to be pronounced at initial stages of swell evolution (of order of 1000 km for typical parameters of the ocean swell). At longer times wave-wave interactions are responsible for a universal angular distribution of wave spectra in a wide range of initial conditions.Comment: Submitted to Journal of Geophysical Research 18 July 201

Experimental evidence of hydrodynamic instantons : the universal route to rogue waves

A statistical theory of rogue waves is proposed and tested against experimental data collected in a long water tank where random waves with different degrees of nonlinearity are mechanically generated and free to propagate along the flume. Strong evidence is given that the rogue waves observed in the tank are hydrodynamic instantons, that is, saddle point configurations of the action associated with the stochastic model of the wave system. As shown here, these hydrodynamic instantons are complex spatiotemporal wave field configurations which can be defined using the mathematical framework of large deviation theory and calculated via tailored numerical methods. These results indicate that the instantons describe equally well rogue waves created by simple linear superposition (in weakly nonlinear conditions) or by nonlinear focusing (in strongly nonlinear conditions), paving the way for the development of a unified explanation to rogue wave formation

A hybrid approach coupling mlpg-r with QALE-FEM for modelling fully nonlinear water waves

The paper reports a progress on the development of a hybrid approach coupling the Meshless Local Petrov-Galerkin Method based on Rankine Solution (MLPG-R) and the Quasi Arbitrary Langangian-Eulerian Finite Element Method (QALE-FEM) for modelling nonlinear water waves. The former is to solve the one-phase incompressible Naiver-Stokes model using a fractional step method (projection method), whereas the latter is to solve the Fully Nonlinear Potential Theory (FNPT) using a time-marching procedure. They are fully coupled using a zonal approach. The hybrid approach takes the advantage of the QALE-FEM on modelling fully nonlinear water waves with relatively higher computational efficiency and that of the MLPG-R on its capacity on dealing with viscous effects and breaking waves. The model is validated by comparing the numerical prediction with the experimental data for a unidirectional focusing wave. A good agreement has been achieved

Storm Tide and Wave Simulations and Assessment

In this Special Issue, seven high-quality papers covering the application and development of many high-end techniques for studies on storm tides, surges, and waves have been published, for instance, the employment of an artificial neural network for predicting coastal freak waves [1]; a reproduction of super typhoon-created extreme waves [2]; a numerical analysis of nonlinear interactions for storm waves, tides, and currents [3]; wave simulation for an island using a circulation–wave coupled model [4]; an analysis of typhoon-induced waves along typhoon tracks in the western North Pacific Ocean [5]; an understanding of how a storm surge prevents or severely restricts aeolian supply [6]; and an investigation of coastal settlements and an assessment of their vulnerability [7]

A zonal hybrid approach coupling FNPT with OpenFOAM for modelling wave-structure interactions with action of current

This paper presents a hybrid numerical approach, which combines a two-phase Navier- Stokes model (NS) and the fully nonlinear potential theory (FNPT), for modelling wave-structure interaction. The former governs the computational domain near the structure, where the viscous and turbulent effects are significant, and is solved by OpenFOAM/InterDyMFoam which utilising the finite volume method (FVM) with a Volume of Fluid (VOF) for the phase identification. The latter covers the rest of the domain, where the fluid may be considered as incompressible, inviscid and irrotational, and solved by using the Quasi Arbitrary Lagrangian- Eulerian finite element method (QALE-FEM). These two models are weakly coupled using a zonal (spatially hierarchical) approach. Considering the inconsistence of the solutions at the boundaries between two different sub-domains governed by two fundamentally different models, a relaxation (transitional) zone is introduced, where the velocity, pressure and surface elevations are taken as the weighted summation of the solutions by two models. In order to tackle the challenges associated and maximise the computational efficiency, further developments of the QALE-FEM have been made. These include the derivation of an arbitrary Lagrangian- Eulerian FNPT and application of a robust gradient calculation scheme for estimating the velocity. The present hybrid model is applied to the numerical simulation of a fixed horizontal cylinder subjected to a unidirectional wave with or without following current. The convergence property, the optimisation of the relaxation zone, the accuracy and the computational efficiency are discussed. Although the idea of the weakly coupling using the zonal approach is not new, the present hybrid model is the first one to couple the QALE-FEM with OpenFOAM solver and/or to be applied to numerical simulate the wave-structure interaction with presence of current