Numerical simulation of wave interaction with a pair of fixed large tandem cylinders subjected to regular non-breaking waves

This paper presents the application of a two-phase Computational Fluid Dynamics (CFD) model to carry out a detailed investigation of nonlinear wave field surrounding a pair of columns placed in the tandem arrangement in the direction of wave propagation and corresponding harmonics. The numerical analysis is conducted using the Unsteady Reynolds-Averaged Navier-Stokes/VOF model based on the OpenFOAM framework combined with the olaFlow toolbox for wave generation and absorption. For the simulations, the truncated cylinders are assumed vertical and surface piercing with a circular cross-section subjected to regular, non-breaking fifth-order Stokes waves propagating with moderate steepness in deep water. Primarily, the numerical model is validated with experimental data for a single cylinder. Future, the given simulations are conducted for different centre-to-centre distances between the tandem large cylinders. The results show the evolution of a strong wave diffraction pattern and consequently, high wave amplification harmonics around cylinders are apparent.

Three-Dimensional Numerical Modeling of a Coastal Highway Bridge under Stokes Waves

This article investigated the effect of structural flexibility on a coastal highway bridge subjected to Stokes waves through a three-dimensional numerical model. Wave-bridge interaction modeling was performed by an FSI model with the coupling of finite element and finite volume methods. An experimental model validated the FSI numerical analysis. Eventually, the overall results of hydrodynamic and structural analyses are presented and discussed. The results illustrate that the structural flexibility significantly increases the initial shock of the wave force on the flexible bridge. In contrast, the fixed bridge tolerates the least forces in the initial shock of the wave force. Then, by adding a wedge-shaped part to the bridge structure, an attempt was made to reduce the initial shock of the wave force to the structure. The results showed the wedge-shaped part with an angle of 30° reduces the initial shock of wave forces down to 50% for horizontal force and 43% for vertical force on the flexible structure.

Three-dimensional surface gravity waves of a broad bandwidth on deep water

A new nonlinear Schrödinger equation (NLSE) is presented for ocean surface waves. Earlier derivations of NLSEs that describe the evolution of deep-water waves have been limited to a narrow bandwidth, for which the bound waves at second order in wave steepness are described in leading-order approximations. This work generalizes these earlier works to allow for deep-water waves of a broad bandwidth with large directional spreading. The new NLSE permits simple numerical implementations and can be extended in a straightforward manner in order to account for waves on water of finite depth. For the description of second-order waves, this paper proposes a semianalytical approach that can provide accurate and computationally efficient predictions. With a leading-order approximation to the new NLSE, the instability region and energy growth rate of Stokes waves are investigated. Compared with the exact results based on McLean (J. Fluid Mech., vol. 511, 1982, p. 135), predictions by the new NLSE show better agreement than by Trulsen et al. (Phys. Fluids, vol. 12, 2000, pp. 2432–2437). With numerical implementations of the new NLSE, the effects of wave directionality are investigated by examining the evolution of a directionally spread focused wave group. A downward shift of the spectral peak is observed, owing to the asymmetry in the change rate of energy in a more complex manner than that for uniform Stokes waves. Rapid oblique energy transfers near the group at linear focus are observed, likely arising from the instability of uniform Stokes waves appearing in a narrow spectrum subject to oblique sideband disturbances.

All-Fiber Tunable Pulsed 1.7 μm Fiber Lasers Based on Stimulated Raman Scattering of Hydrogen Molecules in Hollow-Core Fibers

Fiber lasers that operate at 1.7 μm have important applications in many fields, such as biological imaging, medical treatment, etc. Fiber gas Raman lasers (FGRLs) based on gas stimulated Raman scattering (SRS) in hollow-core photonic crystal fibers (HC-PCFs) provide an elegant way to realize efficient 1.7 μm fiber laser output. Here, we report the first all-fiber structure tunable pulsed 1.7 μm FGRLs by fusion splicing a hydrogen-filled HC-PCF with solid-core fibers. Pumping with a homemade tunable pulsed 1.5 μm fiber amplifier, efficient 1693~1705 nm Stokes waves are obtained by hydrogen molecules via SRS. The maximum average output Stokes power is 1.63 W with an inside optical–optical conversion efficiency of 58%. This work improves the compactness and stability of 1.7 μm FGRLs, which is of great significance to their applications.

Passively Q-Switched KTA Cascaded Raman Laser with 234 and 671 cm−1 Shifts

A compact KTA cascaded Raman system driven by a passively Q-switched Nd:YAG/Cr4+:YAG laser at 1064 nm was demonstrated for the first time. The output spectra with different cavity lengths were measured. Two strong lines with similar intensity were achieved with a 9 cm length cavity. One is the first-Stokes at 1146.8 nm with a Raman shift of 671 cm−1, and the other is the Stokes at 1178.2 nm with mixed Raman shifts of 234 cm−1 and 671 cm−1. At the shorter cavity length of 5 cm, the output Stokes lines with high intensity were still at 1146.8 nm and 1178.2 nm, but the intensity of 1178.2 nm was higher than that of 1146.8 nm. The maximum average output power of 540 mW was obtained at the incident pump power of 10.5 W with the pulse repetition frequency of 14.5 kHz and the pulse width around 1.1 ns. This compact passively Q-switched KTA cascaded Raman laser can yield multi-Stokes waves, which enrich laser output spectra and hold potential applications for remote sensing and terahertz generation.

Nonlinear Fourier Analysis for Two-Dimensional Ocean Surface Waves Described by the Zakharov Equation

<p>The physical hierarchy of two-dimensional ocean waves studied here consists of the 2+1 nonlinear Schrödinger equation (NLS), the Dysthe equation, the Trulsen-Dysthe equation, etc. on to the Zakharov equation. I call this the SDTDZ hierarchy. I demonstrate that the nonlinear Schrödinger equation with arbitrary potential is the natural way to treat this hierarchy, for any member of the hierarchy can be determined by an appropriate choice of the potential. Furthermore, the NLS equation with arbitrary potential can be written in terms of two bilinear forms and thereby has one and two-soliton solutions. To access the inverse scattering approach, I find a nearby equation which has N-soliton solutions: Such an equation is completely integrable by the IST on the infinite plane and by finite gap theory for periodic boundary conditions. In this way the entire SDTDZ hierarchy is closely related to a nearby integrable hierarchy which I refer to as the iSDTDZ hierarchy. Every member of this hierarchy has solutions in terms of ratios of Riemann theta functions and therefore every member has general spectral solutions in terms of quasiperiodic Fourier series. This last step occurs because ratios of theta functions are single valued, multiply periodic meromorphic functions. Once the quasiperiodic Fourier series are found, one can then invert these to determine the Riemann spectrum, namely, the Riemann matrix, wavenumbers, frequencies and phases. This means that the solutions of the nonlinear wave equations of the iSDTDZ hierarchy are generalized Fourier series indistinguishable from those of Paley and Weiner [1935] and therefore allows one to classify nonlinear wave motion in terms of a linear superposition of sine waves. How do the generalized quasiperiodic Fourier series differ from ordinary, standard periodic Fourier series? This can be seen by recognizing that the frequencies are incommensurable, and the phases can be phase locked. The nonlinear Fourier modes are Stokes waves and the coherent structure solutions are nonlinearly interacting, phase-locked Stokes waves, including breathers and superbreathers. Other types of coherent packets include fossil breathers and dromions. Techniques are developed for (1) numerical modeling of ocean waves (a fast algorithm for the Zakharov equation) and for (2) the nonlinear Fourier analysis of two-dimensional measured wave fields and space/time series (a 2D nonlinear Fourier analysis, implemented as a fast algorithm called the 2D NFFT). Examples of both applications are discussed.</p>

Theory of Nonlinear Fourier Analysis: The Construction of Quasiperiodic Fourier Series for Nonlinear Wave Motion

I give a description of nonlinear water wave dynamics using a recently discovered tool of mathematical physics I call nonlinear Fourier analysis (NLFA). This method is based upon and is an application of a theorem due to Baker [1897, 1907] and Mumford [1984] in the field of algebraic geometry and from additional sources by the author [Osborne, 2010, 2018, 2019]. The theory begins with the Kadomtsev-Petviashvili (KP) equation, a two dimensional generalization of the Korteweg-deVries (KdV) equation: Here the NLFA method is derived from the complete integrability of the equation by finite gap theory or the inverse scattering transform for periodic/quasiperiodic boundary conditions. I first show, for a one-dimensional, plane wave solution, that the KP equation can be rotated to a solution of the KdV equation, where the coefficients of KdV are now functions of the rotation angle. I then show how the rotated KdV equation can be used to compute the spectral solutions of the KP equation itself. Finally, I write the spectral solutions of the KP equation as a finite gap solution in terms of Riemann theta functions. By virtue of the fact that I am able to write a theta function formulation of the KP equation, it is clear that the wave dynamics lie on tori and constitute parallel dynamics on the tori in the integrable cases and non-parallel dynamics on the tori for certain perturbed quasi-integrable cases. Therefore, we are dealing with a Kolmogorov-Arnold-Moser KAM theory for nonlinear partial differential wave equations. The nonlinear Fourier series have particular nonlinear Fourier modes, including: sine waves, Stokes waves and solitons. Indeed the theoretical formulation I have developed is a kind of exact two-dimensional “coherent wave turbulence” or “integrable wave turbulence” for the KP equation, for which the Stokes waves and solitons are the coherent structures. I discuss how NLFA provides a number of new tools that apply to a wide range of problems in offshore engineering and coastal dynamics: This includes nonlinear Fourier space and time series analysis, nonlinear Fourier wave field analysis, a nonlinear random phase approximation, the study of nonlinear coherent functions and nonlinear bi and tri spectral analysis.

Routes to stability for spatially periodic breather solutions of a damped NLS equation.

<p> The spatially periodic breather solutions (SPBs) of the nonlinear Schrödinger (NLS) equation, i.e. the heteroclinic orbits of unstable Stokes waves, are typically unstable. In this talk  we examine  the effects of dissipation on the  one- mode SPBs  U<sup>(j)</sup>(x,t) as well as multi-mode SPBs U<sup>(j,k)</sup>(x,t) using a damped  NLS equation which incorporates both uniform linear damping and nonlinear damping  of the mean flow,<br>for a range of parameters typically encountered in experiments. The damped wave dynamics is viewed as near integrable, allowing one to use the spectral theory of the NLS equation to interpret the perturbed flow. A broad categorization of how the route to stability for the SPBs  depends on the mode structure of the SPB and whether the damping is linear or nonlinear is obtained <br>as well as the distinguishing features of the stabilized state.  Time permitting, a reduced, finite dimensional dynamical system that goverms the linearly damped SPBs will be presented </p>

Shape asymmetry of rogue waves

<p>Direct numerical simulations of the directional sea surface gravity waves are carried out within the framework of the primitive potential equations of hydrodynamics using the High Order Spectral Method. The data obtained for conditions of deep water, the JONSWAP spectrum, and various wave intensities are processed and the results are discussed. The statistical and spectral characteristics of the waves evolve over a long period. The particular asymmetry of the profiles of rogue waves is highlighted. We show that besides the conventional crest-to-trough asymmetry of nonlinear Stokes waves, the extreme events are characterized by a specific combination of the troughs adjacent to the large crest, so that the trough behind the crest is typically deeper than the preceding trough. Surprisingly, the extreme wave crest-to-trough asymmetry and the discrimination between the extreme wave troughs exhibit the tendency to grow when the angle spectrum broadens. This effect contradicts the expectation based on the Benjamin – Feir Index that broad-banded waves should behave similar to linear waves, and hence the asymmetries should diminish.</p><p>                                                                 </p><p>The research is supported by the RSF grant No. 19-12-00253.</p><p> </p><p>A. Kokorina, A. Slunyaev, The effect of wave nonlinearity on the rogue wave lifetimes and shapes. Proc. 14th Int. MEDCOAST Congress on Coastal and Marine Sciences, Engineering, Management and Conservation (Ed. E. Ozhan), Vol. 2, 711-721 (2019).</p>