Wenyue Lu

Numerical study of the generation and evolution of breather-type rogue waves

The behaviour of the Peregrine breather-type rogue waves is numerically studied based on the fourth-order nonlinear Schrödinger equation. The wavelet analysis method is adopted in order to analyse the time-frequency energy distribution during the generation and evolution of the Peregrine breather. It shows that the peak of the largest amplitudes of the resulting waves can be described in terms of the Peregrine breather-type solution and leads to the solution of the nonlinear Schrödinger (NLS) equation. Meanwhile, strong energy density is found to surge instantaneously and be seemingly carried over to the high-frequency components at the instant when the large, rogue wave occurs.

Fourth-order split-step pseudo-spectral method for the modified nonlinear Schrödinger equation

Abstract In the field of water waves, the modified nonlinear Schrödinger (mNLS) equation which models the wave propagation in water is numerically solved by using the split-step pseudo-spectral method. In the present paper, the fourth-order split-step pseudo-spectral method is introduced with better numerical results. The proposed method is based on a split-step method which decomposes the original equation into two parts, a linear problem and a nonlinear problem. In order to demonstrate the high accuracy and capability of the newly proposed method, a simple problem of periodic waves is presented to compare the traditional first-order method with the fourth-order method in terms of the conservation error and computational cost. Meanwhile, another numerical experiment concerning the Peregrine breather solution of the nonlinear Schrödinger (NLS) equation is presented by using the fourth-order split-step pseudo-spectral method. It is found that the fourth-order scheme can provide higher conservative accuracy and is computationally more efficient compared with the first-order scheme.

The Effects of Surface Waves and Submergence on the Performance and Loading of a Tidal Turbine

Tidal energy has the advantages of high predictability, high energy density, and limited environmental impacts. As tidal turbines are expected to be used in the most energetic waters where there might be significant waves, the assessment of unsteady hydrodynamic load due to surface waves is of great concern. The objective of this paper is to assess the effects of surface waves and submergence of the turbine on the power performance and loads ∗Address all correspondence to this author. of a tidal turbine by experimental approach. The experiments on a 1 : 25th model tidal turbine were carried out in a towing tank. A wide range of regular waves with periods from 1.0 s to 3.0 s at model scale were generated. Different submergence conditions were considered to investigate the effects of the presence of free surface. The cases with blade tip partly going out of water were also performed. The regular waves did not have significant influences on average loads and power output in the present experiments, but caused large amplitude of the cyclic variation of the loads. The amplitudes of the cyclic load were proved to be 1 Copyright c

Numerical simulation of nonlinearity and viscoelasticity of synthetic fibre rope for taut moorings in deep water

ABSTRACT Synthetic fibre ropes are preferable for taut moorings due to their low weight to strength ratio, which facilitates the reduction in cost. But the fibre ropes exhibit significant nonlinearity and viscoelasticity behaviour, which introduces difficulty in predicting the mooring dynamic response. The present study proposes a lumped mass method to simulate the dynamic response of mooring line. The elastic modulus of the fibre ropes is assumed to increase linearly with the instantaneous tension and a dashpot parallel to the spring is employed to represent the viscoelasticity. Six mooring configurations are employed and different types of motion are imposed to the fairlead. The energy dissipated by the hydrodynamic force and the viscoelastic force is calculated by the work done, which clarifies the damping characteristics of taut mooring lines.

Current Effects on the Generation and Evolution of the Peregrine Breather-Type Rogue Wave

Rogue wave is a kind of surface gravity waves with much larger wave heights than expected in normal sea state. Since this extreme sea event always occurred in the areas with strong currents, the wave-current interaction was considered to be one of the physical mechanics of the formation of the rogue wave. Some breather type solutions of the NLS equation have been considered as prototypes of rogue waves in ocean which usually appears from smooth initial condition only with a certain disturbance. In this paper, we have numerically studied evolutionary process of the Peregrine breather rogue wave based on the current modified fourth order nonlinear Schrodinger equation (the CmNLS equation). During the generation and evolution of the Peregrine breather rogue wave, the effects of the steady current was investigated by comparing with the results without current. The differences of the focusing position/time were observed due to the current influence.Copyright

Study on Breather-Type Rogue Wave Based on Fourth-Order Nonlinear Schrödinger Equation

Rogue wave is a kind of wave that possesses concentrated energy, strong nonlinear and enormous devastating. When it interacts with the deep-sea structures, the structure will suffer a serious threat, and it may even cause significant harm to the offshore staff and property. Studies on the mechanism of rogue wave are of great significance to the platform design and security. It is also one of the hot issues on the waves of hydrodynamic studies. Some breather-type solutions of NLS equation have been considered as prototypes of rogue waves in ocean. They can appear from smooth initial condition only with a certain disturb given by the exact solution of NLS. In this paper, we have numerically studied rogue waves based on fourth order nonlinear Schrodinger equation. We show that the peaks of the largest amplitude of the resulting waves can be described in terms of the Peregrine breather-type solution as the solution of NLS equation.Copyright