Many ocean engineering problems involve bound harmonics which are slaved to some underlying assumed close to linear time series. When analyzing signals we often want to remove the bound harmonics so as to “linearise” the data or to extract individual bound harmonic components so that they may be studied. For even moderately broadbanded systems filtering in the frequency domain is not sufficient to separate components as they overlap in frequency. One way to overcome this difficulty is to use input signals with the same linear envelope but with different phases and then use simple addition and subtraction of the resulting signals to extract different harmonics. This approach has been established for the analysis of wave groups. In this paper we examine whether this approach can be used on random time series as well. We analyse random wave time series of wave elevation from the towing tank in Shanghai Jiao Tong University and force measurements on a cylinder taken in the Kelvin tank at the University of Strathclyde.

In this paper, Fast Multipole Boundary Element Method (FMBEM) is developed to build a numerical wave tank, which is used to simulate a linear irregular wave train. Comparison is illustrated between the simulated and theoretical waves to validate the precision of FMBEM. Furthermore, the time consumptions of FMBEM are also compared with the traditional BEM to demonstrate its high efficiency. Besides, this effective numerical method is used to simulate the wave propagation with the influence of a fixed surface piercing body. All the results demonstrate that the proposed method is an effective numerical technique to study the linear irregular wave propagation with both high accuracy and efficiency.

In this paper, the Homotopy Analysis Method (HAM) is applied to solve the fully nonlinear partial differential equation for the steady propagating periodic gravity wave of finite water depth. The series solution of the wave elevation and the velocity potential function are obtained. And then the velocity and pressure fields are plotted and discussed carefully. In order to overcome the drawback of the integral calculations with complex free surface elevation, the discrete integration and fitting procedure based on high-order Fourier series is developed. Based on the accurate HAM solution and fitting technique, the mass, momentum and energy conservation equations are validated. At last, the corresponding mean fluxes are calculated and the velocities of the mass transport and energy transport are supplied accurately.

The interaction of nonlinear progressive waves and uniform currents in water of finite depth is investigated analytically by means of the homotopy analysis method (HAM). In the HAM, the velocity potential of the wave is expressed by Fourier series and the nonlinear free surface boundary conditions are satisfied by continuous mapping. The present approach does not depend on any small parameters, thus the solutions are suitable for steep waves and strong currents. To verify the HAM solutions, experiments are conducted in wave-current flume of Education Ministry Key Laboratory of Hydrodynamics at SJTU. It is shown that the HAM solutions are in good agreement with experimental measurements. The present study demonstrated that the great potential of the HAM to solve more complex wave-current interaction problems leading to engineering applications in traditional offshore industry and marine renewable energy sector.

In this paper, the Homotopy Analysis Method (HAM) is applied to obtain high accuracy series solutions of roll motions of a ship, which encounters a nonlinear wave of large amplitude. Comparisons are made between roll responses in linear and nonlinear beam waves with identical wave slope and frequency. Furthermore, Floquet theory is applied to analyze the stability of HAM series solutions. Besides that, numerical simulation is used to verify the analytical solution and study the behaviors of the system under disturbance. All the results demonstrate that the proposed scheme is an effective analytic technique to study nonlinear ship rolling equation, and the stability analysis reveals the significance of researching ship roll motion in large amplitude nonlinear wave.

The vortex-induced vibration (VIV) phenomenon is result of fluid-structure interaction which occurs in many engineering fields. The study of VIV of a circular cylinder is of practical importance (such as in marine cables and flexible risers in petroleum production). In this paper, one classical phenomenological VIV model — the motion of the cylinder is modeled by a simple linear equation, and the fluctuating nature of the vortex wake oscillation is modeled by a van der Pol oscillator, is analyzed. Firstly, the homotopy analysis method (HAM), a powerful technique for highly nonlinear problems, is developed to solve the coupled fluid-structure dynamical system with the convergence of the homotopy series solutions being demonstrated. Based on the HAM solutions, some properties of the fully nonlinear classical coupled VIV model are presented. All the results proved that the proposed HAM scheme has potential to be an effective analytic technique to study the VIV problems.