We construct the Hirota bilinear form of the nonlocal Boussinesq(nlBq) equation with four arbitrary constants for the first time. It is special because one arbitrary constant appears with a bilinear operator together in a product form. A straightforward method is presented to construct quasiperiodic wave solutions of the nl Bq equation in terms of Riemann theta functions. Due to the specific dispersion relation of the nl Bq equation, relations among the characteristic parameters are nonlinear, then the linear method does not work for them. We adopt the perturbation method to solve the nonlinear relations among parameters in the form of series. In fact, the coefficients of the governing equations are also in series form.The quasiperiodic wave solutions and soliton solutions are given. The relations between the periodic wave solutions and the soliton solutions have also been established and the asymptotic behaviors of the quasiperiodic waves are analyzed by a limiting procedure.
An improved coupling of numerical and physical models for simulating 2D wave propagation is developed in this paper.In the proposed model,an unstructured finite element model(FEM)based Boussinesq equations is applied for the numerical wave simulation,and a 2D piston-type wavemaker is used for the physical wave generation.An innovative scheme combining fourth-order Lagrange interpolation and Runge-Kutta scheme is described for solving the coupling equation.A Transfer function modulation method is presented to minimize the errors induced from the hydrodynamic invalidity of the coupling model and/or the mechanical capability of the wavemaker in area where nonlinearities or dispersion predominate.The overall performance and applicability of the coupling model has been experimentally validated by accounting for both regular and irregular waves and varying bathymetry.Experimental results show that the proposed numerical scheme and transfer function modulation method are efficient for the data transfer from the numerical model to the physical model up to a deterministic level.
Based on the wave radiation and diffraction theory, this paper investigates a new type breakwater with upper arcshaped plate by using the boundary element method(BEM). By comparing with other three designs of plate type breakwater(lower arc-shaped plate, single horizontal plate and double horizontal plate), this new type breakwater has been proved more effective. The wave exiting force, transmission and reflection coefficients are analyzed and discussed. In order to reveal the wave elimination mechanism of this type of breakwater, the velocity field around the breakwater is obtained. It is shown that:(1) The sway exciting force is minimal.(2) When the ratio of the submergence and wave amplitude is 0.05, the wave elimination effect will increase by 50% compared with other three types of breakwater.(3) The obvious backflow is found above the plate in the velocity field analysis.
In physical model tests for highly reflective structures, one often encounters a problem of multiple reflections between the reflective structures and the wavemaker. Absorbing wavemakers can cancel the re-reflective waves by adjusting the paddle motion. In this paper, we propose a method to design the controller of the 2-D absorbing wavemaker system in the wave flume. Based on the first-order wavemaker theory, a frequency domain absorption transfer function is derived. Its time realization can be obtained by designing an infinite impulse response(IIR) digital filter, which is expected to approximate the absorption transfer function in the leastsquares sense. A commonly used approach to determine the parameters of the IIR filter is applying the Taylor expansion to linearize the filter formulation and solving the linear least-squares problem. However, the result is not optimal because the linearization changes the original objective function. To improve the approximation performance, we propose an iterative reweighted least-squares(IRLS) algorithm and demonstrate that with the filters designed by this algorithm, the approximation errors can be reduced. Physical experiments are carried out with the designed controller. The results show that the system performs well for both regular and irregular waves.
