Long Waves Associated with Bichromatic Waves

A numerical model of low frequency waves is presented. The model is based on that of Roelvink (1993), but the numerical techniques used in the solution are based on the so-called Weighted- Average Flux (WAF) method with Time-Operator- Splitting JOS) used for the treatment of the source terms. This method allows a small number of computational points to be used, and is particularly efficient in modeling wave setup. The short wave (or primary wave) energy equation is solved with a traditional Lax-Wendroff technique. A nonlinear wave theory is introduced. The model described in this paper is found to be satisfactory in modeling low frequency waves associated with incident bichromatic waves.

NONLINEAR DIFFRACTION OF BICHROMATIC WAVES BY A VERTICAL CYLINDER

We present in this paper a semi-analytical solution for second-order wave diffraction by a vertical circular cylinder in bichromatic waves. On the base of the usual assumption of an irrotational flow, the wave-diffraction problems at second-order sum-frequency and difference-frequency are considered. The corresponding second-order diffraction potentials are decomposed into three parts, these are associated with the second-order incident wave, the quadratic forcing terras on the free-surface due to the first-order potential, and the linearised free-wave component resulting from the boundary condition on the body surface. A particular solution which exactly satisfies the inhomogeneous free-surface condition has been derived. Numerical results for the quadratic transfer functions of the second-order force components are given, and are compared with those obtained using numerical solutions (Kim & Yue, 1990,Moubayed & Williams 1995). These quadratic functions are useful in calculating the exciting forces on a circular cylinder of large dimension, fixed in irregular wave fields.

TESTS AND APPLICATIONS OF A BOUSSINESQ MODEL WITH AMBIENT CURRENT

A new type Boussinesq model is proposed and applied for wave propagation in a wave flume of uniform depth and over a submerged bar with current present or absent,respectively.Firstly,for the propagation of monochromatic incident wave with current absent,the Boussinesq model is tested in its complete form,and in a form without the introduction of utility velocity variables.It is validated that the introduction of utility velocity variables can improve the characteristics of velocity field,dispersion and nonlinearity.Both versions of the Boussinesq models are of higher accuracy than the fully-nonlinear fourth-order model,which is one of the best forms among the existing traditional Boussinesq models that do not incorporate breaking mechanism in one dimension.Secondly,the Boussinesq model in its complete form is applied to simulating the propagation of bichromatic incident waves with current present or absent,respectively,and the modeled results are compared to the analytical ones or the experimental ones.The modeled results are reasonable in the case of inputting bichromatic incident waves with the strong opposing current present.