A two dimensional rectangular basin containing an incompressible inviscid homogeneous fluid, initially at rest with a horizontal free surface of finite extent is considered to generate and propagate nonlinear, long-crested waves. A depth profile for the potential is assumed, giving us a waveform relaxation method, thereby drastically reducing the computational cost of solving Laplace's equation. A multichromatic stochastic wavemaker employing a Dirichlet type boundary condition is applied, with the latter following a standard wave energy spectrum. Laplace's equation is solved using a non-orthogonal boundary fitted curvilinear coordinate system, which follows the free surface, and the full nonlinear kinematic and dynamic free surface boundary conditions are employed. The behavior of this model is studied using standard signal processing tools and a discussion of the results is given. In addition, statistical properties of the output of the model are related to the corresponding statistical properties of the input.
A two-dimensional rectangular basin containing an incompressible inviscid homogeneous fluid initially at rest with a horizontal free surface of finite extent is considered to generate and propagate longcrested waves. On the left vertical boundary a wavemaker is positioned while at the right hand side is the radiation boundary. The same numerical beach is used as in Parsons and Baddour (2002), and a depth profile for the potential is assumed, giving us a waveform relaxation method, and thereby drastically reducing the computational cost of solving Laplace's equation. A multichromatic deterministic and stochastic wavemaker employing a Dirichlet type boundary condition is applied, see Baddour and Parsons (2003) for a comparison of Dirichlet and Neumann monochromatic wavemakers and Parsons and Baddour (2003) for the bichromatic Dirichlet wavemaker model. This method can easily be extended to the case of a wavemaker utilizing a Neumann type boundary condition.
