Second Order Irregular–Wave Generation in Flumes - Computation of Transfer Functions by an Asymptotic Summation Method

Recently the theory for second order irregular-wave generation (including superharmonics as well as subharmonics) has been rederived for a variety of different types of wave board motion. In addition to the well known transfer functions some new terms appeared. These are related to the first order evanescent modes and accordingly they are significant when the wave board motion makes a poor fit to the velocity profile of the desired progressive wave component. This is for example the case for the high-frequency part of a primary wave spectrum when using a piston type wavemaker. The well known transfer functions are given in a relatively simple form by which the computational effort is reduced substantially. However, the new terms are represented by double infinite series of very slow convergence, which makes straightforward series summation extremely memory and time consuming. The computational effort can be reduced by orders of magnitude by use of the asymptotic expression for large j of the j'th term in the series. The paper focuses on this method for practical computation of the developed transfer functions.