Even if the wave-current- floating body interaction (also called seakeeping at small forward speed) has been extensively studied during the last two decades, it is the authors opinion that it is still not solved in a fully consistent way, especially in the case of finite water depth. In the present paper, we try to give some further clarifications on the subject. Here we concentrate on rather detailed technical points concerning the numerical implementation of the non-secular Green function (Zalar et al., 1999) for the finite water depth case.
The wave current interactions with floating bodies are an important topic in offshore industry. There are two main reasons for that: the first one is the necessity to assess the influence of current on first order quantities, especially the wave run-up which is strongly influenced by the current, the second one is the proper calculation of the so called wave drift damping coefficient (derivative of drift force with respect to the forward speed) which is important for simulations of mooring systems. An correct expression for the Green functions was presented in Zalar et al. (1999) but without implementation in the numerical code. Here we show how this can be done. Boundary Integral Equations All the above BVP are solved using the Boundary Integral Equation (BIE) technique based on the so-called source formulation. Elevation of the free surface Probably the best test of one numerical code, is the calculation of the free surface profile around the body. Indeed, in order to obtain good result, all previous tasks should be solved correctly and in addition some "tricky things" (numerical) happens at the intersection of the free surface and the body. Since this will be the final validation test for our study, we give hereafter the expression for the free surface elevation.