RANKINE source method applying continuous free surface panels is developed to examine two-dimensional linear wave-current coexist problems. The wave-current interaction problem is solved by combination of steady and unsteady potential problem respectively. The boundary integral method can be directly applied to examine the effects of current. Numerical results for both radiation and diffraction problems with current effect are compared with available data and reasonably good agreement is obtained. Apart from some well-known conclusions about the current effect, the pressure distribution of wetted body surface are extensively studied and some new phenomena are observed from our numerical prediction.
Accurate predictions of hydrodynamic loads on floating structures subjected to wave and current are of practical importance in offshore engineering. When the current speed is small the effects of flow separation are usually unimportant and therefore the wave-current interaction problem can be investigated within potential flow framework.
The radiation and diffraction problems in the absence of a current have been investigated extensively by a free surface Green function model or a Rankine source approach. The former model involves with a complicated free surface Green function which requires the singular integral on the free surface boundary (Wehausen and Laitone, 1960). In contrast, the latter (Beck, 1994) only needs to calculate the integration of Rankine sources on free surface and body boundaries.
In the presence of current or forward speed, the free surface Green function model needs to be modified to include the effects of current or forward speed. By following the forward speed Green function originally derived by Haskind (1944), Grue and Palm (1985) studied wave radiation and diffraction problems for a two-dimensional submerged circular cylinder in frequency domain. Wu and Eatock Taylor (1990) developed a new mathematical formulation based on a perturbation series in terms of forward speed and the hydrodynamic force can be directly obtained without forward speed involved. Nossen et al. (1991) derived the Green function for small forward speed in the form of zero-speed Green function and its derivatives. Generally significantly computational difficulties arise due to the complexity in evacuating the forward speed Green function (Sen, 2002).