Slowly varying wave drift forces in shallow water at forward speed

The interaction between water waves and floating or submerged bodies is one of the important issues in fluid dynamics. In the past years many studies have been carried out which were especially focussed on the second order wave forces. These studies can be performed in both the frequency domain and the time domain. An advantage of calculating in the physical time domain is that one is not restricted to harmonic waves and is not forced to implement real time signals depending on every frequency. The frequencies of the slowly varying components may coincide with the natural frequencies of a moored ship and may cause the ship to undergo resonant motions. Therefore this study is focussed on the slowly varying drift-forces due to regular waves. The calculation of these drift-forces is based on the work of Prins [10]. He calculates the mean driftforces and -moments using a pressure intergration technique. When calculating the mean drift-force the contribution of the second order potential is averaged out. In order to give an expression of the lowfrequency component of the drift-force the second order potential has to be determined. We will extend the method of Prins to calculate the contribution of the second order potential. To solve the second order potential the boundary conditions have to be extended up to second order. A filtering procedure is needed in our problem because we are interested in the slowly varying part of the drift force. We have tested the case of a vertical cylinder mounted to the bottom of the sea. Results are compared to results given in literature. We will study the influence of current and radius-height ratio of the cylinder.