Third order irregular deep-water waves with wave-generated current

Airy waves, - or linear Stokes waves, are widely used in offshore engineering. Sometimes second order in the Stokes expansion is applied. These equations do not include the wave number correction, which can make it difficult to compare analyses and model tests of structures. Here it will be argued that the wave number correction is due to a wave-generated current. Potential theory wave equations that include a rotational analogous current should be developed. In this article a potential theory third order formulation that includes wave-generated current is derived, for wave elevation and velocities at the free surface. This method is compared to model tank experiments and CFD with good correspondence for wave elevations and particle velocities. The theory is assumed valid for waves that have traveled moderate distances.