Flow structures around a large-diameter circular cylinder

In ocean and coastal engineering, a widely used tool for the investigation of wave phenomena is the velocity potential, in which both hypotheses of inviscid fluid and irrotational flow are incorporated. In some cases, a close-form analytical expression of the potential can be devised. In other cases, and especially in complex problems of contemporary engineering, no expressions of the potential exist, so that the system of the Euler equations - cast in terms of the potential - is solved numerically, usually by means of numerical techniques of integral nature. It can though be recognized that the assumptions of both inviscid fluid and irrotational flow are rather restrictive. Within this class of problems, if one wants firstly (mainly due to limited computing power available) to give up one of the two previous hypothesis - namely, that of irrotational flow - an appropriate strategy for the investigation of wave-related phenomena is represented by the numerical integration of the Euler equations in the velocity-pressure formulation. Under this viewpoint it becomes of remarkable importance to investigate the differences that exist between a flow field derived from a velocity potential and one resulting from the numerical solution of the Euler equations in primitive variables, as related to the wave case at hand. In this work these issues - relatively unexplored in the literature - are addressed, with reference to the case of the diffraction of water waves caused by a large-diameter, surface-piercing, vertical circular cylinder. The close-form velocity potential for this problem is first analyzed, as related to a number of strictly linear wave cases. Then, some of these cases are simulated numerically by solving the Euler equations in primitive variables, and the results are compared. For further investigation of the flow fields, the swirling-strength criterion for flow-structure extraction is applied to the velocity fields related to one of the wave cases examined. It is found that, in terms of flow structures, remarkable differences exist between the differently derived flow fields.