Experimental and theoretical analysis of the wave decay along a long array of vertical cylinders

A row of fifty identical, truncated vertical cylinders is submitted to regular head waves, with wave periods in a narrow range around the period of the so-called Neumann trapped mode. The free-surface elevation is measured at 14 locations along the array. Response amplitude operators of the free-surface motion are compared with numerical predictions from a potential flow model. Resonance effects, at wave periods equal to or larger than the critical one, are found to be much less than given by the numerical model. It is advocated that these discrepancies are due to dissipative effects taking place in the boundary layers at the cylinder walls. An artificial means is devised to incorporate dissipation in the potential flow model, whereby the cylinder walls are made slightly porous; the inward normal velocity of the flow is related to the dynamic pressure. The coefficient of proportionality is based on existing knowledge for circular cylinders in oscillatory flows. With this modification in the numerical code, excellent agreement is obtained with the experiments. The numerical model is further used for the case of a very long array composed of 1000 cylinders; it is found that with dissipation at the cylinder walls, the wave action steadily decreases along the array, even for wave periods substantially larger than the critical one. On the other hand, at wave periods less than the critical one, dissipation plays a negligible role; the observed decay is solely due to diffraction effects. Implications of these results for very large structures such as column-supported floating airports are discussed. In particular, it is concluded that scale effects may be an important issue in the experimental analysis of such multi-column structures.