We consider three-dimensional water-wave diffraction and radiation by a structure consisting of a number of separate (vertically) non-overlapping members in the context of linearized potential flow. An interaction theory is developed which solves the complete problem, predicting wave exciting forces, hydrodynamic coefficients and second-order drift forces, but is based algebraically on the diffraction characteristics of single members only. This method, which includes also the diffraction interaction of evanescent waves, is in principle exact (within the context of linearized theory) for otherwise arbitrary configurations and spacings. This is confirmed by a number of numerical examples and comparisons involving two or four axisymmetric legs, where full three-dimensional diffraction calculations for the entire structures are also performed using a hybrid element method. To demonstrate the efficacy of the interaction theory, we apply it finally to an array of 33 (3 by 11) composite cylindrical legs, where experimental data are available. The comparison with measurements shows reasonable agreement.The present method is valid for a large class of arrays of arbitrary individual geometries, number and configuration of bodies with non-intersecting vertical projections. Its application should make it unnecessary to perform full diffraction computations for many multiple-member structures and arrays.
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.
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