Interactions of obliquely incident water waves with two vertical obstacles

The diffraction of obliquely incident water waves by two parallel floating rectangular cylinders is examined using linearized potential theory. The "exact" solution is obtained by the method of matched eigenfunction expansions; the resulting matrix equation is solved numerically. Two approximated solutions based on the "wide-spacing approximation" and the "plane-wave approximation" are also obtained for comparison. It is shown that the "wide-spacing approximation" gives much more accurate solutions than the "plane-wave approximation". Moreover, the "wide-spacing approximation" yields accurate results when the drafts of the cylinders are small in comparison with the distance between cylinders, even if the distance is not very large compared with the wavelength. The analytical formula for resonance frequencies of the two-cylinder system is obtained using the "wide-spacing approximation". The corresponding transmission coefficients are also determined.