LINTON, C.M., 2011. Water waves over arrays of horizontal cylinders: band gaps and Bragg resonance. Journal of Fluid Mechanics, 670, pp.504-526.
The existence of a band-gap structure associated with water waves propagating over
infinite periodic arrays of submerged horizontal circular cylinders in deep water is
established. Waves propagating at right angles to the cylinder axes and at an oblique
angle are both considered. In each case an exact linear analysis is presented with
numerical results obtained by solving truncated systems of equations. Calculations for
large finite arrays are also presented, which show the effect of an incident wave having
a frequency within a band gap – with the amount of energy transmitted across the
array tending to zero as the size of the array is increased. The location of the band gaps
is not as predicted by Bragg’s law, but we show that an approximate determination
of their position can be made very simply if the phase of the transmission coefficient
for a single cylinder is known.