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We consider the linear water-wave problem in a periodic channel whichconsists of infinitely many identical containers connected with apertures ofwidth $\epsilon$. Motivated by applications to surface wave propagationphenomena, we study the band-gap structure of the continuous spectrum. We showthat the for small apertures there exists a large number of gaps and also findasymptotic formulas for the position of the gaps as $\epsilon \to 0$: theendpoints are determined within corrections of order $\epsilon^{3/2}$. Thewidth of the first bands is shown to be $O(\epsilon)$. Finally, we give asufficient condition which guarantees that the spectral bands do not degenerateinto eigenvalues of infinite multiplicity.

Spectral gaps for the linear surface wave model in periodic channels