You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
Surface waves in coupled channels and acoustic waves in<br />
coupled ocean layers<br />
I. Yu. Popov ∗ , L.V.Gortinskaya ∗ , E.S.Tesovskaya ∗<br />
The problem of surface water waves in the case of constant depth reduces to<br />
two-dimensional Helmholtz equation. The system of two channels laterally coupled<br />
through small windows is considered. We assume that the Neumann boundary conditions<br />
takes place. The existence of coupling window leads to the existence of quasi<br />
eigenvalue (resonance) near the second (and third, fourth, etc.) threshold. We construct<br />
the asymptotics (in the width of windows) of resonances for the Neumann<br />
Laplacian for this system. The cases of one coupling window, finite number of windows<br />
and periodic system of windows are considered. We use method of matching<br />
of asymptotic expansions of solutions of boundary value problems by A.M.Il’in. Also<br />
the scattering problem is considered for the case of one and two coupling windows.<br />
The developed technique as been applied to the problem of acoustic waves in<br />
layered structures particularly in ocean. Propagation of acoustic waves in weakly<br />
coupled layers of water of different densities(typical ocean structure) is described. If<br />
the layers are coupled in small regions then resonant scattering of acoustic waves is<br />
observed. The direction diagrams for these waves are constructed.<br />
∗∗ St.-Petersburg State University of Information Technologies, <strong>Mechanics</strong> and Optics, Kronverkskii<br />
49, St.-Petersburg, 197101, Russia.<br />
Figure 1: Direction diagrams for different angels of incoming wave (left picture) and<br />
different distance between regions of coupling (right picture)<br />
179
Change language