Український математичний конгрес - 2009

Микола Сербов (Одеський державний екологічний університет, Одесса, Україна)

The sea and ocean 3D acoustic waveguide: stochastic modeling and chaos phenomena

Stochastic phenomena in the sea and ocean 3D acoustic waveguide are considered. [1]. On the basis of Hamiltonian equations of rays it is studied a dynamics of rays. It has been shown that for acoustic waveguide in a shallow sea with non-level bottom under the rays propagation in a waveguide dependence of the of temporal frequency upon the output angle represents a fractal measure in accordance with Abdullaev-Zaslavsky result. For the ocean 3D acoustic waveguide on the basis of solving the eiconal equations in the Hamiltonian form it has been studied the fractal dynamics, including the chaotic one [2]. There are presented the data of numerical solution of equations for the typical acoustic channel in the North-Atlantic region. The conditions for the Arnold diffusion effect realization are discussed.

[1]. S. Abdullaev S., Zaslavsky G.M., Acoust.Journ. 34:578-586, 1981; D.C. Palmer et al, Geophys.Res.Lett. 15:569-574, 1988.
[2]. A.Glushkov, V.Khokhlov, N.Loboda, etal, Stoch Environ.Res Risk Assess. (Springer) 22:777-788, 2008; V.D. Rusov, A.V. Glushkov, A.A. Svinarenko et al, Advances in Space Research. 42:1614-1617 (2008).