Communications in Mathematical Sciences

Volume 13 (2015)

Number 8

Wave propagation in underwater acoustic waveguides with rough boundaries

Pages: 2005 – 2052



Christophe Gomez (Aix Marseille Université, CNRS, Marseille, France)


In underwater acoustic waveguides a pressure field can be decomposed over three kinds of modes: the propagating modes, the radiating modes, and the evanescent modes. In this paper, we analyze the effects produced by a randomly perturbed free surface and an uneven bottom topography on the coupling mechanism between these three kinds of modes. Using an asymptotic analysis based on a separation of scales technique we derive the asymptotic form of the distribution of the forward mode amplitudes. We show that the surface and bottom fluctuations affect the propagating-mode amplitudes mainly in the same way. We observe an effective amplitude attenuation which is mainly due to the coupling between the propagating modes themselves. However, for the highest propagating modes this mechanism is stronger and due to an efficient coupling with the radiating modes.


acoustic waveguides, random media, asymptotic analysis

2010 Mathematics Subject Classification

35Q99, 60F05, 76B15

Published 3 September 2015