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# Influence of Imperfect Internal Waves on Long-Range Underwater Acoustic Propagation

[+] Author and Article Information
T. A. Andreeva

Department of Mathematics, Saint-Petersburg State Polytechnic University, Saint-Petersburg, Russia 195251tatiana@phmf.spbstu.ru

W. W. Durgin

Department of Mechanical Engineering, California Polytechnic State University, San Luis Obispo, CA 93407wdurgin@calpoly.edu

S. E. Wojcik

Department of Mechanical Engineering, Worcester Polytechnic Institute, Worcester, MA 01609

J. Comput. Nonlinear Dynam 5(1), 014501 (Nov 12, 2009) (4 pages) doi:10.1115/1.4000322 History: Received August 30, 2008; Revised May 17, 2009; Published November 12, 2009; Online November 12, 2009

## Abstract

This work presents a numerical analysis of the effect of random fluctuations of internal waves on the chaotic dynamics of ray trajectories in ocean acoustics. The Eikonal equation is considered in a form of the second order, nonlinear ordinary differential equation. Random phase modulations in the form of zero mean Gaussian white noise are considered for modeling an imperfectly periodic single mode internal wave. It is shown that in the presence of random fluctuations the intersection of acoustic rays with the ocean surface occurs sooner and becomes more frequent than predicted by deterministic ocean models.

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## Figures

Figure 1

Spectral density of the proposed model presented in Eq. 7 compared with k−2 behavior

Figure 2

Normalized internal waves with two different intensities of random phase modulations

Figure 4

Ray propagation range before intersection with ocean surface occurs r=g(A) computed for the environment for which δ=0.01 and R=11.2 km. (a) D=0, (b) D=0.01, and (c) D=0.05.

Figure 5

Ray propagation range before intersection with ocean surface occurs r=g(R) computed for the environment for which δ=0.01. (a) D=0, (b) D=0.01, and (c) D=0.05.

Figure 3

Bifurcation diagram z=f(R) computed for environment for which δ=0.005, A=1, and D=0

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