Ray and wave chaos in underwater acoustics

Date of Award




Degree Name

Doctor of Philosophy (Ph.D.)


Applied Marine Physics/Ocean Engineering

First Committee Member

Frederick D. Tappert - Committee Chair


Solutions of the linear parabolic wave equation and nonlinear parabolic ray equation for shallow water sound propagation are analyzed when a small range-dependent perturbation, in the form of a smooth bathymetric variation, is introduced in the environment.Ray trajectories exhibit, under certain conditions, stochastic or chaotic behavior, called ray chaos, and exponential sensitivity to changes in the initial conditions. This kind of behavior is analyzed and quantified by means of the Lyapunov exponent. One of the most important features of the chaotic ray trajectories proved to be the lack of reversibility. The limitations of the ray equation to make predictions is also studied.Wave chaos, if it exists, would be chaotic behavior in the sense of exponential divergence or unpredictability of finite frequency acoustic wave fields, that is, solutions to the parabolic wave equation. However, finite frequency acoustic wave fields do not exhibit chaotic behavior in the sense of exponential divergence or unpredictability. Although the acoustic fields are found to be extremely complex and apparently random, there is no evidence that the solutions, even at high frequencies, behave unpredictably. Also, the acoustic wave fields are reversible, even when their ray counterparts are not. Thus the search for wave chaos is negative.


Physical Oceanography; Engineering, Mechanical; Physics, Acoustics

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