Abstract:

Does the topic of this session make sense? The existence of a connection between chaos and predictability in long-range sound propagation is investigated by asymptotically analyzing the ray solution. Along a regular ray, the Laplacian of the phase oscillates about zero so that the solution of the first transport equation [Jensen et al., Computational Ocean Acoustics (American Institute of Physics, New York, 1994), p. 150] does not grow or decay exponentially. Along a chaotic ray, the Laplacian of the phase tends to be positive so that amplitude decays exponentially. The second transport equation (a correction that is not usually implemented) is identical to the first transport equation but with a forcing function that decays exponentially along a chaotic ray. This problem is closely related to the classical secular problem y[sup ']+y=exp(-x). Numerical techniques are applied to solve the transport equation and illustrate secularity, which implies that the ray solution is nonuniform and breaks down at long range when chaos exists. [Work supported by ONR.]