Research Projects

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Research conducted by: Steven Tomsovic, Nicholas Cerruti, Katherine Hegewisch
Last Modified: 2005

Introduction

The speed of sound in the ocean varies mainly with temperature, pressure and salinity. Near the mid-latitudes, the sound speed has a minimum around 1 km, increases linearly toward the ocean floor and increases exponentially toward the ocean surface. Since sound speed is inversely related to the index of refraction(v=c/n), we note that sound bends toward regions of lower sound speeds (just as light bends towards regions of higher indices of refraction). Thus, sound waves focus along the sound channel axis at 1 km and the sound channel acts as a waveguide for the sound waves.

Internal waves in the ocean are up and down motions of columns of water due to density differences in the ocean. These waves cause range dependent perturbations to the sound speed slightly in the ocean which have been theoretically shown to cause the sound rays to become chaotic.

The Experiments

The Nov 1994 AET(Acoustic Engineering Test) experiment transmitted acoustic(sound) pulse-like signals near the sound channel from San Francisco to Hawaii (roughly 3250 km) and gave experimental evidence that the sound trajectories are predominantly chaotic.

Our work

We use the Garrett-Munk profile to model the sound speed. This model considers the speed due to temperature, pressure, salinity and internal wave contributions. We use the standard parabolic equation (Tappert's equation) to model sound propagation.

We approach the problem from two points of view: classical ray tracing and wave propagation.
Classically: We cast the problem as a Hamiltonian dynamical system, where the range is the 'time-like' variable. We start with a point source and use ray tracing to find the eigenray solutions.
Wave Solution: We use the analogy of Tappert's equation with the Schrodinger equation (hbar => 1/k and t=>r) and use a split step operator method to propagate wave packets.

At a fixed long range from the source, the time fronts as a function of depth take on an 'accordian' pattern. Before analyzing the statistics of the branches of these accordions, we felt it was important to have a model that was going to allow a semiclassical analysis to be successful. We felt that it might be a problem that the wave propagation refracts only from those features of the sound speed model that are larger than its wavelength, while classical rays bend due to all structures in the sound speed model. We constrcted a 'smoothing' of the sound speed model (essentially a low-pass filter which removed structures below a cut-off size) and showed that this 'smoothing' improved the correspondence of ray methods to the wave through the semi-classical construction of the wavefield. This is, of course, a very intuitive idea, but we've shown that it is an important idea that needs to be taken into account. This work was documented in the 2005 paper "Ocean Acoustic wage propagation and ray method correspondence: internal wave fine structure " .

Figures

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Classical rays for the Munk sound speed profile (left) and for the Garrett-Munk(includes internal waves) sound speed profile (right). Initial angles have been restricted to [-10,10] degrees from the sound axis. Note the evidence of caustics.

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The 'accordion' timefront of the pulse arrival for a set of receivers at a fixed range. The white branches are the timefronts for the classical ray propagation through a sound speed model consisting only of Munk's sound speed profile. The contour timefront is for a pulse wave propagated through a sound speed model of Munk's potential and the internal wave effects.