Research Projects

Research conducted by: Steven Tomsovic, Michael Wolfson, Mike Brown (University of Miami)

Introduction

The three dimensional ocean acts as a waveguide in the vertical coordinate for acoustic transmissions. Lateral refractive index inhomogeneities due to oceanic mesoscale structure allow horizontal refraction to take place, which has been conjectured to play a significant role in the wavefield dynamics at multi-megameter range scales of propagation.

Our work

We have recently developed a numerical model which can investigate the relative importance of horizontal refraction through mesoscale ocean waveguide environments.

If the vertical acoustic modes are assumed uncoupled, then a two-dimensional horizontal model for the propagation of the gravest mode along the depth of the acoustic waveguide can be developed. The problem is cast as a Hamiltonian dynamical system, where range is the independent 'time-like' variable. The potential is then taken as a realization of random field that is characterized by having a single scale and isotropic spectrum of sound speed fluctuations, and is assumed stationary in both range and crossrange. A relative diffusion Fokker-Plank type equation derived for this problem in the formal classical limit reveals analytically that the deterministic system is chaotic in the sense of exponential sensitivity of the ray dynamics to the environment.

A central issue is then to understand the limits of using ray asymptotic methods for predicting the behavior of the wavefield at multi-megameter propagation ranges in enironments prone to classical chaos. Using a Maslov Chapman semiclassical prescription for the wavefield, we have found amazing agreement with what the linear wave equation predicts. To obtain this agreement, good dynamical information is required. This is illustrated in the first figure, where the 'time front' from the semi-classical treatment is overlaid with the wave front from a full wave 'benchmark' solution. The time front shows extensive horizontal multi-pathing, caused by exponentially stretching and folding of the Lagrange manifold as it evolves in phase space. The acoustic transmission here is taken as a plane wave initially, and has a center frequency and bandwidth of 1 Hz. The propagation range is 3,000 km, and this environment is much less benign than what is actually measured in the ocean.

Figures

The 'time front' from the semi-classical treatment is overlaid with the wave front from a full wave 'benchmark' solution. The time front shows extensive horizontal multi-pathing, caused by exponentially stretching and folding of the Lagrange manifold as it evolves in phase space.