High frequency normal mode statistics in a shallow water waveguide: the effect of random linear internal waves.

Using transport theory and Monte Carlo numerical simulation, the statistical properties of mode propagation at a frequency of 1 kHz are studied in a shallow water environment with random sound-speed perturbations from linear internal waves. The environment is typical of summer conditions in the mid-Atlantic bight during the Shallow Water 2006 experiment. Observables of interest include the second and fourth moments of the mode amplitudes, which are relevant to full-field mean intensity and scintillation index. It is found that mode phase randomization has a strong adiabatic component while at the same time mode coupling rates are significant. As a consequence, a computationally efficient transport theory is presented, which models cross-mode correlation adiabatically, but accounts for mode coupling using the mode energy equations of Creamer [(1996). J. Acoust. Soc. Am. 99, 2825-2838]. The theory also has closed-form expressions for the internal wave scattering matrix and a correction for an edge effect. The hybrid transport theory is shown to accurately reproduce many statistical quantities from the Monte Carlo simulations.