High-frequency normal-mode statistics in shallow water: the combined effect of random surface and internal waves

In an earlier article, the statistical properties of mode propagation were studied at a frequency of 1 kHz in a shallow water environment with random sound-speed perturbations from linear internal waves, using a hybrid transport theory and Monte Carlo numerical simulations. Here, the analysis is extended to include the effects of random linear surface waves, in isolation and in combination with internal waves. Mode coupling rates for both surface and internal waves are found to be significant, but strongly dependent on mode number. Mode phase randomization by surface waves is found to be dominated by coupling effects, and therefore a full transport theory treatment of the range evolution of the cross mode coherence matrix is needed. The second-moment of mode amplitudes is calculated using transport theory, thereby providing the mean intensity while the fourth-moment is calculated using Monte Carlo simulations, which provides the scintillation index. The transport theory results for second-moment statistics are shown to closely reproduce Monte Carlo simulations. Both surface waves and internal waves strongly influence the acoustic field fluctuations.