A reformulation of the Λ−Φ diagram for the prediction of ocean acoustic fluctuation regimes

Abstract

The Λ-Φ diagram was a tool introduced in the late 1970s to predict ocean acoustic fluctuation regimes termed unsaturated, partially saturated, and fully saturated, where internal wave sound speed fluctuations play a dominant role. The Λ-Φ parameters reflect, respectively, the strength of diffraction and the root-mean-square phase fluctuation along a ray path. Oceanographic knowledge of the small scale part of the internal wave spectrum and high angle Fresnel zone formulations now allow a more stable and accurate calculation of these parameters. An empirical relation between the variance of log-intensity and Λ-Φ provides a more accurate border between the unsaturated regime and stronger fluctuations. The diagram is consistent with six short range, deep water experiments in the Pacific, Atlantic, and Arctic oceans with frequencies ranging from 75 to 16 000 Hz. The utility of the Λ-Φ diagram is that it provides one of the few means to inter-compare experiments at different geographic locations, and at different frequencies and ranges.

Comparing Predicted and Observed Strength and Diffraction Parameters for Characterizing Transmissions through a Fluctuating Water Body

“…(3) where represents the extension of the vertical Fresnel zone radius along the selected ray, and is the vertical wavenumber of the medium sound-speed fluctuations, and the curly brackets indicate an average over the spectrum with the perpendicular wavenumber constraint. For details about the quantities and we refer to the approximated formulas provided in [2][3].…”

“…In these works, these parameters are estimated in acoustic channel setups characterized by long range propagation (hundreds of km) and a deep ocean with a sound channel guiding the acoustic waves. Application of this theory for experimental estimation of Λ-Φ parameters can be found in [3][4][5][6][7]. This paper deals with experimental validation of the path integral theory in shallower environment (experimental areas with bottom depth below in the order of few hundred meters) and short range transmissions (below 20 km).…”