Validity of the Markov approximation in ocean acoustics

Area of Science:

• Ocean acoustics
• Wave propagation in random media
• Statistical physics

Background:

• Moment equations and path integrals are used for wave propagation in random media, notably in ocean acoustics.
• These methods rely on the Markov approximation, which requires a small expansion parameter for validity.
• Previous studies successfully applied fourth moment equations to the Mid-Ocean Acoustic Transmission Experiment (MATE), despite a high Kubo number.

Purpose of the Study:

• To resolve the contradiction between the successful application of moment equations to MATE and the high Kubo number observed.
• To identify a more appropriate expansion parameter for wave propagation in the specific conditions of the ocean.
• To justify the use of moment equations in ocean acoustics under realistic conditions.

Main Methods:

• Analysis of the expansion parameter for the Markov approximation in wave propagation.
• Comparison of the standard Kubo number with a newly derived parameter using van Kampen's methodology.
• Evaluation of the new parameter against the experimental conditions of the MATE.

Main Results:

• The standard Kubo number is found to be overly pessimistic for ocean acoustic scenarios.
• A new, necessary, and sufficient expansion parameter is derived, which is significantly smaller than the Kubo number.
• This new parameter is shown to be small for the MATE experimental regime.

Conclusions:

• The newly derived parameter justifies the application of moment equations and path integrals to ocean acoustics problems.
• The Markov approximation is valid for MATE, resolving the previous contradiction.
• The findings provide a more accurate theoretical basis for understanding wave propagation in random ocean environments.