Dynamically orthogonal narrow-angle parabolic equations for stochastic underwater sound propagation. Part II:...

Area of Science:

• Underwater acoustics
• Computational physics
• Wave propagation modeling

Background:

• Accurate modeling of acoustic fields in uncertain underwater environments is crucial.
• Stochastic methods are needed to capture variations in sound speed, bathymetry, and source location.
• Existing methods like Monte Carlo simulations are computationally intensive.

Purpose of the Study:

• To exemplify and describe the properties and capabilities of stochastic dynamically orthogonal narrow-angle parabolic equations (DO-NAPEs).
• To validate DO-NAPE results against deterministic solutions and direct Monte Carlo predictions.
• To assess the computational advantages and stochastic convergence of DO-NAPEs.

Main Methods:

• Application of DO-NAPEs to three 2D stochastic test cases (range-independent and range-dependent).
• Inclusion of uncertainties in sound speed, bathymetry, and source location.
• Validation against analytical solutions and direct Monte Carlo (MC) predictions of acoustic pressure and transmission loss.

Main Results:

• DO-NAPEs accurately predict stochastic range-dependent acoustic fields and non-Gaussian probability distributions.
• Significant computational savings (several orders of magnitude) compared to direct MC methods.
• DO-NAPEs provide accurate statistics (mean, variance, multiple modes, full distributions) and reconstructed realizations.

Conclusions:

• DO-NAPEs offer a computationally efficient and accurate approach for modeling stochastic acoustic fields in complex underwater environments.
• The method's coupling properties and adaptive nature effectively handle dominant uncertainties.
• DO-NAPEs outperform traditional methods in terms of speed and accuracy for predicting complex acoustic field statistics and realizations.