Ray convergence in a flux-like propagation formulation

Area of Science:

• Underwater acoustics
• Waveguide propagation modeling
• Computational physics

Background:

• Energy flux formulation simplifies waveguide propagation but omits convergence and modal interference.
• Incoherent mode sum is related to energy flux, enabling efficient algorithms for reverberation and target echo strength.

Purpose of the Study:

• To develop a hybrid formulation for waveguide propagation that includes convergence effects with minimal computational overhead.
• To offer efficient computational solutions for acoustic propagation by evaluating modal intensity cross terms.

Main Methods:

• Starting with a coherent mode sum, rapid interference is rejected while retaining beats on a ray cycle distance scale.
• Modal intensity cross terms are evaluated using Taylor expansions, reducing a double summation to a single numerical sum via analytical solutions.
• Three solutions are derived: an efficient analytical-numerical hybrid, a local range average, and a local depth average.

Main Results:

• The hybrid formulation successfully incorporates convergence into waveguide propagation models.
• Favorable comparisons are made between the three proposed solutions and the Orca wave model in an upward refracting duct.
• A relationship between averaging window size, effective modes, and the waveguide invariant is established.

Conclusions:

• The hybrid model provides a computationally efficient method to include convergence in waveguide propagation.
• The derived solutions offer practical alternatives for modeling acoustic phenomena in complex environments.
• The study highlights the connection between spatial averaging, modal solutions, and waveguide invariants.