A Legendre-Galerkin spectral method for constructing atmospheric acoustic normal modes

Area of Science:

• Atmospheric acoustics
• Computational physics
• Numerical methods

Background:

• Atmospheric acoustic normal modes are crucial for understanding sound propagation.
• Previous methods for calculating these modes can be computationally intensive.
• Modeling sound propagation requires accurate representation of ground impedance.

Purpose of the Study:

• To develop and apply a novel Legendre-Galerkin spectral method for atmospheric acoustic normal modes.
• To replace complex eigenvalue searches with a more tractable complex symmetric matrix eigenvalue problem.
• To accurately compute the acoustic field and validate the method against established programs.

Main Methods:

• Application of the Legendre-Galerkin spectral method to project acoustic normal modes onto Legendre polynomials.
• Formulation of a complex symmetric matrix eigenvalue problem to find modal eigenvalues.
• Utilizing readily available public domain software for solving the matrix eigenvalue problem.
• Computation of the acoustic field from a harmonic point source using the derived normal modes.

Main Results:

• The method successfully constructs atmospheric acoustic normal modes above level ground with complex impedance.
• The complex symmetric matrix formulation avoids the need for prior knowledge of eigenvalue locations.
• The computed acoustic field includes discrete modes radiating into the upper atmosphere.
• Validation of the acoustic field calculation through comparison with the fast field program.

Conclusions:

• The Legendre-Galerkin spectral method provides an efficient and accurate approach for calculating atmospheric acoustic normal modes.
• The complex symmetric matrix eigenvalue problem simplifies modal analysis and enhances computational feasibility.
• The method's validity is confirmed by its agreement with established acoustic propagation models.