A wide angle and high Mach number parabolic equation

Area of Science:

• Acoustics
• Atmospheric science
• Wave propagation

Background:

• Traditional parabolic equations for advected acoustic waves rely on small Mach number and narrow angle assumptions, limiting their atmospheric acoustics applications.
• Existing models struggle with accuracy at large distances and significant atmospheric variations.

Purpose of the Study:

• To derive a parabolic equation solution for advected acoustic waves that is valid beyond small Mach number and narrow angle limitations.
• To develop a model suitable for atmospheric acoustics at frequencies of 0.1 Hz and above.
• To account for cumulative effects of atmospheric variable derivatives for accurate long-range sound propagation.

Main Methods:

• Derived a parabolic equation solution in the weak shear limit, applicable to atmospheric acoustics.
• Scaled variables to manage small derivative terms of sound speed, density, and wind speed.
• Incorporated linear terms of first derivatives of atmospheric variables for long-range validity.
• Developed a scalar wave equation for advected waves, addressing non-commuting depth operators.

Main Results:

• A novel parabolic equation is presented, removing prior restrictive assumptions.
• The derived equation accounts for atmospheric variations, improving accuracy for sound propagation.
• An approximate factorization addresses challenges posed by non-commuting operators, enabling outgoing/incoming wave separation.

Conclusions:

• The new parabolic equation offers improved validity and accuracy for atmospheric acoustics, particularly at lower frequencies.
• The method effectively models long-range sound propagation by considering atmospheric gradients.
• This work provides a more robust framework for analyzing acoustic wave behavior in complex atmospheric environments.