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Evolution of Staircase Structures in Diffusive Convection

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Published on: September 5, 2018

Nonlinear progressive wave equation for stratified atmospheres.

B Edward McDonald¹, Andrew A Piacsek

¹Naval Research Laboratory, 4555 Overlook Avenue Southwest, Washington, D.C. 20375, USA. ed@nova.org

The Journal of the Acoustical Society of America

|November 18, 2011

Summary

This study modifies the nonlinear progressive wave equation to account for atmospheric changes, preserving acoustic energy and enabling new solutions for sound propagation in stratified environments.

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Area of Science:

Acoustics
Atmospheric Physics
Computational Physics

Background:

The nonlinear progressive wave equation (NPE) is crucial for modeling sound propagation.
Existing NPE models struggle with atmospheric variations like density and sound speed changes with altitude.
Previous linear models incorporated stratification, but nonlinear models lacked this feature.

Purpose of the Study:

To modify the nonlinear progressive wave equation (NPE) for atmospheric stratification.
To ensure the modified NPE accurately models acoustic energy in changing atmospheric conditions.
To derive new analytic solutions for nonlinear sound waves in stratified atmospheres.

Main Methods:

Incorporated a stratification term into the nonlinear progressive wave equation.
Adapted methods from linear range-stepping calculations and Khokhlov-Zabolotskaya-Kuznetsov models.
Analyzed acoustic energy preservation within a ray tube.

Main Results:

The modified nonlinear progressive wave equation successfully accommodates atmospheric density, pressure, and sound speed variations.
The model preserves acoustic energy in a ray tube.
Analytic similarity solutions were obtained for vertically propagating N waves in isothermal and stratified atmospheres.

Conclusions:

The modified NPE provides a more robust framework for nonlinear acoustics in realistic atmospheric conditions.
This advancement facilitates accurate prediction of sound propagation in environments with significant altitude changes.
The derived solutions offer valuable insights into nonlinear wave behavior in stratified media.