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Approximate formulas and physical interpretations for horizontal acoustic modes in a shelf-slope front model
Brendan J DeCourcy1, Ying-Tsong Lin2, William L Siegmann1
1Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York 12180, USA.
The Journal of the Acoustical Society of America
|August 1, 2016
Summary
This study analyzes acoustic modes in ocean shelf-slope fronts using the Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) method. It provides insights into trapped, leaky, and transition modes, validating approximations with numerical solutions.
Area of Science:
- Oceanography
- Acoustics
- Geophysics
Background:
- Shelf-slope fronts are critical oceanographic features influencing acoustic propagation.
- Understanding horizontal acoustic modes is essential for acoustic modeling in these regions.
Purpose of the Study:
- To analytically examine the structure and behavior of horizontal acoustic modes in a 3D shelf-slope front model.
- To develop simple expressions and gain physical insight into different mode types (trapped, leaky, transition).
Main Methods:
- Analytical investigation using the Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) method.
- Determining validity regions for WKBJ approximations based on slope and frontal parameters.
- Employing asymptotic formulas for Hankel functions outside WKBJ validity regions.
Main Results:
- Derived simple expressions for horizontal acoustic modes.
- Identified distinct regions for trapped, leaky, and transition modes.
- Demonstrated high accuracy of combined WKBJ and asymptotic approximations through comparison with numerical solutions.
Conclusions:
- The WKBJ method, augmented by asymptotic formulas, accurately describes horizontal acoustic modes in shelf-slope fronts.
- The findings offer valuable physical insight and improved computational tools for acoustic propagation studies.
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