Normal modes analysis for sound waves in an ocean with an ice cap and a perfectly reflecting bottom

Abstract

The normal mode analysis for acoustic waves in a stratified ocean with an ice cap and a perfectly reflection bottom is considered in the paper. Using a transmutation method we obtain a result on the spectrum distribution, and then we study the problem of determining the refraction index n(z). Using asymptotic method we obtain a number of asymptotic estimtes for eigenvalues. These results are used to determine the positions and sizes of the jump discontinuity of n(z).

Keywords:

• Holmholtz equation
• wave guides with ice cover
• asymtotic estimate for eigenvalues
• refraction index

†Mathematics Department, Zhongshan University, GuangZhou 510275, China

‡Department of Mathematics, University of Tennssee at Chattanooga, Chattanooga, TN 37403 U.S.A.

†Mathematics Department, Zhongshan University, GuangZhou 510275, China

‡Department of Mathematics, University of Tennssee at Chattanooga, Chattanooga, TN 37403 U.S.A.

Notes

†Mathematics Department, Zhongshan University, GuangZhou 510275, China

‡Department of Mathematics, University of Tennssee at Chattanooga, Chattanooga, TN 37403 U.S.A.