Committee Chair

Belinskiy, Boris P.; Weerasena, Lakmali

Committee Member

Cox, Christopher L.; Wang, Jin; Ebiefung, Aniekan; Gao, Lani


Dept. of Computational Science


College of Engineering and Computer Science


University of Tennessee at Chattanooga

Place of Publication

Chattanooga (Tenn.)


We consider acoustic wave propagation in a layered ocean waveguide covered by thick ice. The standard method of separation of variables leads to a Sturm-Liouville problem in the crosssection of the waveguide. We are specifically interested in the two leading modes, the separated solutions for the maximal eigenvalues. We first consider the homogeneous waveguide. We prove the differentiability of the eigenvalues with respect to the frequency, the monotonicity of the eigenvalues with respect to the frequency, and the existence of the cut-off frequency. We compare these eigenvalues with the eigenvalues for the case of a waveguide with a free surface. To obtain some information about the influence of global warming on ice covers, we find the change in these eigenvalues with respect to air temperature. We further consider a layered medium. Assuming that the speed of propagation varies within the given limits, we develop a numerical algorithm, based on the formalism for layered media, that allows evaluating the minimum and maximum of the wavenumbers of the leading modes for a given continuous profile of the speed and the given values of Young's Modulus and ice thickness. We compare some of these numerical results with the Machine Learning results. After finding numerical results, we compare them with the results of the asymptotic considerations and find the simplified dispersion relations. We further consider the model of pack ice, a limiting case of thick ice. Like the case of thick ice, we find the analytical, numerical, and asymptotic results for this case. These results were compared with the results of the model of thick ice. With the help of our results, we hope to develop the corresponding inverse problem methods for future work to study the influence of global warming on ice covers.


I would like to thank the Computational Science Ph.D. program at the University of Tennessee at Chattanooga and Dr. Anthony Skjellum from the Center for Excellence in Applied Computational Science and Engineering at the University of Tennessee at Chattanooga for providing partial support for this project. This project would not have been possible without Dr. Boris P. Belinskiy and Dr. Lakmali Weerasena. I would also like to thank Dr. Christopher L. Cox, Dr. Jin Wang, Dr. Lani Gao, and Dr. Aniekan A. Ebiefung for providing thoughtful suggestions to improve the overall presentation of the material.


Ph. D.; A dissertation submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Doctor of Philosophy.




Wave guides--Mathematical models; Ocean waves--Mathematical models


ocean waveguide; ice cover; Sturm-Liouville problem; wavenumbers; numerical analysis; machine learning


Applied Mathematics

Document Type

Doctoral dissertations




xii, 108 leaves