{"id":{"repo_id":"utc","oai_identifier":"oai:scholar.utc.edu:theses-1970"},"canonical_url":"https://search.dev.ndltd.org/etd/utc/oai:scholar.utc.edu:theses-1970","repository":{"repo_id":"utc","name":"University of Tennessee - Chattanooga","base_url":"https://scholar.utc.edu/do/oai/"},"display":{"title":"Numerical evaluation of wavenumbers of the acoustic waves propagating in an ice-covered ocean","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Khan, Mohammad"],"institution":"University of Tennessee at Chattanooga","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Belinskiy, Boris P.; Weerasena, Lakmali","Cox, Christopher L.; Wang, Jin; Ebiefung, Aniekan; Gao, Lani","College of Engineering and Computer Science"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T05:47:06Z","subjects":["Wave guides--Mathematical models","Ocean waves--Mathematical models"],"languages":["English","eng"],"rights":[],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"https://scholar.utc.edu/theses/790","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Belinskiy, Boris P.; Weerasena, Lakmali","Cox, Christopher L.; Wang, Jin; Ebiefung, Aniekan; Gao, Lani","College of Engineering and Computer Science"]},{"key":"dc:creator","label":"Author","values":["Khan, Mohammad"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2023-05-01T07:00:00Z"]},{"key":"dc:publisher","label":"Institution","values":["University of Tennessee at Chattanooga","Chattanooga (Tenn.)"]},{"key":"dc:relation","label":"Dc Relation","values":["Masters Theses and Doctoral Dissertations"]},{"key":"dc:type","label":"Dc Type","values":["Doctoral dissertations","Text"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Wave guides--Mathematical models","Ocean waves--Mathematical models"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholar.utc.edu/theses/790"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Dept. of Computational Science","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."]},{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["Numerical evaluation of wavenumbers of the acoustic waves propagating in an ice-covered ocean"]}]}],"canonical_facts":{"dc:contributor":["Belinskiy, Boris P.; Weerasena, Lakmali","Cox, Christopher L.; Wang, Jin; Ebiefung, Aniekan; Gao, Lani","College of Engineering and Computer Science"],"dc:creator":["Khan, Mohammad"],"dc:date":["2023-05-01T07:00:00Z"],"dc:description":["Dept. of Computational Science","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."],"dc:description.abstract":["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."],"dc:identifier":["https://scholar.utc.edu/theses/790"],"dc:language":["English","eng"],"dc:publisher":["University of Tennessee at Chattanooga","Chattanooga (Tenn.)"],"dc:relation":["Masters Theses and Doctoral Dissertations"],"dc:rights":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Wave guides--Mathematical models","Ocean waves--Mathematical models"],"dc:title":["Numerical evaluation of wavenumbers of the acoustic waves propagating in an ice-covered ocean"],"dc:type":["Doctoral dissertations","Text"]},"updated_at":"2026-07-24T05:47:06Z"}