The UTC Graduate School is pleased to announce that Mohammad Khan will present Doctoral research titled, Numerical Evaluation of Wavenumbers of the Acoustic Waves Propagating in an Ice-Covered Ocean on 03/03/2023 at 2:00 pm in Lupton 393. Everyone is invited to attend.
Computational Science
Chair: Boris Belinskiy
Co-Chair: Lakmali Weerasena
Abstract:
We consider acoustic wave propagation in a layered ocean waveguide covered by a thick ice cover. Standard separation of variables leads to a Sturm-Liouville problem in the cross-section of the waveguide. We are specifically interested in the two leading modes that are 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 better understand the influence of global warming on ice covers, we study the change of 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 the 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. 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. We also find the analytical, numerical, and asymptotic results for this limiting case. These results were compared with the results of the thick ice model. With the help of our results, we hope to develop the corresponding inverse problem methods for future work to further study the influence of global warming on ice covers.