Date of Award

12-2013

Degree Name

Master of Science

Department

Mechanical and Aeronautical Engineering (to 2013)

First Advisor

Dr. Tianshu Liu

Second Advisor

Dr. Parviz Merati

Third Advisor

Dr. Christopher Cho

Fourth Advisor

Dr. Javier Martin Montefort-Sanchez

Access Setting

Masters Thesis-Open Access

Abstract

In this work, the system of equations for a large- scale long lived rotating layer of fluid with the deformable upper free surface and non-deformable lower free surface heated underneath has been reviewed and derived. The quasi-geostrophic approximation, the beta effect and the method of multi-scale expansions have been employed to and as a result, an equation governing the evolution of large-scale perturbations, has been derived. The effect of each term present in the upper surface deformation equation has been analyzed and the analytical solutions have been obtained by virtue of employing auxiliary Riccati equation method. The soliton solutions obtained contributes to the sustenance of the vortex structure of the long-lived rotating layer of fluid due to the existence of two terms namely the nonlinear term or the so-called beta effect and the diffusion term resulted from the presence ofheating energy from below.

The solution obtained, has been also applied to the case of long-lived vortex structure of the Great red spot of Jupiter and the results for the large-scale perturbations and averaged dominant terms of non-dimensional components of the velocity fields have been presented. The results show the correlation between the heating of the fluid motion from the lower layers, which is one of the fundamental features of the Great Red spot of Jupiter, and the sustenance ofthe vortex structure.

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