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In addition, the vanishing viscousity limit of the solutions for viscous lake equations with the Navier type boundary conditions is obtained for both the smooth and non-smooth initial data., The aim of the thesis is to understand the dynamics and interactions between the Ekman layer and thermal layer which are very important issues in the studies of geophysical flows. We obtain some new results on the primitive equations of the atmosphere and the incompressible Navier-Stokes equations with rotating terms. We study the asymptotic limits of the solutions to the initial boundary value problem for the three dimensional primitive equations. We have constructed the asymptotic ansatz which is uniformly valid up to the boundary to derive the quasi-geostrophic equations and the corresponding boundary layer systems. These equations are also important and widely studied in the geophysical flows. The uniform convergence to the solutions for quasi-geostrophic equations is obtained rigorously., Niu Dongjuan., "June 2006.", Adviser: Zhouping Xin., Source: Dissertation Abstracts International, Volume: 68-03, Section: B, page: 1675., Thesis (Ph.D.)--Chinese University of Hong Kong, 2006., Includes bibliographical references (p. 96-106)., Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web., Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web., s in English and Chinese., School code: 1307., http://library.cuhk.edu.hk/record=b6074264, Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)

In addition, the vanishing viscousity limit of the solutions for viscous lake equations with the Navier type boundary conditions is obtained for both the smooth and non-smooth initial data., The aim of the thesis is to understand the dynamics and interactions between the Ekman layer and thermal layer which are very important issues in the studies of geophysical flows. We obtain some new results on the primitive equations of the atmosphere and the incompressible Navier-Stokes equations with rotating terms. We study the asymptotic limits of the solutions to the initial boundary value problem for the three dimensional primitive equations. We have constructed the asymptotic ansatz which is uniformly valid up to the boundary to derive the quasi-geostrophic equations and the corresponding boundary layer systems. These equations are also important and widely studied in the geophysical flows. The uniform convergence to the solutions for quasi-geostrophic equations is obtained rigorously., Niu Dongjuan., "June 2006.", Adviser: Zhouping Xin., Source: Dissertation Abstracts International, Volume: 68-03, Section: B, page: 1675., Thesis (Ph.D.)--Chinese University of Hong Kong, 2006., Includes bibliographical references (p. 96-106)., Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web., Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web., s in English and Chinese., School code: 1307., http://library.cuhk.edu.hk/record=b6074264, Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)