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\samstitle{Nonlinear Multi-components Diffusive Convection in Rotating Cylindrical annulus }
\samsauthor{O. A.I. Noreldin$^*$ } { osman@aims.edu.gh } %% Put $^*$ after the surname of the presenting author
\samsauthor{P. Sibanda} { sibandap@ukzn.ac.za\
School of Mathematics, Statistics \& Computer Science
University of KwaZulu-Natal\
Private Bag X01\
Scottsville\
Pietermaritzburg 3209\
South Africa }
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In this talk, we investigate thermal convective instabilities in the form of thermal Rossby waves in a cylindrical annulus rotating about its axis of symmetry. The annulus has contained a fluid with three different diffusing properties and heated from outside. The conditions for the onset of the critical Rayleigh number for thermal Rossby wave is derived and the influence of parameters such as Prandtl number, Coriolis force and concentration Rayleigh numbers on the onset of convection are discussed. In nonlinear regime, investigated the dynamics of evolution amplitudes convection that by driving a set of ordinary differential equations that describes time evolution of a multi-component convection.
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\begin{thebibliography}{9}
\bibitem{simitev2011double}
Simitev, R D.
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Physics of the Earth and Planetary Interiors, 186: 183-190, 2011.
\bibitem{Griffiths}
Griffiths R W.
\textit{The influence of a third diffusing component upon the onset of convection},
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\bibitem{Busse}
Busse, F H.
\textit{ Is low Rayleigh number convection possible in the Earth`s core},
Geophysical Research Letters, 29: 1105, 2002.
\bibitem{Turner}
Turner, J S.
\textit{ Multicomponent convection},
Annual review of fluid mechanics, 17: 1-44, 1986
\end{thebibliography}
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