Jezabel Curbelo, Ana M. Mancho
This article proposes spectral numerical methods to solve the time evolution of a convection problem with viscosity depending exponentially on temperature. The set-up is a 2D domain with periodic boundary conditions along the horizontal coordinate. At a fixed aspect ratio, the analysis is assisted by bifurcation techniques such as branch continuation, which has proven to be a useful, systematic method for gaining insight into the possible stationary solutions satisfied by the basic equations. Stable stationary solutions become unstable through a Hopf bifurcation, after which the time-dependent regime is solved by the spectral techniques proposed for that purpose in this article. The morphology of the plume is described and compared with others obtained in the literature.
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http://arxiv.org/abs/1201.3298
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