Abstract
Different types of steady columnar patterns in an annular container with a fixed value of the radius ratio are analyzed for a low Prandtl number Boussinesq fluid. The stability of these convection patterns as well as the spatial interaction between them resulting in the formation of mixed modes are numerically investigated by considering the original nonlinear set of Navier-Stokes equations. A detailed picture of the nonlinear dynamics before temporal chaotic patterns set in is presented and understood in terms of symmetry-breaking bifurcations in an O(2)-symmetric system. Special attention is paid to the strong spatial 1:2 resonance of the initially unstable modes with wavenumbers n=2 and n=4, which leads to bistability in the system
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© 2003 Springer Basel AG
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Alonso, A., Net, M., Sánchez, J. (2003). Spatially Resonant Interactions in Annular Convection. In: Buescu, J., Castro, S.B.S.D., da Silva Dias, A.P., Labouriau, I.S. (eds) Bifurcation, Symmetry and Patterns. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7982-8_7
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DOI: https://doi.org/10.1007/978-3-0348-7982-8_7
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9642-9
Online ISBN: 978-3-0348-7982-8
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