Effects of a small magnetic field on homoclinic bifurcations in a low-Prandtl-number fluid
| Autor: | Basak, Arnab, Kumar, Krishna |
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| Rok vydání: | 2016 |
| Předmět: | |
| Zdroj: | Chaos 26(123123):1-16 (2016) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1063/1.4972560 |
| Popis: | Effects of a uniform magnetic field on homoclinic bifurcations in Rayleigh-B\'{e}nard convection in a fluid of Prandtl number $Pr = 0.01$ are investigated using direct numerical simulations (DNS). A uniform magnetic field is applied either in the vertical or in the horizontal direction. For a weak vertical magnetic field, the possibilities of both forward and backward homoclinic bifurcations are observed leading to a spontaneous merging of two limit cycles into one as well as a spontaneous breaking of a limit cycle into two for lower values of the Chandrasekhar's number ($Q\leq 5$). A slightly stronger magnetic field makes the convective flow time independent giving the possibility of stationary patterns at the secondary instability. For horizontal magnetic field, the $x\leftrightharpoons y$ symmetry is destroyed and neither a homoclinic gluing nor a homoclinic breaking is observed. Two low-dimensional models are also constructed: one for a weak vertical magnetic field and another for a weak horizontal magnetic field. The models qualitatively capture the features observed in DNS and help understanding the unfolding of bifurcations close to the onset of magnetoconvection. Comment: 17 pages, 18 figures |
| Databáze: | arXiv |
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