Nonlinear Magnetoconvection in a Sparsely Packed Porous Medium
Linear and weakly nonlinear properties of magnetoconvection in a sparsely packed porous medium are investigated. We have obtained the values of Takens-Bogdanov bifurcation points and codimension two bifurcation points by plotting graphs of neutral curves corresponding to stationary and oscillatory c...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
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| Series: | International Journal of Geophysics |
| Online Access: | http://dx.doi.org/10.1155/2011/207123 |
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| Summary: | Linear and weakly nonlinear properties of magnetoconvection in a sparsely
packed porous medium are investigated. We have obtained the values of Takens-Bogdanov bifurcation points and codimension two bifurcation points by plotting
graphs of neutral curves corresponding to stationary and oscillatory convection
for different values of physical parameters relevant to magnetoconvection in a
sparsely packed porous medium near a supercritical pitchfork bifurcation. We
have derived a nonlinear two-dimensional Ginzburg-Landau equation with real
coefficients by using Newell-Whitehead (1969) method. The effect of the parameter
values on the stability mode is investigated and shown the occurrence of
secondary instabilities namely, Eckhaus and Zigzag instabilities. We have studied
Nessult number contribution at the onset of stationary convection. We have also
derived two nonlinear one-dimensional coupled Ginzburg-Landau-type equations
with complex coefficients near the onset of oscillatory convection at a supercritical
Hopf bifurcation and discussed the stability regions of standing and travelling
waves. |
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| ISSN: | 1687-885X 1687-8868 |