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Effects of a magnetic field on chaos for low Prandtl number convection in porous media. (English) Zbl 1215.76087
Summary: The effects of a magnetic field on the route to chaos in a fluid-saturated porous layer were investigated based on the approach of dynamical systems. A low dimensional Lorenz-like model was obtained using Galerkin truncated approximation. The presence of a magnetic field helped delay the convective motion. The transition from steady convection to chaos via a Hopf bifurcation produced a limit cycle which may be associated with a homoclinic explosion at a slightly subcritical value of the Rayleigh number.
MSC:
76S05Flows in porous media; filtration; seepage
76W05Magnetohydrodynamics and electrohydrodynamics
76E25Stability and instability of magnetohydrodynamic and electrohydrodynamic flows
76E06Convection (hydrodynamic stability)
References:
[1]Lorenz, E.N.: Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130–141 (1963) · doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
[2]Chen, Z.M., Price, W.G.: On relation between Rayleigh-Bénard convection and Lorenz system. Chaos Solitons Fractals 28, 571–578 (2006) · Zbl 1084.76026 · doi:10.1016/j.chaos.2005.08.010
[3]Kimura, S., Schubert, G., Straus, J.M.: Route to chaos in porous-medium thermal convection. J. Fluid Mech. 166, 305–324 (1986) · Zbl 0632.76111 · doi:10.1017/S0022112086000162
[4]Vadasz, P., Olek, S.: Transitions and chaos for free convection in a rotating porous layer. Int. J. Heat Mass Transfer 41, 1417–1435 (1998) · Zbl 0935.76085 · doi:10.1016/S0017-9310(97)00265-2
[5]Vadasz, P., Olek, S.: Weak turbulence and chaos for low Prandtl number gravity driven convection in porous media. Transp. Porous Media 37, 69–91 (1999) · doi:10.1023/A:1006522018375
[6]Vadasz, P., Olek, S.: Route to chaos for moderate Prandtl number convection in a porous layer heated from below. Transp. Porous Media 41, 211–239 (2000) · doi:10.1023/A:1006685205521
[7]Vadasz, P.: Local and global transitions to chaos and hysteresis in a porous layer heated from below. Transp. Porous Media 37, 213–245 (1999) · doi:10.1023/A:1006658726309
[8]Vadasz, P.: Small and moderate Prandtl number convection in a porous layer heated from below. Int. J. Energy Res. 27, 941–960 (2003) · doi:10.1002/er.927
[9]Sparrow, C.: The Lorenz Equations: Bifurcations, Chaos and Strange Attractors. Springer, New York (1982)
[10]Vadasz, J.J., Roy-Aikins, J.E.A., Vadasz, P.: Sudden or smooth transitions in porous media natural convection. Int. J. Heat Mass Transf. 48, 1096–1106 (2005) · Zbl 1189.76612 · doi:10.1016/j.ijheatmasstransfer.2004.09.039
[11]Jawdat, J.M., Hashim, I.: Low Prandtl number chaotic convection in porous media with uniform internal heat generation. Int. Commun. Heat Mass Transf. 37, 629–636 (2010) · doi:10.1016/j.icheatmasstransfer.2010.03.011
[12]Rucklidge, A.M.: Chaos in models of double convection. J. Fluid Mech. 237, 209–229 (1992) · Zbl 0747.76089 · doi:10.1017/S0022112092003392
[13]Rucklidge, A.M.: Chaos in magnetoconvection. Nonlinearity 7, 1565–1591 (1994) · Zbl 0813.35093 · doi:10.1088/0951-7715/7/6/003
[14]Bekki, N., Moriguchi, H.: Temporal chaos in Boussinesq magnetoconvection. Phys. Plasmas 14, Art. no. 012306 (2007)
[15]Garandet, J.P., Alboussiere, T., Moreau, R.: Buoyancy-driven convection in a rectangular enclosure with a transverse magnetic field. Int. J. Heat Mass Transf. 35, 741–748 (1992) · Zbl 0753.76194 · doi:10.1016/0017-9310(92)90242-K
[16]Nield, D.A.: Impracticality of MHD convection in a porous medium. Transp. Porous Media 73, 379–380 (2008) · doi:10.1007/s11242-007-9181-9