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Rayleigh-Bénard convection in rotating fluids. (English) Zbl 1137.76058

Summary: Linear and weakly nonlinear properties of Rayleigh-Benard convection in rotating fluids are investigated. Linear stability analysis is studied to investigate analytically the effect of Coriolis force on gravity-driven convection for idealised stress-free boundary conditions. We have derived a nonlinear one-dimensional Landau-Ginzburg equation with real coefficients near the onset of stationary convection at the supercritical pitchfork bifurcation. A coupled Landau-Ginzburg type equations with complex coefficients near the onset of oscillatory convection at the supercritical Hopf bifurcation are derived and discussed the stability regions of travelling and standing waves.

MSC:

76R10 Free convection
80A20 Heat and mass transfer, heat flow (MSC2010)
76U05 General theory of rotating fluids
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
76E15 Absolute and convective instability and stability in hydrodynamic stability
76E07 Rotation in hydrodynamic stability
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References:

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