Effect of Temperature Modulation on Rotating Magnetoconvection

The convective instability of sinusoidal temperature modulation is examined in rotating Rayleigh–Bénard system with magnetic field imposed externally. The analysis is performed by using Floquet method to find out the magnitude of modulation amplitude required to start oscillatory magnetoconvection. The convective flow appears either harmonically or sub-harmonically with temperature modulation. The variation of modulation amplitude $$a$$ with wave number $$k$$ is observed controlling the parameters Taylor number Ta, Chandrasekhar’s number Q, Prandtl number Pr, Rayleigh number Ra and modulation frequency $$\omega $$ . The critical modulation amplitude $${{a}_{0}}$$ increases with sufficient increase in Chandrasekhar’s number Q or Taylor number Ta. It is found that the small change in Q affects $${{a}_{0}}$$ significantly. However a large change in Ta makes a little variation in $${{a}_{0}}$$ . The frequency of harmonic or sub-harmonic waves at the onset of instability is dependent on modulation frequency $$\omega $$ . The solutions and fluid patterns at the threshold of convection are also investigated. The heat flow within the fluid both in $$xz$$ plane and $$xy$$ plane are explored here.