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We present the results of direct numerical simulations of Rayleigh-Bénard convection in the presence of a uniform vertical magnetic field near instability onset. We have done simulations in boxes with square as well as rectangular cross sections in the horizontal plane. We have considered the horizontal aspect ratio η=L(y)/L(x)=1 and 2. The onset of the primary and secondary instabilities are strongly suppressed in the presence of the vertical magnetic field for η=1. The Nusselt number Nu scales with the Rayleigh number Ra close to the primary instability as [{Ra-Ra(c)(Q)}/Ra(c)(Q)](0.91), where Ra(c)(Q) is the threshold for onset of stationary convection at a given value of the Chandrasekhar number Q. Nu also scales with Ra/Q as (Ra/Q)(μ). The exponent μ varies in the range 0.39≤μ≤0.57 for Ra/Q≥25. The primary instability is stationary as predicted by Chandrasekhar. The secondary instability is temporally periodic for Pr=0.1 but quasiperiodic for Pr=0.025 for moderate values of Q. Convective patterns for higher values of Ra consist of periodic, quasiperiodic, and chaotic wavy rolls above the onset of the secondary instability for η=1. In addition, stationary as well as time-dependent cross rolls are observed, as Ra is further raised. The ratio r(o)/Pr is independent of Q for smaller values of Q. The delay in the onset of the oscillatory instability is significantly reduced in a simulation box with η=2. We also observe inclined stationary rolls for smaller values of Q for η=2.

Based on 3D compressible magnetohydrodynamic (MHD) simulations, we explore the interactions between the magnetized wind from a solar-like star and a Mars-like planet – with a gravitionally stratified atmosphere – which is either non-magnetized or hosts a weak intrinsic dipolar field. The primary mechanism for the induction of a magnetosphere around a non-magnetized conducting planet is the pile-up of stellar magnetic fields in the day side region. The magnetopause stand-off distance decreases as the strength of the planetary dipole field is lowered and saturates to a minimum value for the case of a planet with no magnetic field. Global features such as bowshock, magnetosheath, magnetotail and strong current sheets are observed in the imposed magnetosphere. We explore variations in atmospheric mass loss rates for different stellar wind strengths to understand the impact of stellar magnetic activity and plasma winds – and their evolution – on (exo)planetary habitability. In order to simulate a case analogous to the present-day Mars, a planet without atmosphere is considered. The results are found to be in good agreement with observational data from Mars missions such as MGS and MAVEN.

The outflowing magnetized wind from a host star shapes planetary and exoplanetary magnetospheres dictating the extent of its impact. We carry out three-dimensional (3D) compressible magnetohydrodynamic (MHD) simulations of the interactions between magnetized stellar winds and planetary magnetospheres corresponding to a far-out star-planet system, with and without planetary dipole obliquity. We identify the pathways that lead to the formation of a dynamical steady-state magnetosphere and find that magnetic reconnection plays a fundamental role in the process. The magnetic energy density is found to be greater on the night-side than that on the day-side and the magnetotail is comparatively more dynamic. Magnetotail reconnection events are seen to associated with stellar wind plasma injection into the inner magnetosphere. We further study magnetospheres with extreme tilt angles keeping in perspective the examples of Uranus and Neptune. High dipole obliquities may also manifest due to polarity excursions during planetary field reversals. We find that global magnetospheric reconnection sites change for large planetary dipole obliquity and more complex current sheet structures are generated. We discuss the implications of these findings for injection of interplanetary species and energetic particles into the inner magnetosphere, auroral activity and magnetospheric radio emission. This study is relevant for exploring star planet interactions in the solar and extra-solar systems.

A model for three-dimensional Rayleigh-Bénard convection in low-Prandtl-number fluids near onset with rigid horizontal boundaries in the presence of a uniform vertical magnetic field is constructed and analyzed in detail. The kinetic energy K, the convective entropy Φ and the convective heat flux (N u − 1) show scaling behaviour with ǫ = r − 1 near onset of convection, where r is the reduced Rayleigh number. The model is also used to investigate various magneto-convective structures close to the onset. Straight rolls, which appear at the primary instability, become unstable with increase in r and bifurcate to three-dimensional structures. The straight rolls become periodically varying wavy rolls or quasiperiodically varying structures in time with increase in r depending on the values of Prandtl number P r. They become irregular in time, with increase in r. These standing wave solutions bifurcate first to periodic and then quasiperiodic traveling wave solutions, as r is raised further. The variations of the critical Rayleigh number Raos and the frequency ωos at the onset of the secondary instability with P r are also studied for different values of Chandrasekhar's number Q.