Model for hydromagnetic convection in a magnetized fluid

We consider convection in a horizontally magnetized viscous fluid layer in the gravitational field heated from below with a vertical temperature gradient. Following Rayleigh-Benard scenario and using a general magnetohydrodynamic approach, we obtain a simple set of four ordinary differential equations. In addition to the usual three-dimensional Lorenz model a new variable describes the profile of the induced magnetic field. We show that nonperiodic oscillations are influenced by anisotropic magnetic forces resulting not only in an additional viscosity but also substantially modifying nonlinear forcing of the system. On the other hand, this can stabilize convective motion of the flow. However, for certain values of the model parameters we have identified a deterministic intermittent behavior of the system resulting from bifurcation. In this way, we have identified here a basic mechanism of intermittent release of energy bursts, which is frequently observed in space and laboratory plasmas. Hence, we propose this model as a useful tool for the analysis of intermittent behavior of various environments, including convection in planets and stars. Therefore, we hope that our simple but still a more general nonlinear model could shed light on the nature of hydromagnetic convection.