The interaction of convection with rotation and magnetic fields plays an important role in determining the dynamics of many geophysical and astrophysical phenomena. In particular, this interaction is thought to be associated with the generation of large-scale mean flows as observed, for example, in the atmospheres of the giant planets and in the interior of the Sun. This study examines the interaction of convection with rotation and magnetic fields in a simplified, two-dimensional, plane layer model. We consider the case where the fluid rotates about an axis that is oblique to gravity, and is in the presence of a horizontal magnetic field. Also considered, is the case where a horizontal temperature gradient maintains a thermal wind. The fluid is taken to be either incompressible, using the Boussinesq approximation, or compressible, using the anelastic approximation. An examination of the linear behaviour is undertaken to investigate the conditions required for the onset of convection, in a number of different regimes. The existence of an unexpected symmetry is proved in the anelastic case. A pseudospectral numerical code, developed in order to solve the nonlinear equations, is then described. The code is employed to investigate the dynamics in the nonlinear regime and determine the underlying physical interactions for mean flow maintenance. It is shown that whether convection acts to decrease or increase the thermal wind shear, depends on the Prandtl number and the angle of tilt of the rotation vector. Furthermore, the asymmetries introduced when a background stratification is present, manifest themselves in the time-dependent nature of the mean flows driven. We also show that an imposed horizontal magnetic field not only inhibits mean flow generation but also affects the vertical structure of the flows. To finish, a discussion of the applicability of the work to astrophysical phenomena is given
