Vorticity and magnetic dynamo from subsonic expansion waves

Abstract: This work concentrates on the effect of an irrotational forcing on a magnetized flow in the presence of rotation, baroclinicity, shear, or a combination of them. By including magnetic field in the model we can evaluate the occurrence of dynamo on both small and large scales. We aim at finding what are the minimum ingredients needed to trigger a dynamo instability and what is the relation between dynamo and the growth of vorticity. We use the Pencil code to run resistive MHD direct numerical simulations. We report no dynamo in all cases where only rotation is included, regardless on the equation of state. Conversely, the inclusion of a background sinusoidal shearing profile leads to an hydrodynamic instability that produces an exponential growth of the vorticity at all scales, starting from small ones. This is know as vorticity dynamo. The onset of this instability occurs after a rather long temporal evolution of several thousand turbulent turnover times. The vorticity dynamo in turn drives an exponential growth of the magnetic field, first at small scales, then also at large one. The instability then saturates and the magnetic field approximately reaches equipartition with the turbulent kinetic energy. During the saturation phase we can observe a winding of the magnetic field in the direction of the shearing flow. By varying the intensity of the shear we see that the growth rates of this instability change. The inclusion of the baroclinic term delays the onset of the vorticity dynamo but leads to a more rapid growth. We demonstrate how in the presence of shear, even a purely irrotational forcing amplifies the field to equipartition. At the same time, we confirm how this forcing alone does not lead to vorticity nor magnetic field growth, and this picture does not change in the presence of rotation or baroclinicity up to $256^3$ meshpoints.