Implications of mean field accretion disc theory for vorticity and magnetic field growth

In addition to the scalar Shakura-Sunyaev alpha (ss) turbulent viscosity tr ansport term used in simple analytic accretion disc modelling, a pseudo-sca lar transport term also arises. The essence of this term can be captured ev en in simple models for which vertical averaging is interpreted as integrat ion over a half-thickness and each hemisphere is separately studied. The ad ditional term highlights a complementarity between mean field magnetic dyna mo theory and accretion disc theory treated as a mean field theory. Such ps eudo-scalar terms have been studied, and can lead to large-scale magnetic f ield and vorticity growth. Here it is shown that vorticity can grow even in the simplest azimuthal and half-height integrated disc model, for which me an quantities depend only on radius. The simplest vorticity growth solution s seem to have scales and vortex survival times consistent with those requi red for facilitating planet formation. In addition, it is shown that, when the magnetic back-reaction is included to lowest order, the pseudo-scalar d riving the magnetic field growth and that driving the vorticity growth will behave differently with respect to shearing and non-shearing flows: the fo rmer pseudo-scalar can more easily reverse sign in the two cases.