accretion disc theory for vorticity and magnetic field growth

In addition to the scalar Shakura-Sunyaev αss turbulent viscosity transport term used in simple analytic accretion disc modeling, a pseudoscalar transport term also arises. The essence of this term can be captured even in simple models for which vertical averaging is interpreted as integration over a half-thickness and one separately studies each hemisphere. The additional term highlights a complementarity between mean field magnetic dynamo theory and accretion disc theory treated as a mean field theory. Such pseudoscalar terms have been studied, and can lead to large scale magnetic field and vorticity growth. Here it is shown that vorticity can grow even in the simplest azimuthal and half-height integrated disc model, for which mean quantities depend only on radius. The simplest vorticity growth solutions seem to have scales and vortex survival times consistent those required for facilitating planet formation. Also it is shown that when the magnetic back-reaction is included to lowest order, the pseudoscalar driving the magnetic field growth and that driving the vorticity growth will behave differently with respect to shearing and non-shearing flows: the former can reverse sign in the two cases, while the latter will have the same sign.