Fluctuation dynamos at high Rm : a succesful mean field approach

By Wietze Herreman (LRA, ENS)

Room D18 (2nd floor) at ENS, 24 rue Lhomond, 13:30 to 14:00

In many dynamo theory textbooks, the classical high conductivity limit analysis for fluctuation flows is often one of the first examples that leads to explicit formulas for alpha and beta tensors. From numerical simulations of dynamo problems at high Rm, we know however that these formulas generally do not represent physical reality. In the present work, we reconsider a mean field theory which only uses temporal averaging. We reveal how general spatially dependent formulas for alpha and beta tensors,can in fact be drastically simplified for broad classes of fluctuation flows, and that this leads to a much simpler mean field effect than expected. The mean field itself satisfies an induction equation, with a spatially dependent magnetic pumping. We test our findings on a well chosen example, in which we realise a G.O. Roberts magnetic pumping flow, using periodic or even random fluctuation flows at low magnetic diffusivity. This is probably the first time that a SOCA mean-field theory models the dynamo correctly in the high conductivity limit. The theory is then applied to study whether single inertial waves can drive mean field dynamos in different fluid domains.