Alpha tensor and dynamo excitation in turbulent fluids with anisotropic conductivity fluctuations. Issue 3 (7th February 2023)

• Record Type: Journal Article
• Authors: Gressel, Oliver; Rüdiger, Günther; Elstner, Detlef
• Is Part Of: Astronomische Nachrichten. Volume 344:Issue 3(2023)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2023-02-07
• Subjects: astrophysical plasma -- dynamo theory; Astronomy -- Periodicals; 520.5
• DOI: 10.1002/asna.20210039
• Languages: English
• ISSNs: 0004-6337

Abstract

Abstract: A mean‐field theory of the electrodynamics of a turbulent fluid is formulated under the assumption that the molecular electric conductivity is correlated with the turbulent velocity fluctuation in the (radial) direction, g $$ \kern0.0em \boldsymbol{g}\kern0.1em $$ . It is shown that for such homogeneous fluids a strong turbulence‐induced field advection anti‐parallel to g $$ \kern0.0em \boldsymbol{g}\kern0.1em $$ arises almost independently of rotation. For rotating fluids, an extra α $$ \alpha $$ effect appears with the known symmetries and with the expected maximum at the poles. Fast rotation, however, with Coriolis number exceeding unity suppresses this term. Numerical simulations of forced turbulence using the nirvana code demonstrate that the radial advection velocity, γ $$ \gamma $$, always dominates the α $$ \alpha $$ term. We show finally with simplified models that α 2 $$ {\alpha}^2 $$ dynamos are strongly influenced by the radial pumping: for γ < α $$ \gamma <\alpha $$ the solutions become oscillatory, while for γ > α $$ \gamma >\alpha $$ they become highly exotic if they exist at all. In conclusion, dynamo models for slow and fast solid‐body rotation on the basis of finite conductivity–velocity correlations are unlikely to work, at least for α 2 Ω $$ {\alpha}^2\Omega $$ dynamos without strong shear.