Year: 2025
Type: article
Abstract: In MHD dynamo theory well-known necessary criteria for dynamo action are formulated in terms of lower bounds either on the maximum modulus of the velocity field (Childress-type) or the maximum strain of the velocity field (Backus-type). We generalize these criteria for spherical dynamos by introducing a radially varying weight f ( r ) f(r) . The corresponding l ower b ound Reynolds numbers R l b C [ f ] R_{lb}^C [f] (based on velocity) and R l b B [ f ] R_{lb}^B [f] (based on strain) are determined for two types of such weights: a power law profile f ( r ) = r α f(r) = r^\alpha , 0 ≤ α ≤ 2 0\leq \alpha \leq 2 , and an optimal radial profile f v f_\mathbf {v} depending on the velocity field v \mathbf {v} in question. To assess the quality of these lower bounds we compare them with weighted critical Reynolds numbers R c C R_c^C (Childress-type) and R c B R_c^B (Backus-type), respectively, for the onset of dynamo action of the well-known efficient s 2 t 2 s_2t_2 velocity field [Dudley and James, Time-dependent kinematic dynamos with stationary flows , Proc. Roy. Soc. London Ser. A 425 (1989), no. 1869, 407–429] and
Source: Quarterly of Applied Mathematics
DOI: 10.1090/qam/1729
Authors: Ralf Kaiser, Andreas Tilgner
Institutions: University of Bayreuth, University of Göttingen
Language: English
Subfield: Molecular Biology
Domain: Life Sciences
Open Access status: green
OpenAlex ID: W4415438602