On dynamo action in a steady flow at large magnetic reynolds number

摘要

Recently Galloway and Frisch (1986) have reported numerical results for kinematic dynamos caused by steady spatially periodic flows at large magnetic Reynolds number,Rm. For their special case of two-dimensional (z*-independent) motion, the asymptotic theory developed by Childress (1979) is valid as Rm#x2192;#x221E;. According to that theory models of given z*-wave number,j*, grow at a rate,p*, proportional toRm#x2212;#xBD;. This power law behaviour was not isolated by Galloway and Frisch (1986), who considered values ofRmup to 1500. Nevertheless, their numerical values forp* agree well with the asymptotic theory developed by Soward (1987). That asymptotic theory, which depends upon a second expansion parameter linked toj*, is outlined briefly. It shows that the ChildressRm#x2212;#xBD;-power law is achieved in the limitj*(Rm#x2212;#xBD;InRm)#x2192;0. Moreover, when the results of the double expansion are applied to the Galloway and Frischj* equals;2 model, for which detailed results are available, it is clear thatRm#x2212;#xBD;-power law is achieved only whenRmexceeds approximately 104.