Turbulent 2.5 dimensional dynamos

Abstract

We study the dynamo instability driven by a turbulent two dimensional flow with three components of the form (u(x, y, t), v(x, y, t), w(x, y, t)) sometimes referred to as a 2.5 dimensional flow. This type of flows provides an approximation to very fast rotating flows often observed in nature. The low dimensionality of the system allows the investigation of a wide range of fluid Reynolds number Re, magnetic Reynolds number Rm and forcing length scales relative to the domain size that is still prohibited for full three dimensional numerical simulations. We were thus able to determine the properties of the dynamo onset as a function of Re and and the asymptotic behavior of the most unstable mode in the large Rm limit. In particular it has been shown that: In a non-helical flow in an infinite domain the critical magnetic Reynolds number Rmc becomes a constant in the large Re limit. A helical flow always results in dynamo in agreement with mean field predictions. For thin layers for both helical and nonhelical flows the Rmc scales as a power-law of Re. The growth-rate of fastest growing mode becomes independent of Re and Rm when their values are sufficiently large. The most unstable length scale in this limit scales linearly with the forcing length scale. Thus while the mean field predictions are valid, they are not expected to be dominant in the large Rm limit.