  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.
