a phenemenological modification of the velocity field has in fact been used by Pouquet [*et al.*]{} (1976) and Zeldovich [*et al.*]{} (1983) (pg. 183) to discuss nonlinear modifications to the alpha effect.

The velocity field ${\bf v}_n$ is taken to be prescribed independent of the magnetic field. We will assume ${\bf v}_n$ has a turbulent stochastic component ${\bf v}_T$ over and above a smooth component ${\bf v}_0$, that is ${\bf v}_n = {\bf v}_0 + {\bf v}_T$. Since ${\bf v}_T$ is stochastic, Eq. (\[basic\]) becomes a stochastic partial differential equation. Its solution depends on the statistical properties of the velocity field ${\bf v}_T$.

We assume ${\bf v}_T$ to be an isotropic, homogeneous, Gaussian random velocity field with zero mean. For simplicity, in this work, we also assume ${\bf v}_T$ to have a delta function correlation in time (Markovian approximation) and its two point correlation to be specified as $$<v^i_T({\bf x},t)v^j_T({\bf y},s) > = T^{ij}(r) \delta (t-s)$$ with $$T^{ij}(r) =
T_{NN}[\delta^{ij} -({r^i r^j \over r^2})] +
 T_{LL}({r^i r^j \over r^2}) +
C\epsilon_{ijf} r^f .$$ Here $<>$ denotes averaging over an ensemble of the stochastic velocity field ${\bf v}_T$, $r = \vert {\bf x} -{\bf y} \vert$, $r^i = x^i -y^i$ and 