  The Batchelor passive advection is an advection by a smooth velocity field.
If the velocity field is a delta-correlated in time random Gaussian process,
then the problem is reduced to quantum mechanics of fluctuating velocity
gradient u'(t). For the finite-time correlated velocity field, such a reduction
does not exist. To illustrate this point, the second moment of a passively
advected magnetic field is considered, and the stochastic calculus is used to
find finite-time corrections to its growth rate. The growth rate depends on
large scale properties of the velocity field. Moreover, the problem is not
universal with respect to the short-time regularization: different
regularizations give different answers for the growth rate.
