  We explore very fine scales of scalar dissipation in turbulent mixing, below
Kolmogorov and around Batchelor scales, by performing direct numerical
simulations at much finer grid resolution than is usually adopted in the past.
We consider the resolution in terms of a local, fluctuating Batchelor scale and
study the effects on the tails of the probability density function and
multifractal properties of the scalar dissipation. The origin and importance of
these very fine-scale fluctuations are discussed. One conclusion is that they
are unlikely to be related to the most intense dissipation events.
