  Maxima of the scalar dissipation rate in turbulence appear in form of sheets
and correspond to the potentially most intensive scalar mixing events. Their
cross-section extension determines a locally varying diffusion scale of the
mixing process and extends the classical Batchelor picture of one mean
diffusion scale. The distribution of the local diffusion scales is analysed for
different Reynolds and Schmidt numbers with a fast multiscale technique applied
to very high-resolution simulation data. The scales take always values across
the whole Batchelor range and beyond. Furthermore, their distribution is traced
back to the distribution of the contractive short-time Lyapunov exponent of the
flow.
