  We report an extensive numerical study of the small-scale turbulent dynamo at
large magnetic Prandtl numbers Pm. A Pm scan is given for the model case of
low-Reynolds-number turbulence. We concentrate on three topics: magnetic-energy
spectra and saturation levels, the structure of the field lines, and the
field-strength distribution. The main results are (1) the folded structure
(direction reversals at the resistive scale, field lines curved at the scale of
the flow) persists from the kinematic to the nonlinear regime; (2) the field
distribution is self-similar and appears to be lognormal during the kinematic
regime and exponential in the saturated state; and (3) the bulk of the magnetic
energy is at the resistive scale in the kinematic regime and remains there
after saturation, although the spectrum becomes much shallower. We propose an
analytical model of saturation based on the idea of partial
two-dimensionalization of the velocity gradients with respect to the local
direction of the magnetic folds. The model-predicted spectra are in excellent
agreement with numerical results. Comparisons with large-Re, moderate-Pm runs
are carried out to confirm the relevance of these results. New features at
large Re are elongation of the folds in the nonlinear regime from the viscous
scale to the box scale and the presence of an intermediate nonlinear stage of
slower-than-exponential magnetic-energy growth accompanied by an increase of
the resistive scale and partial suppression of the kinetic-energy spectrum in
the inertial range. Numerical results for the saturated state do not support
scale-by-scale equipartition between magnetic and kinetic energies, with a
definite excess of magnetic energy at small scales. A physical picture of the
saturated state is proposed.
