  We constructed hydrodynamical model atmospheres for mid M-type main-, as well
as pre-main-sequence (PMS) objects. Despite the complex chemistry encountered
in these cool atmospheres a reasonably accurate representation of the radiative
transfer is possible, even in the context of time-dependent and
three-dimensional models. The models provide detailed information about the
morphology of M-type granulation and statistical properties of the convective
surface flows. In particular, we determined the efficiency of the convective
energy transport, and the efficiency of mixing by convective overshoot. The
convective transport efficiency was expressed in terms of an equivalent
mixing-length parameter alpha in the formulation of mixing-length theory (MLT)
given by Mihalas (1978). Alpha amounts to values around 2 for matching the
entropy of the deep, adiabatically stratified regions of the convective
envelope, and lies between 2.5 and 3.0 for matching the thermal structure of
the deep photosphere. For current spectral analysis of PMS objects this implies
that MLT models based on alpha=2.0 overestimate the effective temperature by
100 K and surface gravities by 0.25 dex. The average thermal structure of the
formally convectively stable layers is little affected by convective overshoot
and wave heating, i.e., stays close to radiative equilibrium conditions. Our
models suggest that the rate of mixing by convective overshoot declines
exponentially with geometrical distance to the Schwarzschild stability
boundary. It increases at given effective temperature with decreasing
gravitational acceleration.
