  We constructed hydrodynamical model atmospheres for mid M-type main-, as well
as pre-main-sequence objects. Despite the complex chemistry encountered in such
cool atmospheres a reasonably accurate representation of the radiative transfer
is possible. The detailed treatment of the interplay between radiation and
convection in the hydrodynamical models allows to study processes usually not
accessible within the framework conventional model atmospheres. In particular,
we determined the efficiency of the convective energy transport, and the
efficiency of mixing by convective overshoot. The convective transport
efficiency expressed in terms of an equivalent mixing-length parameter amounts
to values around ~2 in the optically thick, and ~2.8 in the optically thin
regime. The thermal structure of the formally convectively stable layers is
little affected by convective overshoot and wave heating, i.e. stays close to
radiative equilibrium. Mixing by convective overshoot shows an exponential
decline with geometrical distance from the Schwarzschild stability boundary.
The scale height of the decline varies with gravitational acceleration roughly
as g^(-1/2), with 0.5 pressure scale heights at log(g)=5.0.
