  Turbulent convection models are thought to be good tools to deal with the
convective overshooting in the stellar interior. However, they are too complex
to be applied in calculations of stellar structure and evolution. In order to
understand the physical processes of the convective overshooting and to
simplify the application of turbulent convection models, a semi-analytic
solution is necessary.
  We obtain the approximate solution and asymptotic solution of the turbulent
convection model in the overshooting region, and find some important properties
of the convective overshooting:
  I. The overshooting region can be partitioned into three parts: a thin region
just outside the convective boundary with high efficiency of turbulent heat
transfer, a power law dissipation region of turbulent kinetic energy in the
middle, and a thermal dissipation area with rapidly decreasing turbulent
kinetic energy. The decaying indices of the turbulent correlations $k$,
$\bar{u_{r}'T'}$, and $\bar{T'T'}$ are only determined by the parameters of the
TCM, and there is an equilibrium value of the anisotropic degree $\omega$.
  II. The overshooting length of the turbulent heat flux $\bar{u_{r}'T'}$ is
about $1H_k$($H_k=|\frac{dr}{dlnk}|$).
  III. The value of the turbulent kinetic energy at the convective boundary
$k_C$ can be estimated by a method called \textsl{the maximum of diffusion}.
Turbulent correlations in the overshooting region can be estimated by using
$k_C$ and exponentially decreasing functions with the decaying indices.
