three-dimensional LESs of compressible turbulent convection were used to test the relations proposed by [@schmitt84] and [@zahn91]. They confirmed $\Delta_{\rm
d}\propto v_{\rm zo}^3/F_{\rm b}$ for nearly adiabatic penetration and $\Delta_{\rm d}\propto F^{1/2}_{\rm b}$ for non-adiabatic penetration where $v_{\rm zo}$ is the root mean square (rms) vertical velocity at the unstable-stable interface. Using the same technique, [@saikia2000] found that the numerical aspects of the model, such as aspect ratio, grid number could greatly affect the penetrative distance. [@brummell2002] performed a large number of high-resolution, three-dimensional DNSs for the purpose of investigating the penetration and overshooting of the turbulent compressible convection. In their study, the effects of rotation were included. Recently, penetration below a stellar type rotating convection zone were estimated by [@pal2007] with a set of LESs. [@rogers2006] reported a two-dimensional simulation of gravity waves induced by overshooting below the solar convection zone. In these numerical experiments, only ideal gas with a polytropic initial distribution was considered. However, for a practical model, the realistic radiation opacity and the equation of state(EOS) should be used.

According to the stellar evolution theory, at the base of the giants branch in the Hertzsprung-Russell diagram, convection occurs in the outer region of the envelope and 