  Recent 3D-simulations have shown that the turbulent kinetic flux (TKF) is
significant. We discuss the effects of TKF on the size of convection zone and
find that the TKF may help to solve the solar abundance problem. The solar
abundance problem is that, with new abundances, the solar convection zone
depth, sound speed in the radiative interior, the helium abundance and density
in the convective envelope are not in agreement with helioseismic inversions.
We have done Monte Carlo simulations on solar convective envelope models with
different profile of TKF to test the effects. The solar abundance problem is
revealed in the standard solar convective envelope model with AGSS09
composition, which shows significant differences ($\rm{\sim 10 %}$) on density
from the helioseicmic inversions, but the differences in the model with old
composition GN93 is small ($\rm{\sim 0.5 %}$). In the testing models with
different imposed TKF, it is found that the density profile is sensitive to the
value of TKF at the base of convective envelope and insensitive to the
structure of TKF in the convection zone. Required value of turbulent kinetic
luminosity at the base is about $\rm{-13%\sim-19%L_{\odot}}$. Comparing with
the 3D-simulations, this value is plausible. This study is for the solar
convective envelope only. The evolutionary solar models with TKF are required
for investigating its effects on the solar interior structure below the
convection zone and the whole solar abundance problem, but the profile of TKF
in the overshoot region is needed.
