  Both observations and numerical simulations show that stellar convective
motions are composed of semi-regular flows of convective rolling cells and the
fully developed turbulence. Although the convective rolling cells are crucial
for the properties of the stellar convection that transports heat and mixes
materials in the stellar interior, their contributions have not been included
in turbulent convection models proposed up to now. We simplify the structure of
the convective rolling cells as a cellular pattern moving circle by circle with
different angular velocities around the center, estimating their typical size
by solving approximately for the temperature difference over the stationary
temperature background and their average shear of velocity by evaluating
approximately their kinetic energy transformed by themselves working as thermal
engines from the heat involved in the convective rolling cells. We obtain a
steady state solution in the fully local equilibrium which is similar to what
is obtained in the standard mixing-length theory, by applying such model
assumptions to the standard $k$-$\varepsilon$ model and properly choosing the
model parameter $c_{\varepsilon 3}$. Accordingly, we propose a $k$-$\omega$
model to include the transport effect of turbulence in stars. Preliminary
results of their applications to the sun and other stars with different masses
and in different evolutionary stages show good agreements with results of the
standard mixing-length theory and results of numerical simulations for the
stellar convection.
