The efficiency of convective energy transport in the sun

Mixing length theory (MLT) utilizes adiabatic expansion (as well as radiative transport) to diminish the energy content of rising convective elements. Thus in MLT, the rising elements lose their energy to the environment most efficiently and consequently transport heat with the least efficiency. On the other hand Malkus proposed that convection would maximize the efficiency of energy transport. A new stellar envelope code is developed to first examine this other extreme, wherein rising turbulent elements transport heat with the greatest possible efficiency. This other extreme model differs from MLT by providing a small reduction in the upper convection zone temperatures but greatly diminished turbulent velocities below the top few hundred kilometers. Using the findings of deep atmospheric models with the Navier-Stokes equation allows the calculation of an intermediate solar envelope model. Consideration is given to solar observations, including recent helioseismology, to examine the position of the solar envelope compared with the envelope models.