In the first place, this is an unphysical picture. Turbulent convection is best pictured as upflows and downdrafts that can extend over many pressure and density scale heights. MLT is a local theory, where the flow velocities and temperature fluctuations are determined by local conditions. In reality, the entropy and temperature fluctuations are determined primarily by radiative cooling in the thin surface thermal boundary layer.
The free parameter, the mixing length , is not determined within the theory and varies across the Hertzsprung–Russell diagram according to 3D convection simulations (Abbett et al., 1997; Ludwig et al., 1999; Freytag et al., 1999). Hence, numerical convection simulations are needed to calibrate the mixing length parameter. Furthermore, standard MLT does not allow for overshoot of convective motions into the surrounding stable layers (Deng and Xiong, 2008, but see). It can not, for instance, account for phenomena such as reverse granulation or the observed destruction of lithium in the Sun by mixing below the convection zone. Finally, even with a mixing length that produces the correct interior adiabat, MLT produces a different mean atmosphere structure than given by the numerical simulations. This leads to disagreements between calculated and observed p-mode oscillation frequencies (Rosenthal et al., 1999). However, the mixing length scaling of temperature fluctuations and velocity with the convective flux,et al., 2005). Other works that attempt a connection between mixing-length theory and numerical simulations are the ones by Kim et al. (1996) and Robinson et al. (2003).
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