  Convection is one of the fundamental energy transport processes in physics
and astrophysics, and its description is central to allstellar models. In the
context of stellar astrophysics, the mixing length theory is the most
successful approximation to handle theconvection zones inside the stars because
of its simplicity and rapidity. The price to pay is the mixing length parameter
that isintroduced to derive the velocity of convective elements, the
temperature gradients in the convective regions and finally the energy flux
carried by convection. The mixing length is a free parameter that needs to be
calibrated on observational data. Pasetto et al. (2014) have proposed a new
theory that determines all the properties of convective regions and the
convective transport of energy with no need for a free parameter. In this
study, we aim to discuss the merits of this new approach and the limits of its
applicability in comparison with the mixing length theory. We present an
analytical and numerical investigation of the main physical assumptions made by
Pasetto et al. (2014) and compare them with the counterparts of the mixing
length theory. We also present here the homogeneous isotropic limit of the
Pasetto et al. (2014) theory and discuss some numerical examples to address and
clarify misconceptions often associated with the new formalism.
