This Joint Discussion (Number 13), took place on August 22, 1994 at The Hague, in connection with the XXII General Assembly of the IAU. At the one-day long meeting, there were presentations by 15 invited speakers and 15 posters.

The Joint Discussions had been organized in response to the considerable progress made in this field of research during the previous decade. Although it had long been known that the prevailing mixing length theory (MLT), used extensively and very successfully in Astrophysics for several decades had become needlessly limited, until recently it was impractical to contemplate more realistic approaches. The situation has changed recently as a consequence of advances in numerical techniques and computational capabilities, and thus JD 13 was organized to discuss the advances, and perhaps to understand the strengths and weaknesses of each approach.

There were two presentations which addressed the main issues in convection theory (E. Schatzman), and the astrophysical implications (P. Demarque). Several talks covered current numerical codes, which included deep convection in a rotating reference frame (K. Chan), convection in the presence of magnetic fields (P. Fox), and shallower solar convection simulations on a wide range of spatial scales (A. Nordlund). Although these approaches have enriched (and are continuing to enrich) our understanding of the physics of convective fluids, they are much too detailed (both in space and in time) to be integrated in the study of stellar evolution. To overcome this shortcoming, S. Sofia described a technique developed together with Lydon and Fox to use relationships between dynamical and thermodynamic properties of convective flows derived in numerical models to be applied in stellar structure and evolution codes by performing small modifications of the standard MLT formalism. The advantage of this technique is that it does not contain a mixing length or any other arbitrary parameter, and it was used successfully in modeling the evolution of the Sun and other solar analogues. V. Canuto also presented a formulation of convection both amenable to be used in stellar evolution studies, and not requiring an arbitrary mixing length-like parameter. His formulation uses the Reynolds stress method, which has the advantage of modeling the full eddy spectrum of the turbulence, rather than the narrow wave number range for energy containing eddies assumed in the MLT. Additionally, this technique can address the problems of non-locality and overshoot. M. Stix also addressed non-locality and overshoot by presenting results of a non-local mixing length model of the Sun derived from the Shaviv and Salpeter model.