In 1968, Saffmann and Spalding independently proposed the use of a two-equation model of which the first dependent variable was the energy, KE, and the second, here referred to as VO, was a measure of the fluctuations of vorticity.
Since it was two-dimensional boundary-layer flows which were chiefly thought of at that time, it was the direction of the vorticity which was thought of was that normal both to the main flow and to the plane in which it was confined. However, this assumption had no effect on the form of the equations.
In accordance with the requirements of dimensional analysis, then efective-viscosity formula took the form:
EV = const * KE / VO**0.5
PG Saffmann (1970) "A model for inhomogeneous turbulent flow"; Proc Roy Soc London vol A317 pp 417-433
DB Spalding (1969) "The prediction of two-dimensional steady turbulent elliptic flows" ICHMT Seminar, Herceg Novi, Yugoslavia
Some discussion of the model will be found in the following:
BE Launder and DB Spalding (1972) "Mathematical Models of Turbulence", Academic Press