A generalized eddy viscosity function &sgr;, is introduced in order that the Reynolds stress in an incompressible fluid be expressible as a linear combination of the Kronecker and rate‐of‐strain tensors. A transport equation for the eddy viscosity is derived from the general turbulence energy equation, thereby introducing two additional functions, the specific turbulence kinetic energyq, and a scale variables.To determine the three variables, a transport equation forsis postulated, and a modified Prandtl—Wieghardt relation among the three variables is accepted. The theory is expressed in universal, invariant form, and validity is demonstrated by application to several problems.