Difference-quotient turbulence model: A generalization of Prandtl’s mixing-length theory

A difference mean-velocity turbulence model to calculate quasistationary fully developed turbulent motion is presented. It takes account of the various eddy sizes in turbulent flows. As a consequence, some gaps between semiempirical closure models and sophisticated theories, describing eddy energy cascades, are reduced. In a first-order expansion, the model is identical to Prandtl's mixing-length theory, which is still contained in modern numerical computation schemes, e.g., k-{ε} models.