Revised Prandtl mixing length model applied to the two-dimensional turbulent classical wake

• The turbulent classical described by Prandtl׳s mixing length model is studied.
• A revised Prandtl mixing length model is introduced.
• Lie symmetry methods are used to generate the invariant solution.
• The revised model is shown to be more accurate in predicting the width of the wake.

Previous applications of Prandtl׳s mixing length model to turbulent wake flows, which neglect the kinematic viscosity of the fluid, have underestimated the width of the boundary layer. In this paper, we present a revised Prandtl mixing length model by including the kinematic viscosity of the fluid. We show that this model predicts a boundary that lies outside the one predicted by Prandtl. We also prove that the results for the two models converge for very large Reynolds number wake flows.