Investigation of Rotta’s kL Equation using LES data for Complex Wake Flows

Rotta’s kL equation describes the dynamics of large-scale turbulence. This makes it attractive to stakeholders seeking to improve the predictive capability of length scale determining equations. We study the individual terms of the kL transport equation, by extracting numerical data from LES using a turbulent boundary layer with its wakes subjected to zero and adverse pressure gradients. These results are useful for calibrating existing and future RANS-models of turbulence. The production term of the kL-equation involves two-point correlations that are usually modelled using higher-order derivatives of the mean velocity. Our results show that the higher-order terms of the production term are rather small for free wakes. Hence, certain previous RANS models which build on such higher-order terms lack physical justification.