Self-similar temporal turbulent boundary layer flow

Abstract

Direct numerical simulations of temporally evolving boundary layer flows are considered with solutions restricted to self-similar profiles. A new set of modified Navier–Stokes equations is solved with periodic boundary conditions in the streamwise direction, and solutions reach statistically steady states, independent of the initial conditions. The results are presented for different cases, with and without a pressure gradient, and found to be in agreement with existing results of spatial turbulent boundary layer flows. Thus, self-similar temporal solutions are able to reproduce the general features of turbulent boundary layer flows. Finally, the model is applied to simulate a turbulent spot in equilibrium, which is difficult to obtain otherwise.