Turbulence essential

This introduction presents the main properties of all turbulent flows (e.g. non-linearity, non-locality, presence of vorticity, finite turbulence dissipation, randomness) and their implications. It then follows with the Reynolds decomposition and the Reynolds-Averaged Navier-Stokes (RANS) equation and various ways to physically interpret Reynolds stresses. The RANS equations are then applied to fully-developed turbulent channel flow with a resulting discussion of turbulent skin friction, sweeps and ejections and various derivations of the log-law of the wall and their limitations. The general closure problem resulting from non-linearity and non-locality is presented along with some notable closures. The course then delves into energy balances, turbulence production is explained as an essentially linear phenomenon and a derivation is given of the regeneration cycle in turbulent channel flow. This is followed by a study of turbulence dissipation and interscale energy transfers and Kolmogorov’s 2/3 law. Finally, the introductory course wraps up with a presentation of turbulent boundary layers with various pressure gradients.