Modeling and prediction of high-speed turbulent boundary layers

The conversion of kinetic energy into internal energy in high-speed boundary layers creates a non-uniform temperature field, and therefore also non-uniform density and viscosity fields. The variation in fluid properties invalidates many foundational theoretical models of wall-bounded turbulence flow, including the log-law for the mean velocity profile. Modeling and predictions of compressible turbulent boundary layers therefore requires a theoretical means of accounting for fluid property variations, the most famous of which is the so-called ``Van Driest transformation'' that originated in 1951. The talk will describe recent developments in this area, with a focus on the new theoretical propositions during the last decade and applications of the theory to engineering friction estimation methods and the development of wall-models for large eddy simulations.