Inhomogeneous Turbulence and Turbulence Modeling

Class for Students Who Want to Predict Chaotic Flows

Course Objectives

A class that covers in depth concepts of the science and mathematics of turbulence modeling with a historical perspective. Examples are given as much as possible involving contemporary approaches. Statistical quantities, averages, correlations, coherence, the Russian school, law of the wall, chaos, compressible NSE, averaging relations, mean kinetic energy, Re stress transport eqn., boundary layer equations, two-dimensional in laminar and turbulent flows, mixing length concepts, Baldwin-Lomax, Cebeci-Smith, 1/2-equations, one- equation models, Prandtl’s model, Spalart-Allmarus, k-ω and k-ε, Boussinesq, nonlinear relations, stress transport models, closure, applications and examples, physical considerations, Morkovin hypothesis, studies in particular flows. These topics will be related to turbulent flows that are observed in our daily lives and within various fields of engineering.

“Big whorls have little whorls
which feed on their velocity
and little whorls have lesser whorls
and so on to viscosity”
~Lewis Fry Richardson, 1922
(play on Augustus de Morgan’s famous paraphrasing of Jonathan Swift)