Fundamentals of Turbulent Flows

Turbulent flow is an important branch of fluid mechanics with wide-ranging occurrences and applications, from the formation of tropical cyclones to the stirring of a cup of coffee. Turbulence results in increased skin friction and heat transfer across surfaces, as well as enhanced mixing. As such, it is of practical significance, and there is a need to establish predictive methods to quantify turbulent flows. Equally important is a physical understanding of turbulent flows to guide strategies to model and control turbulence-driven phenomena. We focus on the study of turbulent flows and draw on theoretical developments, experimental measurements, and results from numerical simulations. Turbulent flows are governed by the Navier-Stokes equations. The solution of these equations for turbulent flows displays chaotic and multiscale behavior. When averaged, the nonlinear terms in the Navier-Stokes equations lead to the so-called closure problem, where additional unknowns are introduced in the mean flow equations. These unknowns are typically modeled using intuition, experience, and dimensional arguments. We present the scaling and dimensional analysis necessary for model development.