Turbulence Modeling

Inhomogeneous Turbulence and Turbulence Modeling
A Class for Students who Love Turbulence
A series of lectures by Prof. S. A. E. Miller

A turbulent boundary layer.


One might ask, why was this course created and what is it for?

  • Turbulence modeling classes are rare within universities.
  • Science of turbulence modeling is being overcome with empirical nonsense (AI and big data).
  • I wished to create a new course to prepare researchers of the future to create physical models. for prediction. The purpose of theory is prediction. Therefore, I focused on theory and practical prediction.
  • Our graduates enter the research world with a unique perspective of problems we solve with understanding of closure techniques
  • Skepticism is central to the class.

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 equation, 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-Allmaras, 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.

Academician Lev Davidovich Landau. Nobel Prize winner. Turbulence expert.

Course Delivery and Notes

  • The student version of the notes can be downloaded here [link].
  • Delivered in person and recorded for online – lets an international audience study the subject for free.
  • Complete set of notes presented to students – reduces cost to students and allows them to create their own set of notes.
  • Approximately 20 journal articles reviewed in class – integrates original contributions, increases critical review and comprehension for students.
  • Integrated computer project – lets students develop their own solver and implement a simple model.
  • Semester term paper with over-view presentation at end of semester – increases student writing and presentation abilities.

Recorded Lectures

Computer Project Overview

  • A four-part computer programming project will result in a stand-alone marching boundary layer solver. Submissions consist of a short description, results, and source code for each part.
  • Four part project using student’s favorite language.
  • Each part builds upon the previous.
  • Assignments require short technical reports of results and source code.

A Closing Poem

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)

Lewis Fry Richardson