Background: Turbulence is a fundamental and challenging area of physical sciences. Most flows occurring in nature and in engineering applications are turbulent. Examples of applications governed by turbulence include industrial processing of liquid or gases with pipe lines, mixing and reaction processes, aerospace engineering, transport and dispersion phenomena in the atmosphere, solar physics and interstellar gas cloud dynamics.
This course introduces a fundamental study of turbulence for graduate students with an interest in any of these areas. It is designed to provide the necessary background required to study and realistically solve scientific and practical problems involving turbulence.
Objectives: The course intends to provide the basic notions and tools to tackle problems involving turbulence in engineering, earth and atmospheric sciences, astrophysics, and contributes valuable material to students in applied mathematics and physics.
Upon completion of the course, students will gain an understanding of 1) the structure, characteristics, and behavior of turbulent flows; 2) the fundamental physical processes involved in the generation of turbulence; 3) the current modeling approaches and simulation techniques; 4) applicability, advantages, problems and limitations of current theories and computational methods.
Description: The course provides an introduction to turbulence, its modeling approaches, the main computational techniques in use and current directions in turbulence research.
It examines the fundamental physical processes involved in turbulent flows, their features and behavior, the derivation of the descriptive equations, and covers the basics of the statistical theory of turbulence, the equations of fluid motion, and the mean flow equations.
Simple practical flows are examined: boundary layer, channel, pipe, and free shear flows, as well as the structure of atmospheric turbulence. The modeling and simulation techniques covered include direct numerical simulation (DNS), turbulent-viscosity models, Reynolds-stress models, large-eddy simulation (LES) and probability density function (PDF) models.
The course intends to provide the basic notions and tools to tackle problems involving turbulence in engineering, earth and atmospheric sciences, and astrophysics.
Content:
- Overview of nature and features of turbulent flows
- Equations of motion and of advection-diffusion
- Statistical description of turbulence
- Mean-flow Reynolds averaged equations
- Overview of modeling and simulation techniques
- Direct numerical simulation (DNS)
- Turbulent-viscosity models
- Reynolds stress models
- Large-eddy simulation (LES)
- Probability density function (PDF) methods
- Free shear flows: jet, mixing layers and wake
- Wall flows: channel, pipe and boundary layer
- Structure of atmospheric turbulence
Homework and Project: 4-6 assignments
Exams: One midterm and final
Grades: Homework and projects (40%), Midterm (30%), Final Exam (30%)
Note: Presentations in pdf format will be posted online after lectures
Text Book: Pope, S.B., 2003:
Turbulent Flows. Cambridge University Press, 771 pp., ISBN: 0521598869
Supplement Reference Books: Davidson, P.A., 2004:
Turbulence - An Introduction for Scientists and Engineers. Oxford University Press, 657 pp., ISBN: 019852949X