Hydrodynamic Stability & Transition
This course is discontinued.
Course Details
Introduction to flow stability, bifurcation and transition to turbulence. Linear stability theory of parallel shear flows including inviscid and viscous instabilities. Concepts of temporal/spatial, local/global, absolute/convective instabilities. Stability results and transition mechanisms for specific flows, such as free shear, channel, boundary-layer and stratified flows.
This course gives an introduction to the most relevant instability mechanisms and transition processes in incompressible flows. Starting with the basic framework of linear stability theory, we will discuss the stability of several flow configurations of increasing complexity, e.g. free shear flows, 2D and 3D boundary layers and stratified flows. We will introduce the basic mathematical concepts and derive important theoretical results (Rayleigh and Orr-Sommerfeld equations, stability charts). The discussion of linear stability will be followed by a consideration of the laminar-turbulent transition process for selected flows. Different transition scenarios will be studied for technically relevant flows.
Homework assignments are available for download Tuesday morning (see class schedulebelow). They are discussed on Tuesday afternoon and are due the following Friday at 5 p.m. (either electronically or on paper).
Testatbedingung
For getting the attestation (Testat) at least 8 out of 10 homework assignments need to be handed in and accepted (a passed midterm test also counts as one homework). The homework assignments can be downloaded protected pageherelock. Many homework assignments include computations with MATLAB. The required MATLAB programs can be downloaded protected pageherelock.
Lecture notes can be downloaded protected pageherelock.
- W. O. Criminale, T. L. Jackson, R. D. Joslin, Theory and Computation of Hydrodynamic Stability, Cambridge University Press, 2003
- P. J. Schmid, D. S. Henningson, Stability and Transition in Shear Flows, Springer, 2001
- P. G. Drazin, Introduction to Hydrodynamic Stability, Cambridge University Press, 2002
- P. K. Kundu, I. A. Cohen, Fluid Mechanics (Chapter 12), Academic Press, 2008
- R. L. Panton, Incompressible Flow (Chapter 25), Wiley, 2005
- F. M. White, Viscous Fluid Flow (Chapter 5), McGraw-Hill, 2005
- D. J. Tritton, Physical Fluid Dynamics (Chapters 17 & 18), Oxford, 1988
Further references to textbooks and research articles will be provided with the lecture notes. They are good sources for the extended study of certain topics.