ME539 HYDRODYN. INSTAB. VORTEX DYNAM. & TURBU.
| Course Code: | 5690539 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 8.0 |
| Department: | Mechanical Engineering |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | Prof.Dr. IŞIK HAKAN TARMAN |
| Offered Semester: | Fall and Spring Semesters. |
Course Objectives
This course aims to instill/promote the following knowledge, behaviors and skills in the students
1. Analysis of nonlinear nynamical systems for varying a bifurcation parameter
2. Mathematical techniques of reducing PDEs to a system of ODEs
3. Hydrodynamic stability analyis using method of normal modes
Course Content
General formulation of the hydrodynamic stability problems. Rayleigh and Orr-Sommerfeld equations. Vortex instability. Crow and Widnall instabilities. Vortex dynamics, vortex models and vortex interactions. Contour dynamics. Statistical theories of turbulence. Closure problem. Theories before and after Kolmogorov. Intermittency models and fractals. Recent direct numerical simulations of turbulence. Chaos. (R)
Course Learning Outcomes
At the end of this course, the students will be able to 1. Use the concepts and methods of nonlinear dynamical systems for varying a bifurcation paramaters. 2. Reduce PDEs to ODEs using eigensystem methods. 3. Perform hydrodynamic stability analysis using method of normal modes. 4. Understand and perform formulations involving free and deformable surfaces and interfaces. 5. Understand basic hydrodynamic stability problems: Rayleigh-Taylor, Kelvin-Helmholtz, Rayleigh-Plateau (Capillary) instabilities. 6. Undetstand Rayleigh-Benard thermal convection instability. 7. Undetstand shear flow instabilities.