MAK 681E - Hydrodynamic Stability

Course Objectives

- Definition of instability and basic concepts.
- Development of instability and their classifications.
- Description of well-established and known approaches and theories and their scope.

Course Description

Fundamental concepts of stability; Perturbation and types of stability, Some known examples of stability. Kelvin-Helmholtz instability; Shear instability. Surface tension instability of a liquid column. Stability of parallel shear flows; Inviscid flow, linearization of equations of motion. Modal Analysis, Development of linear instability in time and space, Squire's theorem for an inviscid flow, General criteria for instability. Viscous flow; Plane Couette flow. Poiseuille flow, Blasius boundary layer. Tollmien-Schlichting waves, Eigenvalue spectrum. Instability due to streamline curvature; Taylor problem. Instability due to streamline curvature; Görtler problem. Introduction to nonlinear stability; Landau's theory. Resonant wave interactions. Introduction to behaviour of ordinary differential equations. Introduction to bifurcation theory.