ME 7602: Hydrodynamic Stability

Offered as Required


Credit Hours: 3-0-3
Prerequisites: ME 6601 or equivalent, or with the consent of the instructor
Catalog Description: The hydrodynamic stability of fluid flows using linear, energy, and non-linear stability theories. Studies of Taylor-Couette, buoyancy-driven, surface-tension-driven, shear, and thin-film flows.
Textbooks: Philip G. Drazin and William H. Reid, Hydrodynamic Stability; 1st Edition, Cambridge University Press, 1982.
Instructors: Marc K. Smith (ME), Paul Neitzel (ME)
Goals:

The course is structured so that the student can accomplish the following:

  • Learn the fundamentals of three stability theories: linear, energy, and weakly-nonlinear.
  • Study in detail the stability characteristics of the following classical fluid flows: Taylor-Couette, buoyancy-driven, surface-tension-driven, shear, and thin film.
  • Perform a complete stability analysis on a simple flow of their choice and then describe the problem and the results in a publication-quality report.
Topics:

  1. Introduction
  • The notion of an unstable fluid flow. The development of linear, energy, and weakly nonlinear stability theories.
  • Taylor-Couette Flow
    • The unstable behavior of the flow between two concentric rotating cylinders.
  • Buoyancy-Driven Flow
    • The buoyancy-driven instability of a liquid layer heated from below.
  • Thermocapillary Flow
    • The surface-tension-driven instability of a liquid layer heated from below or from the side.
  • Shear Flows
    • The unstable behavior of inviscid and viscous shear flows such as wakes, jets, and boundary layers.
  • Liquid Film Flows
    • The unstable behavior of a thin liquid film flowing down an inclined plane.
  • Time-Dependent Flows
    • The application of stability theory to flows in which the base state is varying with time.