ME 6602: Viscous Flow

Offered Every Spring


Credit Hours: 3-0-3
Prerequisites: ME 6601 or equivalent, or with the consent of the instructor
Catalog Description: The mechanics of Newtonian viscous fluids. The use of modern analytical techniques to obtain solutions for flows with small and large Reynolds numbers.
Textbooks: Ronald Panton, Incompressible Flow, Panton; 2nd Edition, John Wiley; 1995.
Instructors: Marc K. Smith, Paul Neitzel
Goals: This course focuses on flow cases where the effects of viscosity are important. In particular, consideration of the extremes of very large Reynolds number (leading to the appearance of boundary layers) and very small Reynolds number (creeping flow) are treated extensively using methods of asymptotic analysis, complementing the more traditional approaches covered in ME 6601. Emphasis is also placed on developing physical insight into these situations.
Topics:
  1. Governing Equations and Scaling
  • Review derivations of the Navier-Stokes and continuity equations; boundary conditions.
  • Exact Solutions
    • Determination of exact solutions to steady and unsteady viscous flows; similarity solutions.
  • Vorticity
    • Vorticity transport; generation mechanisms; interpretation of exact solutions in terms of vorticity.
  • Introduction to Asymptotic Methods
    • Application of the method of matched asymptotic expansions to a model problem; inner, outer and composite expansions.
  • Boundary Layers
    • Development of the boundary-layer equations using scaling; analysis of steady and unsteady boundary layers using traditional and asymptotic methods; nonlinear effects; multiple decks.
  • Low-Reynolds-Number Flows
    • Stokes and Oseen flow past cylinders and spheres; lubrication theory.
  • Introduction to Hydrodynamic Stability
    • Linear- and energy-stability theories applied to model and real systems.