TAM 532

Dynamics of flow in which viscosity is significant or dominant, and the development and use of theoretical and numerical tools for practitioners of modern fluid mechanics; physics of viscous layers that arise in both high- and low-Reynolds-number flows; dimensional analysis, exact solutions to the Navier-Stokes equations; jets and wakes; microhydrodynamics; fluid stability; turbulence. Course Information: Prerequisite: MATH 285 and TAM 435.

Dynamics of flow in which viscosity is significant or dominant, and the development and use of theoretical and numerical tools for practitioners of modern fluid mechanics; physics of viscous layers that arise in both high- and low-Reynolds-number flows; dimensional analysis, exact solutions to the Navier-Stokes equations; jets and wakes; microhydrodynamics; fluid stability; and an introduction to turbulence. Prerequisite: TAM 435 or equivalent; MATH 380; MATH 385, MATH 386, or MATH 441. 4 graduate hours.

Textbooks: No textbook required.

Topics:

Governing equations for viscous, heat-conducting fluids (6 hr)
Continuity, momentum, and energy equations; elementary thermodynamics, simple constitutive theory; boundary conditions; dimensionless form of governing equations; identification of group parameters

Exact solutions of the Navier-Stokes equations (8 hr)
Steady and unsteady unidirectional flows; two-dimensional steady flows; compressible unidirectional flows

Boundary-layer theory (10 hr)
Inviscid limit and the singular character of the large-Reynolds-number limit; mathematical example of a boundary layer; matched asymptotic expansions; two-dimensional steady flow past a body as a singular perturbation problem; boundary-layer equations, flat-plate boundary layers, displacement thickness, pressure gradients and flow separation; difficulties with boundary-layer theory; approximate techniques (von Kn integrals, Thwaites's method; comparison with numerical solutions); free boundary layers

Low-Reynolds-number flow (6 hr)
The Stokes equations, general methods of solution; axisymmetric flow past a circular cylinder; Whitehead|rsquo;s and Stokes|rsquo;s paradox|mdash;the Oseen equation; lubrication theory

Stability of fluid motion (8 hr)
Definition of stability; linear stability of parallel shear flow, the Orr|ndash;Sommerfeld equation; Squire|rsquo;s theorem; stability of Poiseuille flow

Introduction to turbulent flow (10 hr)
Transition; Reynolds averaging; statistical hydromechanics; turbulent shear flows; turbulent boundary layers; Kolmogorov's theory; coherent structures

Numerical solution of the Navier-Stokes equations (6 hr)
Finite differencing; numerical solution of viscous flow problems; examples and demonstrations

Additional topics (instructor's option) (4 hr)

TOTAL HOURS: 60

9/20/2018