2.25: Advanced Fluid Dynamics Section 1: Continuum viewpoint and the equation of motion Section 2: Static Fluids Section 3: Mass Conservation Section 4: Inviscid flow - differential approach Section 5: Control Volume Theorums Section 6: Navier-Stokes equation and viscous flow Section 7: Similarity and dimensional analysis Section 8: Boundary layers, separation and effect on drag/lift Section 9: Vorticity and circulation Section 10: Potential flows; lift, drag and thrust production Section 11: Surface tension and its effect on flows Section 12: Introduction to turbulence Back to 2.25 Home
Section 9: Vorticity and circulation
9.1 Vorticity  and its physical significance. Vortex lines and vortex tubes.  The solenoidal nature of vortex lines. Examples.
9.2 Circulation G:  its definition and relationship to vorticity.  Vorticity as a "source" of             circulation (Biot-Savart's law).
9.3 Kelvin's theorem on circulation in barotropic flows in irrotational force fields:

For inviscid flows:

9.4

Three vortex theorems for inviscid, barotropic flow in an irrotational force field             (corollaries of Kelvin's theorem):

(a)  Vortex lines move with the fluid.

Examples: behavior of vortex rings; instability of shear layer or vortex sheet; secondary flow induced in bends.

(b)  Once irrotational( ), a fluid particle will remain so forever.

Consequence:  Potential flows.

Example:  solution of steady sink vortex based on constraint that .

(c)            For vortex "tube",

Example: accelerating inviscid flow with transverse velocity gradient.

9.5 Vorticity transport equation in differential form. The effect on vorticity of vortex line stretching and turning; the role of kinematic viscosity as the diffusivity of vorticity.

Fay, pp 271-276
e.g Potter & Foss pp. 179-184, 250-262, 390-392

Problem Set Section 9 (from Shapiro and Sonin)
Problem 10.3
Problem 10.4
Problem 10.5
Problem 10.8
Problem 10.11