For example, consider the special case: For 2D flow,
- 1.
- Translation:
constant,
constant
- 2.
- Pure Strain: (no change in volume)
- 3.
- Angular deformation
- 4.
- Pure Rotation
Pure rotation with angular velocity
i.e. vorticity
2(angular velocity).
For irrotational Flow:
Suppose that at
,
the flow is irrotational,
i.e.
for all closed contours (material or not)
.
Then for ideal fluid under conservative body forces, Kelvin's theorem states that
for all closed material contours
for all time
.
i.e., once irrotational, always irrotational (Special case of Kelvin's theorem).
Karl P Burr
2003-07-07