Geography Reference
In-Depth Information
CHAPTER 4
Circulation and Vorticity
In classical mechanics the principle of conservation of angular momentum is
often invoked in the analysis of motions that involve rotation. This principle pro-
vides a powerful constraint on the behavior of rotating objects. Analogous con-
servation laws also apply to the rotational field of a fluid. However, it should be
obvious that in a continuous medium, such as the atmosphere, the definition of
“rotation” is subtler than that for rotation of a solid object.
Circulation and vorticity are the two primary measures of rotation in a fluid.
Circulation, which is a scalar integral quantity, is a
macroscopic
measure of rota-
tion for a finite area of the fluid. Vorticity, however, is a vector field that gives a
microscopic
measure of the rotation at any point in the fluid.
4.1
THE CIRCULATION THEOREM
The
circulation
, C, about a closed contour in a fluid is defined as the line integral
evaluated along the contour of the component of the velocity vector that is locally
tangent to the contour:
C
≡
U
·
d
l
=
|
U
|
cos αdl
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