Geoscience Reference
In-Depth Information
Figure 6.45. Circulation in a potential vortex. (Top) In a circuit around the vortex (circle with
arrow indicating the direction of the flow and bold dot indicating the center of the vortex) the
circulation is positive because v E dl > 0 all the way around the curve. (Bottom) Around a circuit
inside the previous circuit (curve indicated by smaller circle with arrow indicating the direction
of integration) not including the center of the vortex the circulation is zero because v E dl > 0on
the far side of the circuit, but v E dl <
0 on the near side of the circuit; the contribution at the far
side is at larger radius, so the wind speed is relatively low, while the contribution at the near side
is at smaller radius, so the wind speed is relatively high. But, the length of arc containing the
lower wind speeds at far radius is greater than the length of the arc containing the higher wind
speeds at smaller radius: the net contributions around the circuit add up to zero.
would therefore have to lose all its angular momentum as a consequence of
turbulent mixing in either the radial or vertical direction (if v vanishes at the
ground). How should the azimuthal velocity vary as a function of radius from
where it has zero angular momentum at the origin to the core radius, r c , beyond
which angular momentum is a constant? Also, how far radially inward can an air
parcel be brought before turbulent mixing becomes significant and dominates?
We will address the first question now.
The simplest solution for r Þ is that in the core,
r Þ¼O
r
ð 6
:
28 Þ
 
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