How did they get that the vorticity = 2##\omega##?

  • #1
Hall
343
81
Homework Statement:
Deriving an expression for vorticity.
Relevant Equations:
Vorticity =##2 \omega##
I'm learning Meteorology, and using the book Atmospheric Science by Wallace and Hobbs. We're discussing the kinematics of the winds (fluids). I shall post some images to say what I don't understand. This is how they define their natural coordinate system
At any point on the surface one can define a pair of axes of a sys- tem of natural coordinates (s, n), where s is arc length directed downstream along the local streamline, and n is distance directed normal to the streamline and toward the left,
Screenshot 2022-05-25 at 5.48.06 PM.png

Screenshot 2022-05-25 at 5.51.01 PM.png
Screenshot 2022-05-25 at 5.51.31 PM.png



I know and understand the concepts of angular velocity, shear, curvature, differentiation, and partial differentiation but for some reason, which is latent to me, I cannot understand anything that the book has done. Will you please explain it to me?
 

Answers and Replies

  • #2
anuttarasammyak
Gold Member
1,850
954
I am not sure whether I understand the book but mathematical definition of vorticity says
[tex]\nabla \times \mathbf{u}=2\mathbf {\omega}[/tex]
where
[tex]u_x=- \omega y,\ u_y=\omega x,\,\ u_z=0[/tex]
 
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