Re: [ferret_users] Calculating relative vorticity

[Ryo Furue <furue@xxxxxxxxxx>]

Hi Billy,

| There IS a problem, but it is not with d/dy. 
|
[. . .]
|
| zeta = dv/dx - du/dy + (u/a)tan(phi) , where a is the radius of the  
| earth and phi the latitude.
|
[. . .]
|
| And note that the correction terms will be very small except near the  
| poles.
| 
| Am I still missing something?

What you seems to be missing is that what you call the
"correction term" is actually part of d/dy:

  zeta = dv/dx - du/dy + (u/a)tan(phi)
       = dv/dx - d(u cos(phi))/dy/cos(phi)

The latter is the formula I gave.  (Please note that dy = a d(phi))

If you transform the curl operator from the Cartesian coordinate
system to the spherical system, then the latter form (my form)
is the one you get (after the shallow layer approximation
r = a + z =~ a), showing that that's the "y derivative" of
the x-component of a velocity vector.

So, that's what I meant: du/dy is an approximation to the correct
derivative.  As you noted, it's a very good approximation except
near the poles.

Cheers,
Ryo