R help - Jun 2012 - div, curl, grad, laplacian and Poisson solver.

Good morning/afternoon/evening,


Using R, I am trying to calculate stream function (psi) and velocity potential
(phi) from both 2D zonal (u) and meridional wind (v).

I Stream function

The stream function can be obtained from the vorticity (vorticity):

vorticity = curl(u,v)

or in other terms:?

vorticity?= dv/dx - du/dy + u tan(th)/rad?

This second approach is easily done using the function 'grad' in
'oce' package.

Thus, the stream fuction is obtained solving the following Poisson equation (1):

laplacian(psi) =?vorticity (1)

or:

div grad (psi) =?vorticity


II Vorticity

The vorticity can be obtained from the divergence (divergence):

divergence?= div(u,v)

or in other terms:?

divergence?= du/dx + dv/dy - v tan(th)/rad?

This second approach is also easily done using the function 'grad' in
'oce' package.

Thus, the vorticity is obtained solving the following Poisson equation (2):

laplacian(phi) =?divergence (2)

or:

div grad (phi) =?divergence


Is there a way to solve both Poisson equations (1) and (2) in R?

Best Regards,
Pascal Oettli