Curl of a vector field in the zhat direction

[amélie ch]

Hi all, 

I'm working on a 2D shallow water mhd simulation and I was wondering if there was any way in Dedalus that I could define the substitution (or something of the form):
B = 1/h * curl(A zhat) where B=B(x,y,t) is a vector field, h=h(x,y,t) is a field, A=A(x,y,t) is a field and zhat is the z unit vector.  This is how I want to implement it into my equations (see attachment below).

Thanks, 

Amélie

[Daniel Lecoanet]

Hi Amelie,

I believe you want to use -d3.skew(d3.grad(A)). But you should check the sign.

Daniel

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<swmhd_code.png>

[amélie ch]

Hi!

Thanks for the response. I am now working in spherical coordinates so my unit vector is now rhat. So I want to preform the operation  B = 1/h * curl(A rhat). Would I still use as you said 

-d3.skew(d3.grad(A))?

Thanks,

Amélie

[amélie ch]

** note that I'm using S2Coordinates so I can't really radial unit vectors (as I understand it)

[Daniel Lecoanet]

Yes I believe that is right, but be sure to check the sign!

Daniel

On Feb 8, 2026, at 23:42, amélie ch <ameliec...@gmail.com> wrote:

** note that I'm using S2Coordinates so I can't really radial unit vectors (as I understand it)

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