Free-surface boundary condition on spherical shell basis

[Suprabha Mukhopadhyay]

Hi,

This is a sort of follow-up question from Geoff's yesterday's talk at the "dynamo & solar cycle" RSWG meeting.  

I was wondering if it is possible to have a free surface boundary condition for the spherical shell geometry in Dedalus. Then one could use a very thin spherical shell without significantly affecting the modes which extend to the boundary. I am interested in knowing if this is a possibility, as I would also like to incorporate it into the eigenvalue problem I am solving.

Thanks and Regards,

Sup

[Keaton Burns]

Hi Sup,

Yes it’s definitely possible to implement linearized free surface boundary conditions with a surface height field as an extra variable, and linear extrapolation for the pressure boundary condition. I haven’t experimented with nonlinear free surface conditions, but they may work in limited regimes as well.

Best,

-Keaton

--
You received this message because you are subscribed to the Google Groups "Dedalus Users" group.
To unsubscribe from this group and stop receiving emails from it, send an email to dedalus-user...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/dedalus-users/f8a26a1b-3359-48af-9dc2-dfada3bcd9e2n%40googlegroups.com.

[Suprabha Mukhopadhyay]

Thanks, Keaton, for your quick reply. Are there some example scripts, which I can have a look at to see how I can implement a linear free surface boundary condition? An example would be very helpful, as I have not used the free-surface boundary condition before. I have been using the stress-free impenetrable boundary conditions for solving an eigenvalue problem on the spherical shell geometry. 

Best regards,

Sup

[Keaton Burns]

Hi Sup,

No we don’t have any example scripts implementing this at the moment. The basic idea is to keep track of a surface height field eta, and then apply the boundary conditions using a linearized evaluation of the fields at that height, which turns Dirichlet boundary conditions into Robin conditions, e.g. p(z=eta) = p(z=0) + eta*dz(p)(z=0).  In place of the impenetrability boundary condition, you can apply something like p(z=eta) = 0. And you also have an evolution equation for eta. This is a simple version, though, so I’d really suggest looking into some literature on the topic for more details.

Best,

-Keaton

To view this discussion on the web visit https://groups.google.com/d/msgid/dedalus-users/bfda3dd6-8f37-4cd2-b075-fb3a6302ca7en%40googlegroups.com.

[Suprabha Mukhopadhyay]

Hi Keaton,

Thank you very much for giving the insight into how to implement the free surface boundary condition. This was very helpful. I will look into the literature for details and try to implement it in the problem I am solving.

Best regards,

Sup