[MITgcm-support] Meridional overturning streamfunction and free surface

[Martin Losch]

Andrea,

I am no expert on this, but here's my 5-cent:

- strictly speaking you can only define a streamfunction, if the flow is non-divergent (dv/dy+dw/dz=0)
- your model is generally not non-divergent, so your streamfunction will not be correct, nevertheless you can use is as a diagnostic. I usually integrate from the bottom to the top to make sure that the streamfunction is exactly zero at the bottom (at the expense of having a non-zero stream function at the surface, usually I don't care too much about that).
- I think that the linear free surface is not used in flux computations in the model, so that you should not attempt to include it in the stream-function-computations and your experience confirms this. Only when you turn on the non-linear free surface, the hFac's actually change, so that the diagnostic VVELMASS (=vVel*hFacS at V-points) contains the effect of the varying surface. You can then use VVELMASS to compute the stream function.

Martin

On Nov 15, 2011, at 11:52 AM, cimatori wrote:

> Hi everybody,
> I have a question that is probably obvious to those who know the details
> of the advection algorithm, but I am not one of them and couldn't find
> the answer myself.
> I am computing the meridional overturning streamfunction (in a simple
> geometry, cartesian coordinates, full cells only). It is a simple task
> and the streamfunction at the bottom (integrating from the top) is
> nicely close to zero when averaged in time (order of 10^-6 Sv). Just for
> completeness sake, I wanted to add the effect of the (implicit) free
> surface, so I summed the anomalous eta to the layer thickness of the top
> layer at each time step. Unfortunately, this makes things worse at the
> bottom (that is, the streamfunction is larger than in the case without
> eta taken into account, order 10^-2Sv). Please note that I am working at
> the cell centre (using meridional velocity at the cell centre from the
> diagnostics output and \Deltax_F) so that the error is not due to the
> different position of v and eta on the grid.
> I think that I am misunderstanding how the free surface is actually
> treated in the model. How should I include eta in the overturning
> streamfunction computation?
> 
> Thanks,
> Andrea
> 
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