[MITgcm-support] Meridional overturning streamfunction and free surface

[cimatori]

Martin,
I understand your points. I can only add that I checked the continuity
equation implementation and, as far as I understand, indeed eta is not
taken into account in flux.
Andrea

On 11/16/2011 01:11 PM, Martin Losch wrote:
> 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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