[MITgcm-support] north-south or south-north gridding?

[Baylor Fox-Kemper]

Dear MITgcmers (especially Jill, Martin and Dimitris)

Beware the pseudo-vector!

While true vector operations, e.g., grad, div, addition, scalar  
multiplication, survive a mirror reflection unaffected x,y,z->-x,-y,- 
z (and most physics does, too, except for elementary particle, weak  
force interactions, see http://lhcb-public.web.cern.ch/lhcb-public/ 
html/cpviolationtoc.htm), a pseudo-vector changes sign under mirror  
reflection!  How do you get a pseudo-vector? you take a cross- 
product, or curl.  So, VORTICITY is a PSEUDOVECTOR, and so is f.  The  
problem is, the momentum and tracer equations are rotation and  
reflection invariant, but this is only because there are doubled sign  
reversals, i.e., the coriolis parameter should change sign but the  
coriolis acceleration shouldn't!

So, there are very tricky reconstructions to make when you start  
messing with mirror reflections, as some things should change sign  
and others don't.  It is very easy to get messed up!  I would  
recommend against running a model in such a way that you have to flip  
the sign of some things and not others unless you are very confident  
that you know the sign of everything that's supposed to come out.   
You can really get messed up with potential vorticity and  
streamfunctions, for example, where you will have to flip the sign of  
not only f, but also curl v, etc.  You have to remember to use a  
right-hand rule or a left-hand rule depending on whether you've  
reflected or not.

Cheers, and good luck if you try!
    -Baylor


On Sep 21, 2006, at 11:10 AM, Martin Losch wrote:

>
> On Sep 21, 2006, at 4:13 PM, Dimitris Menemenlis wrote:
>
>> Hi Jill, any MITgcm "feature" that has not been tried before (or  
>> recently) is unlikely work OK the first time around.  There will  
>> possibly/probably be one or two places in the code where a  
>> particular MITgcm contributor was not thinking of NZ at time of  
>> addition.  What about running on a +50 to +80 grid but then  
>> looking at "that" solution through a mirror or, equivalently I  
>> think, plotting it on a -80 to -50 grid.  Would that work?  Dimitris
>
> I think that's perfect! That way, even the direction of the  
> coriolis force would "look" right in the mirror (o:
>
> M.
>
>>
>>
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