[MITgcm-support] Balance of momentum

Wed Dec 4 09:18:24 EST 2013

This has been a very informative discussion. It was interesting (and slightly disturbing) to learn from David's email that you essentially need to hack the code in order to output the necessary terms to close the momentum budget. 

May I humbly suggest that someone add diagnostics for the missing terms? 

-Ryan

Sent from my iPhone

On Dec 4, 2013, at 5:14 AM, David Munday <Munday at atm.ox.ac.uk> wrote:

> Hi Marco,
> 
>> a) I saw from MITGCM manual that Um_Advec includes all the terms of acceleration including Coriolis, explicit diffusive terms , metric and pressure terms. So in my balance should I include only Um_Advec instead of Um_Advec+Um_Cori+Um_diss+Um_ext+Um_HydroP?
> 
> 
> Um_Advec includes Um_Cori, and any metric terms if you're using flux-form I guess. Um_diss, etc, aren't in Um_Advec and so you need to include them in your balance.
> 
> As far as I'm aware, any explicit viscosity terms are also in Um_diss. I use implicit vertical viscosity, though, so I've never checked.
> 
>> b) I have the rigid  -lid and so I should include in  the balance also the term relative to Eta . How can I compute the contribution of Eta ? Is it simply dEta/dx = [Eta(i+1,j)-Eta(i,j)]/dxc(i,j)?or Should I consider to multiply this term for something else?In fact Eta with rigid lid is a pressure and so not an acceleration.Then It’s given on a single level: so should I sum this quantity to each level or dividing/multiplying it for something and then add to each level?
> 
> Are you actually using a rigid lid? Or a linear free surface? Its only if you're using a linear free surface that I think you need to worry about this.
> 
> I output the horizontal gradients of eta, really the gradient in surface potential, from momentum_correction_step.F. The quantities you need are calculated here and then used to update the U and V velocities. Just output phisurfX and phisurfY multiplied by -1 to get the sign right. They're 2D fields, but the same value applies at every vertical model level.
> 
> Once you've got these gradients you should get an extremely well closed momentum budget by following the recipe in the chain of e-mails starting with Emily Shroyer's from December 2010, see http://mitgcm.org/pipermail/mitgcm-support/2010-December/thread.html#6918. These e-mails saved me a whole load of time when I wanted to close the momentum budget (thanks Emily, Matt, and Jean-Michel!)
> 
>> The signs coincide : the values appears to be different..what looks strange to me is also the sign because Uvel is positive.Did I something wrong in the computation? Did I forget some terms?Is it correct TOTUtend/86400?
> 
> 
> The sign of the tendency, total or otherwise, won't tell you the sign of U, just the sign of its change. See the e-mails linked above for what to add together. Yes, TOTUTEND should be divided by 86400 to get /s.
> 
> Best wishes,
> 
> Dave
> 
> On 3 Dec 2013, at 23:08, Marco Reale wrote:
> 
>> Dear MITGCM users , 
>> 
>> following the suggestion of Dr.Losch I posted a question about an analysis that I’m doing. I’m trying to compute a balance of vorticity for a basin : the first assessment (and verification) in this analysis is the computation of balance of momentum . Following a previous post in this mailing list I got during from my simulation the following diagnostics (I will talk only about  U-component):
>> 
>> Uvel,TOTUTEND,Um_Advec,Um_Cori,Um_diss,Um_ext,Um_HydroP,VISrE_Um (i’m using an explicit scheme).
>> 
>> From VISrE_Um I computed :  Um_Expl(:,:,k) =[ VISrE_Um(:,:,k+1) - VISrE_Um(:,:,k) ] /[ rAw(:,:)*drF(k)*hFacW(:,:,k) ]
>> 
>> My simulation have been run with rigid-lid , frequency for the diagnostics 432000 s , step of integration equal to 1200s , flux momentum formulation, 24 levels , 17 x 49 points for each levels, hydrostatic configuration.
>> 
>> So following previous post the balance of momentum should be given for each level : TOTUTEND/86400=Um_Advec+Um_Cori+Um_diss+Um_ext+Um_HydroP+Um_Expl
>> 
>> But :
>> 
>> a) I saw from MITGCM manual that Um_Advec includes all the terms of acceleration including Coriolis, explicit diffusive terms , metric and pressure terms. So in my balance should I include only Um_Advec instead of Um_Advec+Um_Cori+Um_diss+Um_ext+Um_HydroP?
>> 
>> b) I have the rigid  -lid and so I should include in  the balance also the term relative to Eta . How can I compute the contribution of Eta ? Is it simply dEta/dx = [Eta(i+1,j)-Eta(i,j)]/dxc(i,j)?or Should I consider to multiply this term for something else?In fact Eta with rigid lid is a pressure and so not an acceleration.Then It’s given on a single level: so should I sum this quantity to each level or dividing/multiplying it for something and then add to each level?
>> 
>> Finally I considered a point in my domain in the first level and in the center of my domain at the time t=1 and I did the balance : TOTUtend/86400= Um_Advec+[Eta(i+1,j)-Eta(i,j)]/dxc(i,j)+Um_Expl and I got 
>> 
>> TOTUtend/86400=-1.02*10^-9
>> Um_Advec+[Eta(i+1,j)-Eta(i,j)]/dxc(i,j)+Um_Expl=-1.50*10^-9
>> 
>> The signs coincide : the values appears to be different..what looks strange to me is also the sign because Uvel is positive.Did I something wrong in the computation? Did I forget some terms?Is it correct TOTUtend/86400?
>> 
>> 
>> Looking forward to a positive response to my question
>> 
>> 
>> Best regards
>> 
>> 
>> Marco
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>> ***********************************
>> Marco Reale
>> ph.D student "Environmental and Industrial Fluid Mechanics"-XXVII cycle
>> University of Trieste-Department of Mathematics and Informatics
>> National Institute of Geophysics and Oceanography (OGS)
>> International Center for Theorethical Physics (ICTP)
>> Italian Geophysical Association (AGI)
>> Italian Meteorological Society (SMI)
>> European Geophysical Union (EGU)
>> web-page: http://phdfluidmechanics.appspot.com/stud.html?Reale
>> skype: mcreal82
>> phone number: +39 3270888069
>> 
>> ***********************************
>> 
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> 
> *****************************************************************************
> 
> Dr. David R. Munday
> University of Oxford
> Atmospheric, Oceanic, and Planetary Physics
> Clarendon Laboratory
> Parks Road
> Oxford
> OX1 3PU
> U.K.                 01865 282 439
> 
> *****************************************************************************
> 
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