[MITgcm-support] Balance of momentum

[Marco Reale]

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

***********************************

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://mitgcm.org/pipermail/mitgcm-support/attachments/20131204/afee280d/attachment.htm>