[MITgcm-support] phihydlow formula

[Martin Losch]

Benny,
the formulae are all in the documentation, so equation 1.32 on that 
page is it. As I wrote in my previous email to the other thread, for 
height coordinates, b in 1.32 is the scaled density g\rho/\rho_{0}. In 
the code it's actually the scale density anomaly, as Dimitris pointed 
out: g(\rho-\rho_{0})/\rho_{0}, so the phiHyd and phiHydLow is the 
corresponding pressure anomaly scaled by \rho_{0}. If you compute the 
full bottom pressure (including the g\rho_{0}H contribution), then you 
won't see much except topography. Because topography (=depth) dominates 
the bottom pressure, it really only makes sense to look at fluctuations 
of bottom pressure. and for those the choice of \rho_{0} (=rhoConst in 
data) is irrelevant.

There is a paper by John Marshall which also should have all the 
formulae:
Marshall, J. A. Adcroft, J-M Campin and  C. Hill (2004)
  Atmosphere-ocean modeling exploiting fluid isomorphisms. submitted to  
Monthly Weather Review. You can download a preprint from
http://paoc.mit.edu/paoc/marshall/latest_papers.htm
Also in Losch etal 2004 JPO 34(1), pp 306-319, we describe the 
ismorphism and all equations in detail in the appendix (in particulare 
Eq A23 and the following text). Appendix C describes the discretization 
issue I was alluding to earlier. If you don't have access to JPO, you 
can download a preprint from
http://mitgcm.org/~mlosch/nonbouss_pp.pdf

Good luck,
Martin

On Aug 16, 2004, at 11:54 PM, Benny Cheng wrote:

> Could someone show me or email me the exact phihydlow computation ( in
> mathematical notation , not code) used in the MITgcm. It looks rather
> murky to tread through the code... is it close to what is described in
> http://mitgcm.org/sealion/online_documents/node20.html ? thanks.
>
> - Benny
>
>
>
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Martin Losch // mailto:mlosch at awi-bremerhaven.de
Alfred-Wegener-Institut für Polar- und Meeresforschung
Postfach 120161, 27515 Bremerhaven, Germany
Tel./Fax: ++49(471)4831-1872/1797
http://www.awi-bremerhaven.de/People/show?mlosch