[MITgcm-support] ALLOW_ADDFLUID option and U, V momentum equation
Krishnakumar Rajagopalan
krishna_raj_2010 at yahoo.com
Wed Aug 31 21:18:01 EDT 2011
Hi Jean-Michel,
Thanks a lot for your reply. There was an error in my e-mail. uVel and vVel are not velocities of the added-mass. My apologies ...
Let me briefly explain my approach:
Take equation 2.1 and 2.2 of MITgcm manual. They are,
d(u)/d(t) + g d(eta)/d(x) = Gu eqn 2.1
d(v)/d(t) + g d(eta)/d(y) = Gv eqn 2.2 ; ( Letter 'd' stands for partial)
In the presence of the source, these become,
d(u)/d(t) + g d(eta)/d(x) = Gu + (mdot/rho) (u_s - u)
d(v)/d(t) + g d(eta)/d(y) = Gv + (mdot/rho)(v_s -v)
Here u_s and v_s denotes the horizontal velocities of the source and mdot denotes the source strength (kg/m^3/s) . When u_s=u and v_s=v, the new terms equals zero. I believe this is what happens in the case of rain when the ocean current and the wind velocity are the same. In our case u_s, v_s are small and equal zero. We modified mom_fluxform.F to include (mdot/rho)(-u) and (mdot/rho)(-v) as ,
U momentum
//////////////////////////////
gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj) -
& addMass(i,j,k,bi,bj)*uVel(i,j,k,bi,bj)*mass2rUnit/cellvol
V momentum
////////////////////////////
gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj) -
& addMass(i,j,k,bi,bj)*vVel(i,j,k,bi,bj)*mass2rUnit/cellvol
I think it is correct to say that uVel, vVel are the ocean currents at the source location. Please let me know if this approach is correct or if you have anymore questions.
Best regards
Krishnakumar
--- On Wed, 8/31/11, Jean-Michel Campin <jmc at ocean.mit.edu> wrote:
From: Jean-Michel Campin <jmc at ocean.mit.edu>
Subject: Re: [MITgcm-support] ALLOW_ADDFLUID option and U, V momentum equation
To: mitgcm-support at mitgcm.org
Date: Wednesday, August 31, 2011, 3:05 AM
Hi Krishnakumar,
I think I understand the issue (in the ocean, we have similar question
relative to the horizontal momentum that the rain bring when falling into
the ocean).
But I thought that the present implementation (at least in flux-form)
was consitent with rain comming with same horizontal speed as the
ocean current, which translate into addMass arriving/leaving with same
speed as the local wind.
Now, I would like to ask something:
> calling uVel(i,j,k,bi,bj) and vVel(i,j,k,bi,bj) the horizontal velocity components
> of the source (a vertical term would come into play in non-hydrostatic runs)
do you mean the wind speed at the source location ? or the velocity
of the added-mass itself ?
Cheers,
Jean-Michel
On Tue, Aug 30, 2011 at 05:39:38PM -0700, Krishnakumar Rajagopalan wrote:
> Hi Angela, Jason
> Angela: Thanks for your comments on the Mars GCMs. Admittedly, the practical significance of source momentum in geophysical problems is not likely to ever be great.
> Jason : I talked to my post doc advisor, Gérard Nihous (nihous at hawaii.edu) regarding your comments. As you correctly pointed out, the mass from the source changes the pressure distribution, thereby affecting the momentum equations. This ‘mass introduction’ effect comes from mass conservation and is locally isotropic (via a non-zero divergence operator for the velocity field). The source, however, can also have its own momentum (which is directional). For example, taking your analogy of a hose into a tank, we can imagine hoses with very different diameters for a given mass flow rate, that could also be pointing in different directions; in each case, the resulting flow field would be uniquely different due to this ‘jet’ effect.
> I looked into the MITgcm equations (for the hydrostatic case we have been using). Barring any misunderstanding on my part and calling uVel(i,j,k,bi,bj) and vVel(i,j,k,bi,bj) the horizontal velocity components of the source (a vertical term would come into play in non-hydrostatic runs), it seems that the jet effect could be implemented in mom_fluxform.F by adding two terms as follows:
> a) U momentum
> gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj) -
> & addMass(i,j,k,bi,bj)*uVel(i,j,k,bi,bj)*mass2rUnit/cellvol (1)
> b) V momentum
> gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj) -
> & addMass(i,j,k,bi,bj)*vVel(i,j,k,bi,bj)*mass2rUnit/cellvol (2)
> Again, I am grateful to both of you for your comments.
> Best regards
> Krishnakumar
>
> --- On Fri, 8/26/11, Angela Marie Zalucha <azalucha at MIT.EDU> wrote:
>
>
> From: Angela Marie Zalucha <azalucha at MIT.EDU>
> Subject: Re: [MITgcm-support] ALLOW_ADDFLUID option and U, V momentum equation
> To: mitgcm-support at mitgcm.org
> Date: Friday, August 26, 2011, 5:20 PM
>
>
> For Mars the atmosphere (composed of CO2) can condense and sublimate. Usually we assume that if a parcel of atmosphere reaches the condensation temperature, it instantaneously drops to the surface. So in that case if the parcel was moving (and therefore contained momentum), when it fell on the ground it would come to rest, transfering its momentum to the surface and removing it from the atmosphere. The momentum effect is ignored in Mars GCMs.
>
> Angela
>
>
>
>
> On Fri, 26 Aug 2011, Jason Goodman wrote:
>
> > The source/sink terms affect the momentum equation through the pressure field. If I have a tank of water with a hose running into it, how does the water already in the tank "know" to move away from the hose spigot? Pressure. Adding fluid increases the pressure at the source, which causes a pressure gradient pushing nearby water away.
> >
> > The standard MITGCM solves to find the pressure field needed to make the velocity field non-divergent. When ALLOW_ADDFLUID is on, it solves for the pressure field needed to make the velocity field have a prescribed divergence: that pressure field then appears in the momentum equation to push water around.
> >
> > I don't think there *should* be any other terms added to the momentum equations.
> >
> > JCG
> >
> > On 8/26/2011 12:44 PM, Angela Marie Zalucha wrote:
> >> Kumar,
> >>
> >> You're right, the fluid source/sink is assumed not to affect the momentum equations. For planetary applications this term is small, I don't know about the ocean.
> >>
> >> Angela
> >>
> >>
> >>
> >> On Thu, 25 Aug 2011, Krishnakumar Rajagopalan wrote:
> >>
> >>> Hi All,
> >>>
> >>> We have been customizing the 4x4 global ocean simulation (tutorial_global_oce_latlon) to include sources/sinks using the ALLOW_ADDFLUID option. Checking with grep " ALLOW_ADDFLUID" *.F, it seems that sources do not explicitly appear in the U or V momentum equations. If indeed these equations are formally unchanged when the source/sink switch is on, are we correct assuming that this version of MITgcm does not have a provision for (input) source momentum? A source could have an initial vertical momentum as well, although such cases may be more relevant for non-hydrostatic runs.
> >>> Thanks a lot
> >>> Kumar
> >>>
> >>
> >> _-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-
> >> Angela Zalucha, Ph.D.
> >> Postdoctoral Associate
> >> Department of Earth, Atmospheric,
> >> and Planetary Sciences
> >> Massachusetts Institute of Technology
> >>
> >> Office located at Southwest Research Institute
> >> 1050 Walnut Street, Suite 300
> >> Boulder, CO 80302
> >> USA
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> >>
> >>
> >> http://web.mit.edu/azalucha/www/index.html
> >> _-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-
> >>
> >>
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> _-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-
> Angela Zalucha, Ph.D.
> Postdoctoral Associate
> Department of Earth, Atmospheric,
> and Planetary Sciences
> Massachusetts Institute of Technology
>
> Office located at Southwest Research Institute
> 1050 Walnut Street, Suite 300
> Boulder, CO 80302
> USA
> (720) 208-7211
>
>
> http://web.mit.edu/azalucha/www/index.html
> _-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-
>
>
>
>
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