[MITgcm-support] body force in apply_forcing.F

[Bertrand Louis Rene Delorme]

Thank you, Paola and Martin. My answers below:

@Martin: I initialize u with a jet (u0) but since I add a body force in the v-momentum equation that looks like BF = f*u0, then dv/dt = -f*u0 + BF = 0 at t=0. Therefore, I don’t expect an acceleration in the v-direction. Assuming that there is no loss due to viscous processes, I expect the jet to be steady, at least for the time scale that I consider. However, as I said, I see some waves emanating from the jets right from the beginning of the simulation, suggesting that the balance -f*u0 + BF = 0 is actually not perfectly working. Because it is generating those oscillations, I suspected that this is due to a dephasing between the grid that I use for u0 in gendata and for the BF terms in apply_forcing.

@Paola: You were right. Switching to an expression for BF where I average across the neighboring U points gives me what I want. I still have small oscillations generated but with amplitude O(1e-6) relative to the O(1e-4) that I had before. The jet amplitude is O(1e-1) so it might be related to the numerics. Thanks!

Bertrand


De : MITgcm-support <mitgcm-support-bounces at mitgcm.org> au nom de Paola Cessi <pcessi at ucsd.edu>
Répondre à : "mitgcm-support at mitgcm.org" <mitgcm-support at mitgcm.org>
Date : lundi 4 février 2019 à 7:39 AM
À : "mitgcm-support at mitgcm.org" <mitgcm-support at mitgcm.org>
Objet : Re: [MITgcm-support] body force in apply_forcing.F

I wonder if you considered the Coriolis term exactly as in the code, which involves averaging the four neighboring U points around the grid point where P_y falls. To be balanced, the forcing would have to be averaged in the same way.

Paola

On Feb 4, 2019, at 1:30 AM, Martin Losch <Martin.Losch at awi.de<mailto:Martin.Losch at awi.de>> wrote:

Hi Bertrand,

I am not sure if I understand what you want to do: You intialize u with a jet, which you want to make steady, but you add a body force that will change v (dv/dt = …). What is the balance, that you are looking for?

Naively, I would think, it is the geostrophic balance. But in geostrophic balance dv/dt and du/dt = 0 and you have rho*f*u = -dp/dy and and rho*f*v = + dp/dx. If the jet is along x, then v = 0, so dp/dx = 0, and you just have to make sure that in your intial conditions dp0/dy = -rho*f*u0. For a barotropic case that would mean d\eta/dy = f*u0/g in your intial conditions.

Without any extra forcing this jet would decay due to friction in the system (and some v will appear). Depending on your question, you could restore u to the inital conditions (you can use the rbcs package for that), but that will always damp the system

Martin

On 2. Feb 2019, at 23:38, Bertrand Louis Rene Delorme <bdelorme at stanford.edu<mailto:bdelorme at stanford.edu>> wrote:


Hi everyone,

I am trying to set up a configuration with just a steady, deep, zonal jet in the water column balanced by the Coriolis force. To do that, I prescribed the jet as initial condition (u0) and I added a body force (BF) in the v-momentum equation such that dv/dt = -f*u + BF with BF=f*u0. I used apply_forcing.F to incorporate the body force by adding the following lines in APPLY_FORCING_V:

DO j=1,sNy+1
     DO i=0,sNx+1
yv = 0.5*(yC(i,j,bi,bj)+yC(i,j-1,bi,bj))
gV_arr(i,j) = gV_arr(i,j) + 1E-7 * exp(-(rC(k)-mZ)**2/sigZ**2) * exp(-(yv-mY)**2/sigY**2)
     ENDDO
ENDDO

where (mY, mZ) are the coordinates of the center of the jet in the meridional plane, sigZ and sigY the e-folding scale in each direction, and yv is the y-coordinate on the V-grid. Concerning the initial condition for U, I was careful to define it on the U-grid.

However, for some reasons, the jet is not perfectly balanced and low amplitude waves emanate from its center. I feel like I might be doing something inconsistent in apply_forcing.F, like not using the appropriate grid, but couldn't figure out what it is. If anyone has an idea on what might go wrong please let me know.

Thank you,

Bertrand



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