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<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US">Thank you, Paola and Martin. My answers below:<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US">@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.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US">@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!<o:p></o:p></span></p>
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<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US">Bertrand<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
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<p class="MsoNormal"><b><span style="font-size:12.0pt;color:black">De : </span></b><span style="font-size:12.0pt;color:black">MITgcm-support <mitgcm-support-bounces@mitgcm.org> au nom de Paola Cessi <pcessi@ucsd.edu><br>
<b>Répondre à : </b>"mitgcm-support@mitgcm.org" <mitgcm-support@mitgcm.org><br>
<b>Date : </b>lundi 4 février 2019 à 7:39 AM<br>
<b>À : </b>"mitgcm-support@mitgcm.org" <mitgcm-support@mitgcm.org><br>
<b>Objet : </b>Re: [MITgcm-support] body force in apply_forcing.F<o:p></o:p></span></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">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. <o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:15.0pt;font-family:Helvetica;color:black"><br>
Paola<o:p></o:p></span></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">On Feb 4, 2019, at 1:30 AM, Martin Losch <<a href="mailto:Martin.Losch@awi.de">Martin.Losch@awi.de</a>> wrote:<o:p></o:p></p>
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<p class="MsoNormal">Hi Bertrand,<br>
<br>
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?
<br>
<br>
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.
<br>
<br>
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<br>
<br>
Martin<br>
<br>
On 2. Feb 2019, at 23:38, Bertrand Louis Rene Delorme <<a href="mailto:bdelorme@stanford.edu">bdelorme@stanford.edu</a>> wrote:<br>
<br>
<o:p></o:p></p>
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<p class="MsoNormal"><br>
Hi everyone,<br>
<br>
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:<br>
<br>
DO j=1,sNy+1<br>
DO i=0,sNx+1<br>
yv = 0.5*(yC(i,j,bi,bj)+yC(i,j-1,bi,bj))<br>
gV_arr(i,j) = gV_arr(i,j) + 1E-7 * exp(-(rC(k)-mZ)**2/sigZ**2) * exp(-(yv-mY)**2/sigY**2)<br>
ENDDO<br>
ENDDO<br>
<br>
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.
<br>
<br>
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.<br>
<br>
Thank you,<br>
<br>
Bertrand <br>
<br>
<br>
<br>
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