[MITgcm-support] 回复： Non-Zero Meridional Velocity Kelvin Wave

Fri Nov 17 00:15:54 EST 2017

Hi,

I notice that there are discontinuities in your surface plot of the residual of the two terms in PDF file.  It is a little surprising to me, but your PDF plots are really blurred I cannot read the numerics.

I do not know much about normal mode.  But the classical Kelvin wave in the equatorial beta plane is derived from a simplified dynamics e.g., ignoring the nonlinear advection terms.  So I guess you cannot expect a perfect Kelvin wave in the MITgcm as it is based on the primitive equations (there should be exceptions that some solutions perfectly fit the nonlinear terms, rendering an exact cancellation of the nonlinear terms).  You may verify your normal mode perfectly only in the simplified model that your solution is based on.

------------------
 Best regards 

Yu-Kun Qian (钱钰坤) 
Center for Monsoon and Environment Research 
 Department of Atmospheric Sciences
School of Environmental Science and Engineering 
 Sun Yat-sen University 
No. 135 Xingang West Road, Haizhu District 
Guangzhou, 510275, P.R. China 
Tel; 020-84115227 
Email: qianyk at mail3.sysu.edu.cn      

------------------ 原始邮件 ------------------
发件人: "Bertrand Louis Rene Delorme"<bdelorme at stanford.edu>;
发送时间: 2017年11月17日(星期五) 上午10:58
收件人: "mitgcm-support at mitgcm.org"<mitgcm-support at mitgcm.org>; 

主题: Re: [MITgcm-support] Non-Zero Meridional Velocity Kelvin Wave

A little update on my problem (note also that the plot of Vm_dPHdy_Surf in my previous message is wrong):

-          The full baroclinic pressure gradient force (ie: Vm_dPHdy-gravity*(ETAN(i) - ETAN(i-1) )/DYC)  and 

the Coriolis force (in Vm_Advec or Vm_Cori -- same) are the only forces occurring in the v-momentum  equation 

(AB_gV is non-zero but much smaller).

-          I plotted those at the first time step (see enclosed). We can see that they do seem to have opposite spatial structures. 

Yet, looking at the difference of their amplitude ( ABS(f*u) - ABS(dPHI/dy) ), we can see that they do not balance 

each other perfectly. The induced acceleration is consistent with the plot of V.

So, I managed to find where the nonzero values in V come from, but still struggle to know why. 

If anyone has an idea, please let me know. 

Thanks,

Bertrand

De : MITgcm-support <mitgcm-support-bounces at mitgcm.org> au nom de Bertrand DELORME <bdelorme at stanford.edu>
 Répondre à : "mitgcm-support at mitgcm.org" <mitgcm-support at mitgcm.org>
 Date : jeudi 16 novembre 2017 à 12:20 PM
 À : "mitgcm-support at mitgcm.org" <mitgcm-support at mitgcm.org>
 Objet : Re: [MITgcm-support] Non-Zero Meridional Velocity Kelvin Wave

Thank you again, Yu-Kun, for your precious help.

I just checked the model output after the first time-step at t1 (where t0=initial conditions)., and right at t1 v is nonzero. 

In the v-momentum equation, the 3 diagnostics terms that I found to be nonzero at t1 are:

-          AB_gV (~10^-12)

-          Vm_Advec — which is exactly equal to Vm_Cori — (~10^-9)

-          Vm_dPHdy (~10^-9)

I also computed separately the surface pressure horizontal gradient (which is ~10^-8) using the relation:

Vm_dPHdy_Surf = - gravity * ( Eta(i) - Eta(i-1) ) / dyC

The other terms (Vm_Diss and Vm_Ext) are equal to zero.

In the Kelvin wave case, I would expect Vm_Cori and Vm_dPHdy+ Vm_dPHdy_Surf to balance each other perfectly.

Yet, as you can see in the plots enclosed to this email, their spatial structures are very different.

The shape of the Coriolis term looks consistent with the prescribed U velocity at t0.

And from the plot of V at t1, it seems that it is the quantity accelerating a flow in the meridional direction.

Surprisingly, it seems that even if Vm_Cori and Vm_dPHdy are the same magnitude, Vm_dPHdy has no influence on V.

The second problematic thing is the fact that the baroclinic pressure gradient seems to have a different vertical 

wavelength than the temperature anomaly that I prescribe at t=0 (see also enclosed).

Yet, this gradient should depend only on that quantity right (I do not prescribe any S values)?

Please let me know what your thoughts are at the view of this plot.

Best regards,

Bertrand

De :  MITgcm-support <mitgcm-support-bounces at mitgcm.org> au nom de SYSU <qianyk at mail3.sysu.edu.cn>
 Répondre à : "mitgcm-support at mitgcm.org" <mitgcm-support at mitgcm.org>
 Date : mercredi 15 novembre 2017 à 5:52 PM
 À : "mitgcm-support at mitgcm.org" <mitgcm-support at mitgcm.org>
 Objet : Re: [MITgcm-support] Non-Zero Meridional Velocity Kelvin Wave

Hi, 

You may want to find the time v becomes nonzero.  You can output probably the 2nd step to see if v becomes nonzero, and then using diagnostics to do the full v momentum budget to find the reason.

A possible reason is that you use analytic normal mode as IC, if specified to c-grid mitgcm, may generate truncation error, so that at the 2nd step v becomes nonzero.

------------ 

Best regards 

Yu-Kun Qian (钱钰坤)

Center for Monsoon and Environment Research 

Department of Atmospheric Sciences

Sun Yat-sun University

Guangzhou, China

 在 2017年11月16日，09:27，Bertrand Louis  Rene Delorme <bdelorme at stanford.edu>  写道：

Thank you very much, Yu-Kun, for your suggestion. Unfortunately, it is not the origin of my problem. 
 My 1st grid number is the boundary, and my 76th grid number is centered exactly at the Equator. 
 I also checked my IC variables and those are perfectly symmetric about the equator (assuming that I am defining my initial U and V velocity at cell center, right?).

Let me know if you have any other suggestions, and thank you again.

Best,

Bertrand

De :  MITgcm-support <mitgcm-support-bounces at mitgcm.org> au nom de SYSU <qianyk at mail3.sysu.edu.cn>
 Répondre à : "mitgcm-support at mitgcm.org" <mitgcm-support at mitgcm.org>
 Date : mercredi 15 novembre 2017 à 4:33 PM
 À : "mitgcm-support at mitgcm.org" <mitgcm-support at mitgcm.org>
 Objet : Re: [MITgcm-support] Non-Zero Meridional Velocity Kelvin Wave

Hi Bertrand, 

Not sure but I guess the symmetry of your grid about the equator is important.

Your Y-grid number is 150, so make sure the 75th grid is located exactly at equator, not the 75.5th (center btw 75th and 76th).  Make sure the IC setup by normal mode is also symmetric about equator.  That is the 1st and 149th, 2nd and  148th, ..., are exactly the same, as the 150th is the boundary.

------------ 

Best regards 

Yu-Kun Qian (钱钰坤)

Center for Monsoon and Environment Research 

Department of Atmospheric Sciences

Sun Yat-sun University

Guangzhou, China

 在 2017年11月16日，03:05，Bertrand Louis  Rene Delorme <bdelorme at stanford.edu>  写道：

Dears,

I am trying to set-up a very simple experiment to generate baroclinic Kelvin waves over an equatorial beta-plane. 

My approach so far has been to prescribe initial conditions for U, V, T and ETA based on the normal-mode solutions of the wave.

I managed to get a nice modal structure (both in the vertical and horizontal plane), which propagates without attenuation throughout the simulation. 

Here is my problem: in my initial conditions, I set V=0, but right after the first iteration V get non-zero values. 

As I am generating a Kelvin wave, I would expect V to stay equal to zero throughout the simulation, if the flow is well-balanced.

In my case, V ends up with an amplitude approximately one order of magnitude lower than U, which is still pretty high.

From the patterns I get in the outputs, it seems that the model is using dV/dy balance dU/dx in the continuity equation.

As I prescribed an initial free-surface, I was expecting W to play this role alone.

My issue can be link to an error in the normal-mode solutions that I use, which I checked carefully without finding any mistakes.

Another possibility would be that it comes from the set-up of my experiment.

I am using a domain centered at the equator with 60x150x200 grid points, with a resolution high enough to resolve the wave.

The only package that I am using is the MNC package, and my data file is pretty simple (see below).

If any of you has an idea of what I should check/test to understand where those non-zero values come from, please let me know.

Best,

Bertrand

&PARM01

sBeta=0.0,

selectCoriMap=1,

f0=0,

beta=2.29E-11,

readBinaryPrec=64,

writeBinaryPrec=64,

&

&PARM02

&

&PARM03

startTime=0.,

endTime=1600000,

deltaT=200,

dumpFreq=16000,

monitorFreq=1600000,

monitorSelect=1,

&

&PARM04

usingCartesianGrid=.TRUE.,

ygOrigin=-1050000,

delXfile='delXvar',

delYfile='delYvar',

delRfile='delZvar',

&

&PARM05

bathyFile='topog.flat',

hydrogThetaFile='Tini.bin',

uVelInitFile='Uini.bin',

vVelInitFile='Vini.bin',

pSurfInitFile='ETAini.bin',

&

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