## The problem about creating an idealized warm ocean eddy

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Alex5
Posts: 12
Joined: Tue Oct 08, 2013 4:46 pm
Location: HongKong

### The problem about creating an idealized warm ocean eddy

Dear all,

I want to create an idealized warm ocean eddy (symmetric structure in terms of temperature). I used several temperature profiles to make the initial condition, but the structure was a square area as shown in following figure. Do you have any idea about how to create the initial condition to get a more realistic eddy (circular).

Alex
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kate
Posts: 3770
Joined: Wed Jul 02, 2003 5:29 pm
Location: IMS/UAF, USA

### Re: The problem about creating an idealized warm ocean eddy

This solves a different problem but creates an initial shape with circular symmetry:

Code: Select all

``````! Linear background
DO k=1,N(ng)
DO j=JstrT,JendT
DO i=IstrT,IendT
val1 = -0.02*z_r(i,j,k)
t(i,j,k,1,itemp)=val1
t(i,j,k,1,isalt)=0.0
END DO
END DO
END DO
DO k=1,N(ng)
DO j=JstrT,JendT
DO i=IstrT,IendT
val1 = sqrt( ((xr(i,j)-40.e+3_r8)/10000.)**2 + &
&                   ((yr(i,j)-40.e+3_r8)/10000.)**2 + &
&                   ((z_r(i,j,k) + 500.)/200.)**2 )
IF (val1 .le. 1) THEN
t(i,j,k,1,itemp)=10.
t(i,j,k,1,isalt)=1.0
END IF
END DO
END DO
END DO``````
Did you take geometry courses?

patrickm
Posts: 24
Joined: Fri Apr 30, 2004 6:41 pm
Location: IRD, FRANCE
Contact:

### Re: The problem about creating an idealized warm ocean eddy

a square vortex is possible, but you need some resonant vortex Rossby waves. See this plot by Schubert et al. (1999). I also heard that G. Roullet (LPO, France) has presented some results at the Ocean Sciences meeting where he could make a square vortex using some flux-corrected advection schemes ...
Attachments
Fig.3 from Schubert et al., JAS, 1999
Schubert_etal_JAS1999_fig3.png (404.23 KiB) Viewed 2681 times

rduran
Posts: 139
Joined: Fri Jan 08, 2010 7:22 pm
Location: Theiss Research

### Re: The problem about creating an idealized warm ocean eddy

I recall my undergrad adviser (physical oceanography) saying: I am sure you can find a square wave in the ocean. That actually makes sense if one thinks in terms of representing waves as a linear combination of trigonometric functions (Fourier series) -- you get a square with two step functions and you can approximate a step function by adding the right sines and cosines (i.e. the right waves) and in fact you don't even need too many terms in the series to get a decent convergence. Thus in physical ocean it is conceivable that if the right waves add up and you get a square. The question is how much will the square last?

That is a very interesting example Patrick, it proves my adviser right, and it looks like it lasted for about an hour or two ...

kate
Posts: 3770
Joined: Wed Jul 02, 2003 5:29 pm
Location: IMS/UAF, USA

### Re: The problem about creating an idealized warm ocean eddy

Patrick's example is pretty cool, but Alex could try starting from his square and seeing what happens - might be fun!

Alex5
Posts: 12
Joined: Tue Oct 08, 2013 4:46 pm
Location: HongKong

### Re: The problem about creating an idealized warm ocean eddy

Guys, thanks very much for all your suggestions . I will try it.