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).
Thanks in advance.
Alex
The problem about creating an idealized warm ocean eddy
The problem about creating an idealized warm ocean eddy
 Attachments

 woe_ini.png (9.63 KiB) Viewed 2851 times
Re: The problem about creating an idealized warm ocean eddy
This solves a different problem but creates an initial shape with circular symmetry:
Did you take geometry courses?
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
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 fluxcorrected advection schemes ...
 Attachments

 Fig.3 from Schubert et al., JAS, 1999
 Schubert_etal_JAS1999_fig3.png (404.23 KiB) Viewed 2827 times
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 ...
That is a very interesting example Patrick, it proves my adviser right, and it looks like it lasted for about an hour or two ...
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!
Re: The problem about creating an idealized warm ocean eddy
Guys, thanks very much for all your suggestions . I will try it.