The problem about creating an idealized warm ocean eddy

[Alex5]

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

[kate]

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]

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 ...

[rduran]

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]

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

[Alex5]

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