VERY IMPORTANT: corrected bug in ATM_PRESS term for shallow-water applications

[arango]

There is a sign error when adding the ATM_PRESS term in step2d for shallow-water applications (SOLVE3D off). So we need to have the following code instead:

#if defined ATM_PRESS && !defined SOLVE3D
          rhs_ubar(i,j)=rhs_ubar(i,j)-                                  &
     &                  fac3*on_u(i,j)*                                 &
     &                  (h(i-1,j)+h(i,j)+                               &
     &                   gzeta(i-1,j)+gzeta(i,j))*                      &
     &                  (Pair(i,j)-Pair(i-1,j))
#endif
...
#if defined ATM_PRESS && !defined SOLVE3D
            rhs_vbar(i,j)=rhs_vbar(i,j)-                                &
     &                    fac3*om_v(i,j)*                               &
     &                    (h(i,j-1)+h(i,j)+                             &
     &                     gzeta(i,j-1)+gzeta(i,j))*                    &
     &                    (Pair(i,j)-Pair(i,j-1))
#endif

We need to use a minus sign for the contribution—many thanks to Shunpei Matsuo for ​reporting this bug.

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I noticed the sign issue when coding the adjacent term for the TIDE_GENERATING_FORCES option in step2d_LF_AM3.h for a similar shallow water configuration. I was supposed to set a test case for the air pressure forcing inverted barometer effect in the barotropic pressure gradient. But it was low on my long priority list. So, I forgot. Thus, Shunpei Matsuo's cyclone application is suitable for testing the ATM_PRESS this term.

A cyclone rotates counterclockwise around a center of low atmospheric pressure in the northern hemisphere. Consequently, the inverted barometer effect causes the water level to rise to form a dome around the low-pressure center, as shown below:

Notice that the opposite would happen over a cell of high air pressure causing the water level to drop.

Above Figure is taken from the SWELLNET, which is used by surfers.