# Reproduction of Haidvogel and Rhines (1983)’s results using the HIM model - Exp2_a¶

## Summary¶

Presented below is the first interesting run that reproduces the results of Haidvogel and Rhines (1983; hereafter HR83). Value of layer thickness, bottom drag and wind stress are again chosen ad hoc to reproduce HR83 and some reasoning needs to be done to support these values.

## Specification of the model¶

• One 500-m layer
• 20° by 20° closed basin
• 120 points by 120 points providing a resolution of about 0.17°
• No horizontal friction
• Bottom drag law: CDRAG=0.001 and DRAG_BG_VEL=0.10
• Wind stress has a curl centered in the middle of the basin with an exponential decay of 1° as in HR83
• Wind stress applied over the 100 m of the surface layer
• Wind stress amplitude is 3.3e-3 dyn/cm2

## Results¶

As in HR83, we obtain an eastward flow at the latitudes of the forcing and westward flows on each side (Fig. 1a). The sea surface height (SSH) is also qualitatively similar to the mean stream function of HR83 (Fig. 1b) –neglecting the increase of the Coriolis parameter f with latitude.

Figure 1: 500-1000-day averaged (a) zonal velocity (U) and (b) SSH in Run 1. The dashed lines show the distance r0 from the domain center, where r0 is the exponential decay of the Gaussian (see 2.2 in HR83).

Fig. 1 has been produced using an average over days 500 to 1000. This average is stationary over longer time scale (Fig. 2) and an average over days 400 to 500 would be a close estimate.

Figure 2: 100-day running time averaged (a) zonal velocity (U) and (b) SSH in Run 1 at x=7.5°E.

The run has reached a “statistically” steady state after 100 days (Fig. 3) –actually, if I would have found the correct coefficient to use for the potential energy, I expect that the sum of the kinetic and potential energy should have been close to be stationary in time.

Figure 3: Domain-averaged kinetic energy.