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Results with 3 layers, steady forcing, with or without sponges

Summary

The two simulations prove the point that with no dissipation in the middle layer, the mean motion is zero (or, if not exactly zero, negligible compared to the mean motion in the upper layer). The addition of the sponge prevents the instability in the upper layer to form but generates an artificial circulation in the lower layer on the other hand.

Run overview

The two experiments are forced by the steady wind that has the same spatial pattern than in Haidvogel and Rhines (1983): patch in the middle of the basin with zero basin-averaged curl. The experiments differ from exp2_g in that all layers are 4 times thicker. A thickening of the layers enables to fasten the spin-up which a priori was not done in exp2_g. The experiments differ in that exp2_i has a sponge layer along the western boundary.

Results

The results are overall similar between the two runs: see 100-day mean zonal circulation U in Fig. 1, time series of U at y=1230 km in Fig. 2 and Fig. 3, and time series of U at x=555 km and y=1230 km in Fig. 3. The main differences are:

  • In the upper layer, without sponge, an instability arises after day 500 along the western boundary and propagates eastward making the mean circulation noiser,
  • In the lower layer, with sponge, a mean circulation is present near the western boundary.

The motion in the middle layer is not, however, too different between the two cases, disappearing after day 500 with only a noisy and unstructured residual along the western boundary and at the latitudes of forcing that is not removed totally by the presence of the sponge layer. Notice that the instability in the upper layer starts once the mean circulation in the middle layer has disappeared in the interior.

exp2_i (with sponge) exp2_j (without sponge)
Fig1a Fig1b
Figure 1: Time-mean of zonal velocity (U) between days 900 and 1000 for exp2_i (left) and exp2_j (right): (a) upper, (b) middle and (c) lower layers.

../../../../../_images/u_y1230km_exp2_i.png

Figure 2: U along y=1230 km for exp2_i (with sponge): (a) upper, (b) middle and (c) lower layers.


../../../../../_images/u_y1230km_exp2_j.png

Figure 3: U along y=1230 km for exp2_j (without sponge): (a) upper, (b) middle and (c) lower layers.


../../../../../_images/u_y1230km_x555km_exp2_i_j.png

Figure 3: U at x=555 km and y=1230 km in the (a) upper, (b) middle and (c) lower layers.


In conclusion, I would say that these two simulations prove the point that with no dissipation in the middle layer, the mean motion is zero (or, if not exactly zero, negligible compared to the mean motion in the upper layer). The addition of the sponge prevents the instability in the upper layer to form but generates an artificial circulation in the lower layer on the other hand.