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Description of results for exp2_b, exp2_c, exp2_d and exp2_e

Summary

Four experiments with stronger forcing and more realistic Eulerian and Lagrangian mean flows are described. Cases with two-layer, lower bottom friction and higher resolution are studied.

In all experiments, the mean flow stays eastward at the latitudes of forcing and westward on both sides; this is true for each layer. However, there are some secondary qualitative and quantitative differences between 1) the cases with one and two layers and 2) between the upper and lower layers. The main difference is that the 100-day Eulerian mean in the upper layer increases linearly with time while in the layers with bottom friction (either single-layer case or bottom layer in two-layer cases), the Eulerian mean flow does saturate. This suggests that the saturation is provided by the bottom friction; in the upper layer, nothing can prevent the mean flow to increase until it becomes strong enough to become baroclinically unstable.

The zonal Lagrangian mean flow is estimated using the zonal displacement of a meridional bar of anomalous salinity. In the upper layer, the Lagrangian mean flow is independent of bottom friction and resolution; in the lower layer, the Lagrangian mean flow has increased with half the bottom friction but stays independent of a doubling of the resolution.

Run overview

These four runs have been forced by a wind forcing of about 0.3 dyn/cm2, that is stronger by a factor of 100 than the wind forcing used in exp2_a. One layer is used for exp2_b, two for exp2_c, exp2_d and exp2_e. The drag coefficient is divided by 2 in exp2_d and exp2_e and the resolution goes from 1/6° in exp2_b, exp2_c and exp2_d to 1/10° in exp2_e.

  exp2_b exp2_c exp2_d exp2_e
forcing amplitude (dyn/cm2) 0.3 0.3 0.3 0.3
# of layers 1 2 2 2
drag coefficient 1e-3 1e-3 0.5e-3 0.5e-3
resolution (of a °) 1/6 1/6 1/6 1/10

All four experiments are also initialized with same temperature and salinity in both layers but as long as NONLINEAR_EOS and CORRECT_DENSITY are undefined, they are not involved in the computation of the layer density. Instead, layer densities are fixed (with ADIABATIC defined) and computed from the reduced gravity given in init.h.

Results

First, a general comment. In all these experiments, the instantaneous velocity field is in the order of 3-6 cm/s and the 100-day mean field in the order of 1-2 cm/s.

The mean flow in exp2_b is similar to the one in exp2_a except that it is stronger (Fig. 1). As in exp2_a, the 100-day mean flow is stabilized after 150 days (Fig. 2). This is also shown in Fig. 3 where the time series of the 100-day mean zonal velocity (U) at x=600 km and y=1110 km is shown: After 100 days, the mean flow has reached an equilibrium value.

../../../../../_images/mu_d400_500_exp2_b.png

Figure 1: 400-500-day mean U in exp2_b.

../../../../../_images/u_runm_d100_600km_exp2_b.png

Figure 2: Time series of 100-day mean U at x=600 km.

../../../../../_images/u_runm_d100_600km_1110km_exp2_bcde.png

Figure 3: Time series of 100-day mean U at x=600 km and y=1110 km: (a) upper and (b) lower layer. For exp2_b (single layer), the curve is plotted in (a).

The 100-day mean U obtained with the two-layer configuration (exp2_c) is overall similar to the single-layer case (Fig. 4), although there are qualitative and quantitative differences. The same is true for the comparison between the mean flows obtained in the upper and lower layers. Notice, also, the grid-size instabilities that develop near the western boundary in the upper layer. A smaller time step does not prevent these instabilities to develop.

../../../../../_images/mu_d400_500_exp2_c.png

Figure 4: 400-500-day mean U in exp2_c: (a) upper and (b) lower layer.

Unlike in the single-layer case, the mean flow in the upper layer increases linearly with time and after 500 days, has not reached an equilibrium (Fig. 3). On the other hand, the mean flow in the lower layer does equilibrate after about 350 days.

At day 500, a meridional bar of anomalous salinity to the west of the forcing area has been initialized and the model run for 100 more days. An animation of the evolution of the salinity anomaly during these 100 days is shown in Fig. 5.

../../../../../_images/movie_salt_exp2_c.gif

Figure 5: Animation of the evolution of the salinity anomaly from days 500 to 600: (a) upper and (b) lower layer.

This evolution is used to estimate the Lagrangian flow. The zonal limits of the bar are computed at day 500 and day 600 and the distance reached during these 100 days provides an estimate for the zonal Lagrangian mean flow. Fig. 6 displays the estimate for the different two-layer cases.

../../../../../_images/estimated_lagrangian_exp2_cde.png

Figure 6: Zonal Lagrangian mean flow estimated from the zonal displacement of the salinity anomaly from day 500 to day 600.: (a) upper and (b) lower layer. The legend is the same as in Fig. 3.

As for the Eulerian mean flow, the Lagrangian mean flow has the same structure in both layers but is weaker in the lower one.

With half the bottom drag (exp2_d) and half the bottom drag and doubled resolution (exp2_e), the Eulerian and Lagrangian mean flows stay similar to those of exp2_c. In particular, the grid-size instabilities near the western boundary do not disappear suggesting that the resolution is not a problem and maybe horizontal friction –at least in the upper layer–, might be needed to prevent these instabilities to develop.

The evolution of the Eulerian mean flow is also similar (Fig. 3), although the rate of increase with time of the mean flow in the upper layer is larger and the mean flow in the lower layer is stronger.

The zonal Lagrangian mean flow is also similar (Fig. 6). They stay the same in the upper layer, suggesting an independence of that flow with respect to bottom friction and grid resolution. However, the Lagrangian mean flow in the lower is stronger with weaker bottom friction. If the model is physically right, that means we are on the branch where the drag is strong and a decrease in the drag increases the Lagrangian mean flow and a much further decrease in the drag would be needed to see potentially the decrease of the Lagrangian mean flow with decreasing bottom drag. But I am afraid we might meet some numerical problems.