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Is it an instability or a slow rectification ?ΒΆ

With twice a stronger forcing in exp2_m than in exp2_l, one noted difference was the development of an instability starting from the western boundary and slowly propagating eastward (see Fig. 3 in this note). I re-run exp2_m with a baroclinic time step of 300 s instead of 1200 s and we obtain the same result. Now, I am wondering if this is really a numerical instability or simply a slow adjustment of the 100-day averaged mean flow. Fig. 1 shows the 100-day mean zonal flow in the upper layer for four different times. The adjustment is a strengthening of the eastward mean flow together with a decrease in its meridional scale. The run is not long enough to see if the adjustment stops or if it is followed by something else. I have, furthermore, no explanation for this adjustment, if it is one, and I am wondering if we should worry about it or not –even if we are focusing on the middle layer, we might want to know what is going on in the upper layer especially if we want to use these simulations for a proposal.

../../../../../_images/u_runm_100d_upper_exp2_m.png

Figure 1: 100-day averaged U in the upper layer in exp2_m. Time above each panel shows the central time over which the average is performed.


To have further insight into what is going on in the upper layer, exp2_m has been run for 1000 more days (until day 2500) and exp2_n was run with a forcing four times stronger than in exp2_l. The 100-day averaged zonal flow (U) in the upper layer is shown for the three experiments in Fig. 2.

../../../../../_images/u_runm_100d_upper_exp2_l_m_n.png

Figure 2: 100-day averaged U in the upper layer in exp2_l, exp2_m and exp2_n at y = 1110 km. The flow has been divided by 4 in (b) and 16 in (c).

  1. There may be an instability as well in exp2_l but one that develops much slower than in exp2_m and exp2_n: a small band of increased flow along the western boundary widens slowly with time in Fig. 2a.
  2. After 2250 days and until at least day 2500 in exp2_m, the 100-day averaged flow seems to have reached a quasi-stationary steady state.
  3. However, in exp2_n, a quasi-stationary state is reached after day 1250 but then collapses 500 days later; the 100-day mean flow at the end of the simulation (days 2400 to 2500) has the same large-scale structure –eastward at the central latitude of forcing and westward flow on its edge–, but with a much higher level of small-scale structure.

This set of simulations suggests that there may be a consistency between the experiments but also that the flow may always evolve without reaching a quasi-stationary state, especially with higher amplitude. This picture might change, however, if dissipation is used in the interior.