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03.17.2014: LPV analysis of exp39 compared to exp2_w3

We here compare two simulations, exp39 and exp2_w3. The two simulations are the same except that exp39 has biharmonic friction with AH=1.2e12 m4/s instead of Laplacian friction and it was run with a time step of 60 s (that is because there is a maximum bound for AH which is inversely proportional to the time step – see run_description.rst of exp39 for more details).

Note that the choice of AH for exp39 was initially to see the equivalent to exp2_w5 – which has a KH of 50 m2/s –, not of exp2_w3 – which has a KH of 250 m2/s. This choice was made assuming that friction acts on the same wave field with a horizontal scale of 1000 km/(2*pi). Visually, however, the Eulerian-mean flow of exp39 appears closer to the Eulerian-mean flow of exp2_w3 than of exp2_w5 (see Figs. 1 and 2 as well as Fig. 1 in Eulerian-and-Lagrangian-mean-flow-exp2_w-to-exp2_w6) and that is why we choose this comparison here. It needs to be seen why this is so: Is it because my estimate of the horizontal scale is biased (because I should have been more precise and/or look at other directions than in longitude)? Or because the wave field is actually different?

Leaving this issue aside, Figs. 1 and 2 compare the Eulerian-mean flow, Figs. 3 and 4 the Lagrangian-mean flow and Figs. 5 and 6 the LPV analysis. Overall, the two simulations are similar. In particular, the Lagrangian-mean flow in both simulations displays a different structure than the Eulerian-mean flow with more jets in the latter case. The jets in the Lagrangian-mean flow in the biharmonic case appears a bit more symmetric around the central latitude, a bit stronger as well as with more developed jets at the extreme north and south of the circulation than in the Laplacian case. Although some of these differences could be due to the relative difference in the level of friction, the difference in the number of jets can be attributed to the higher order of spatial derivation in the biharmonic case compared to the Laplacian case.

In Figs. 7 and 8 are shown a time series and a snapshot of the meridional velocity (V). The comparison indicates that, at least at first order, the wave field is the same between the two simulations so that the difference in the Lagrangian-mean flow (especially the number of jets) can be attributed to the form chosen for the parameterization of friction.

../../../../../_images/UE_VE_one_cycle_100day_long_day2125_exp2_w3.png

Figure 1: 100-day Eulerian-mean flow (days 2125-2225) in the middle layer in exp2_w3.

../../../../../_images/UE_VE_one_cycle_100day_long_day2125_exp39.png

Figure 2: Same as Fig. 1 except for exp39.

../../../../../_images/UL_VL_VC_one_cycle_100day_long_day2125_exp2_w3.png

Figure 3: 100-day Lagrangian-mean flow (days 2125-2225) in the middle layer in exp2_w3.

../../../../../_images/UL_VL_VC_one_cycle_100day_long_day2125_exp39.png

Figure 4: Same as Fig. 3 except for exp39.

../../../../../_images/diag_VC_one_cycle_100day_long_day2125_exp2_w3.png

Figure 5: LPV analysis for exp2_w3 over one wave cyle (days 2125-2225).

../../../../../_images/diag_VC_one_cycle_100day_long_day2125_exp39.png

Figure 6: Same as Fig. 5 except for exp39. Note that in this figure, we have used VC3_b_i (that is the friction output) instead of VC3_a_i (that is the friction determined from velocity field) because we have a much better match with the former than with the latter (possibly because the biharmonic friction involves a lot more derivatives, and thus larger errors, than the Laplacian friction).

../../../../../_images/V_ts_snap_exp2_w3.png

Figure 7: (left) Time series of the meridional velocity (V) along 30°N and (right) snapshot of V in the middle layer in exp2_w3.

../../../../../_images/V_ts_snap_exp39.png

Figure 8: Same as in Fig. 7 but for exp39. (Note that the time range is different, however, between the two figures.)


Figures 1 to 6 were plotted with plot_LPV_analysis.m using Matlab files produced by theory_test_script.m. These files are in RESEARCH/MODELISATION/HIM/studies/PV_and_dissipation/forced_damped_wave/exp39/ and RESEARCH/MODELISATION/HIM/studies/diss_train_of_eddies/exp2/exp2_w3/analysis_1d/ on the main disk on ipu1.