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04.19.2013: GLM analysis of exp33_sponge over 60 cyclesΒΆ

In this note, I showed that we get a better GLM balance when using a higher resolution for the analysis. In Fig. 1, I perform the calculation (still over a small domain) over 60 cycles and show the results averaged over these cycles. We see that 1) dQL/dt is still not eliminated, 2) that lhs of the GLM balance (lower left panel) is stronger than the dissipative term (lower middle panel) and 3) that <UL.gradQL> (upper middle panel) is not equal to <UL>.grad<QL>.

Fig. 2 shows how the GLM balance converges over successive averaging and Fig. 3 shows the same thing but in the case where we use the model resolution for the analysis. We see that the convergence is faster with higher resolution, but only for the dQL/dt term and the convergence is not much faster.

Figs. 4 and 5 show the Lagrangian-mean flow after 60 cycles using four time the model resolution and after 15 cycles using the model resolution. We see that, unlike assumed several days ago, the Lagrangian-mean flow does not seem to converge to zero. Figs. 6 and 7 show the test of convergence for the Lagrangian-mean flow. These terms converge to their statistically steady value at the same speed in both cases (suggesting that for these terms at least, we do not need higher resolution).

../../../../../_images/diag_VC_60th_cycle_100day_long_rand_day4000to6000_small_region_4_ress_exp33_sponge.png

Figure 1: GLM analysis after averaging over 60 cycles in exp33_sponge over a small domain and using four times the model grid resolution.

../../../../../_images/LPV_steady_balance_test_conv_60_cycles_small_region_4_ress_exp33_sponge.png

Figure 2: Test of convergence of the GLM terms over successive averaging over a small domain and using four times the model grid resolution.

../../../../../_images/LPV_steady_balance_test_conv_15_cycles_small_region_exp33_sponge.png

Figure 3: Same as Fig. 2 but using the model grid resolution for the analysis

../../../../../_images/UL_VL_60th_cycle_100day_long_rand_day4000to6000_small_region_4_ress_exp33_sponge.png

Figure 4: The Lagrangian-mean flow after averaging over 60 cycles and using four times the model resolution.

../../../../../_images/UL_VL_15th_cycle_100day_long_rand_day4000to6000_small_region_exp33_sponge.png

Figure 5: The Lagrangian-mean flow after averaging over 15 cycles and using the model resolution.

../../../../../_images/UL_VL_steady_balance_test_conv_60_cycles_small_region_4_ress_exp33_sponge.png

Figure 6: Test of convergence of the Lagrangian-mean flow over successive averaging over a small domain and using four times the model grid resolution.

../../../../../_images/UL_VL_steady_balance_test_conv_15_cycles_small_region_exp33_sponge.png

Figure 7: Same as Fig. 6 but using the model grid resolution.


The figures were made with LPV_steady_balance_test_conv.m in RESEARCH/MODELISATION/HIM/studies/PV_and_dissipation/forced_damped_wave/exp33_sponge/ on the main disk on ipu1.