01.23.13: Comparison of 100 day and 1000 day averagesΒΆ
We compare the result of the GLM analysis of the PV equation for exp20 for two different averages: 1 wave cycle (100 days) and 10 wave cycles (1000 days). In Fig. 1 are shown the equivalent velocity in the Lagrangian-mean PV equation for the term from the time rate of change of Lagrangian-mean PV and for the Lagrangian-mean dissipation term. We see that the time rate of change is weaker over 10 wave cycles than over 1 wave cycle. We also know (not shown) that it is getting weaker monotonically; if we extrapolate linearly, it may need up to 60 wave cycles (6000 days) to reach zero. This suggests that we may get the balance only between the velocity across Lagrangian-mean PV contours and dissipation after a long average but this limit may not be practically reachable.
Figure 1: Equivalent velocity in the Lagrangian-mean PV equation for the term from the time rate of change of Lagrangian-mean PV (left) and for the Lagrangian-mean dissipation term (right) after either 1 wave cycle (upper) or 10 wave cycles (lower). Note that the left hand side is actually deduced from the difference between the dissipative term and the velocity across Lagrangian-mean PV contours but the directly calculation of the time rate of change gives the same large-scale pattern (except that the latter is noisy).
computed with theory_test_cumsum_script.m in RESEARCH/MODELISATION/HIM/studies/PV_and_dissipation/forced_damped_wave/exp20 on the main ipu1 disk. The Matlab file is VC_smallregion_d2015_from100dto1000d_av_exp20.mat in that same directory.