Below is a link to an animation showing the evolution of the leading singular vector in Eady's model for k = 2.5; i.e., just on the neutral side of the shortwave cutoff. The initial condition consists of a highly tilted PV anomaly that tips over due to advection by the linear shear. This SV is the optimally growing structure over 10 non-dimensional time units (~96 h). In fact, when measured by the streamfunction-amplitude norm, this SV amplifies by 148 times its initial amplitude, compared with 22 times for the most unstable mode. The second plot shows energy as a function of time.
Singular vector loop.
Energy plot.
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