The models of ENSO for SOI and proxy records apply sloshing dynamics to describe the quasi-periodic behavior. see J. B. Frandsen, “Sloshing motions in excited tanks,” Journal of Computational Physics, vol. 196, no. 1, pp. 53–87, 2004.

The following GIF animations are supplementary material from S. S. Kolukula and P. Chellapandi, “Finite Element Simulation of Dynamic Stability of plane free-surface of a liquid under vertical excitation.”

Detuning Effect.gif shows the animation of sloshing fluid for the fourth test case, with frequency ratio Ω3 = 0.5 and forcing amplitudeV = 0.2: test case 4 as shown in Figure 4. This case corresponds to instability in the second sloshing mode lying in the first instability region. Figure 8(b) shows the free-surface elevation and Figure 9 shows the moving mesh generated in this case.

Dynamic Instability.gif shows the animation of sloshing fluid for the second test case which lies in the unstable region, with frequency ratio Ω1 = 0.5 and forcing amplitude kV =0.3: test case 2 as shown in Figure 4. Figure 6 shows the free-surface elevation and Figure 7 shows the moving mesh generated in this case.

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