Synchronization in a Pair of Thermally Coupled Rotating Baroclinic Annuli: Understanding Atmospheric Teleconnections in the Laboratory

Synchronization phenomena in a fluid dynamical analogue of atmospheric circulation is studied experimentally by investigating the dynamics of a pair of thermally coupled, rotating baroclinic annulus systems. The coupling between the systems is in the well-known master-slave configuration in both periodic and chaotic regimes. Synchronization tools such as phase dynamics analysis are used to study the dynamics of the coupled system and demonstrate phase synchronization and imperfect phase synchronization, depending upon the coupling strength and parameter mismatch.

Figure 1

A detailed diagram of the system coupled via the outer cooling water circuit highlighting the location of electric valves and the auxiliary heater. If valves No. 1 and No. 4 are closed, a coupled configuration is obtained.

Figure 2

(i) Time variation of the phase difference $\Delta \varphi$ between the master system and the slave system, and (ii) histograms of $\Delta \varphi$ (mod $2\pi$), in the periodic AV regime, showing the transition from unsynchronized to partial and full phase synchronization for a constant coupling strength of $\eta =2.1\times {10}^{-3}$ for (a) ${\tau }_M=158.6\mathrm{s}$, (b) ${\tau }_M=162.3\mathrm{s}$, (c) ${\tau }_M=165.5\mathrm{s}$, (d) ${\tau }_M=171.6\mathrm{s}$.

Figure 3

Plots of oscillation period difference $\Delta \tau$ as function of $\eta$. A clear plateau is observed for small mismatches for the weakly coupled cases.

Figure 4

As in Fig. 2 for the chaotic case. Demonstrating the transition to a synchronized state with constant $\eta =1.25\times {10}^{-2}$ for (a) ${\tau }_M=152\mathrm{s}$, (b) ${\tau }_M=156.4\mathrm{s}$, (c) ${\tau }_M=160.7\mathrm{s}$, (d) ${\tau }_M=164.9\mathrm{s}$.

Figure 5

As in Fig. 3 but for the chaotic case. Relatively large coupling strengths resulted in complete (phase) synchronization for a large range of mismatches.