PIV- and LDV-measurements of baroclinic wave interactions in a thermally driven rotating annulus

Already in the 1950s, an elegant laboratory experiment had been designed to understand how the atmospheric circulation transports heat from equatorial to polar latitudes. It consists of a cooled inner and heated outer cylinder mounted on a rotating platform, mimicking the heated tropical and cooled polar regions of the earth's atmosphere. Depending on the strength of the heating and the rate of rotation, different flow regimes had been identified: wave-regimes that can be classified by pro-grade propagating waves of different wavenumbers and quasi-chaotic regimes where waves and small-scale vortices coexist. In the present paper, we will use multivariate statistical techniques to understand better the variability of the heated rotating flow (i) in the transition region between regular waves with zonal wave number 3 and 4 and (ii) in the transition region to the quasi-chaotic regime. The former regime is studied by applying the complex empirical orthogonal function (CEOF) method to particle image velocimetry data, the latter by applying the multichannel singular spectrum analysis (M-SSA) to laser Doppler velocimetry (LDV) data. In the annulus, interactions between the dominant mode and the so-called weaker modes, explaining less variance than the dominant mode, can lead to low-frequency amplitude and wave structure vacillations. The CEOF analysis reveals the coexistence of a dominant and a weak mode in the 3-4 wave transition region. This finding confirms earlier ideas on wave dispersion in transition regions between regular waves. Increasing the annulus' rotation leads to a growth of the weak mode until this mode becomes the dominant one. No coexistence of modes could be found for the regular 4-wave regime but a slight structural vacillation was present. The M-SSA was applied to LDV data corresponding with much faster annulus rotation for which the flow becomes more irregular. The analysis reveals a coexistence of a dominant 4 mode and a much weaker 5 mode for this regime. Our results complement previous observations recovered primarily by thermocouple arrangements.