Choice of flow regime in a wide spherical layer under the action of acceleration of the inner sphere

Wave number selection in the presence of noise: Experimental results

“…It means that, at a constant and sufficiently small noise level N<0.011 and dRe/dτ no larger than 2000, there is only one change of dominant wavenumber from m=4 to m=3 (or one needs to increase dRe/dτ still further to find the other alteration of wavenumber). Just the same results -a 0→3 transition instead of 0→4 with dRe/dτ increasing -were observed earlier in experiments without additional noise [15], where control settings provided a smaller minimal N in comparison with the same quantity used in the present work.…”

“…Because the end of damping and subsequent stage of growth for two competing linear modes occur after Refin is reached [15], we calculate value of N after the end of the acceleration phase. In our experiments, control settings were able to maintain Ω(t) to a precision N less than 0.95% from the prescribed values of Ω, and this was effectively the minimum level of noise in these experiments.…”

“…Near the threshold of instability in the case of δ=1, λ3 < λ4 [11], suggesting that an azimuthal wave with m=4 would be preferred. Uncertainties are always present in experiments, but with small noise levels it is found that mode m=4 remains the preferred azimuthal wave, which is always established under conditions of quasistatic increases in Reynolds number [10,15]. After the first instability, hysteresis between azimuthal wave numbers, m, was observed in experiments between either a quasi-static increase of Re (favouring m=4) or a decrease (favouring m=3).…”

“…This interpretation is consistent with the observed change in wave number from 0→4 to 0→3 under the action of an acceleration. It was shown in some range of initial values of Reinit at small acceleration rates that the preferred mode (m=4) is the same as for a quasi-static increase of Re, while with larger acceleration rates the wavenumber selection became essentially random [15]. It was suggested that random wave number selection, with acceleration values increasing within a restricted range of initial Re, can be explained by the influence of noise imposed in the form of deviations of the inner sphere rotational velocity from given values [17].…”

“…After the first instability, hysteresis between azimuthal wave numbers, m, was observed in experiments between either a quasi-static increase of Re (favouring m=4) or a decrease (favouring m=3). When the final Reynolds number, Refin, was held constant and lies inside the observed region of hysteresis (462 < Re < 525), a loss of stability with increasing acceleration rate or decreasing initial Reynolds number results in a transition from 0→3 instead of 0→4, where '0' denotes the basic axisymmetric flow [15].…”