Quasi-periodic and chaotic flow regimes in a thermally driven, rotating fluid annulus

Abstract

Results are presented from analyses of high-precision time series of measurements of temperature and total heat transport obtained in a high-Prandtl-number (Pr = 26) fluid contained in a rotating, cylindrical annulus subject to a horizontal temperature gradient. Emphasis is placed on regions of parameter space close to the onset of irregular and/or chaotic behaviour. Two distinct transitions from oscillatory to apparently chaotic flow have been identified. The first occurs in an isolated region of parameter space at moderate to high Taylor number in association with a transition to a lower azimuthal wavenumber, in which a quasi-periodic (m = 3) amplitude vacillation (on a 2-torus) gives way to a low-dimensional (D ∼ 3) chaotically modulated vacillation at very low frequency (apparently organized about a 3-torus). The spatial structure of the chaotic flow exhibits the irregular growth and decay of azimuthal sidebands suggestive of a nonlinear competition between adjacent azimuthal wavenumbers. The other main transition to aperiodic flow occurs at high Taylor number as the stability parameter Θ is decreased, and is associated with the onset of ‘structural vacillation’. This transition appears to be associated with the development of small-scale instabilities within the main m = 3 baroclinic wave pattern, and exhibits a route to chaos via intermittency. The nature of the apparent chaos in these two aperiodic regimes is discussed in relation to possible mechanisms for deterministic chaos, apparatus limitations, and to previous attempts to model nonlinear baroclinic waves using low-order spectral models.