Transition to geostrophic turbulence in a rotating differentially heated annulus of fluid

Abstract

Results are presented of an experimental study on the transition to geostrophic turbulence, and the detailed behaviour within the turbulence regime, in a rotating, laterally heated annulus of fluid. Both spatial and temporal characteristics are examined, and the results are presented in the form of wavenumber and frequency spectra as a function of a single external parameter, the rotation rate.The transition to turbulence proceeds in a sequence of steps from azimuthally symmetric (no waves present) to chaotic flow. The sequence includes doubly periodic flow (amplitude vacillation), semiperiodic flow (structural vacillation), and a transition zone where the characteristics undergo a gradual change to chaotic behaviour. The spectra in the transition zone are characterized by a gradual merging of the background signal with the spectral peaks defining regular wave flow as the rotation rate is increased.Within the geostrophic turbulence regime, the wavenumber spectra are characterized by a broad peak at the baroclinic scale and a power dependence of energy density on wavenumber at the high-wavenumber end of the spectrum. Our data reveal a significant dependence of the slope on the thermal Rossby number, ranging from −4.8 at RoT = 0.17 to −2.4 at RoT = 0.02. The frequency spectra also show a power dependence of the energy density on frequency at the high-frequency end of the Spectrum. We find a nominal −4 power which does not appear to be sensitive to changes in Rossby or Taylor number.