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.

Experiments on the structure of baroclinic waves and zonal jets in an internally heated, rotating, cylinder of fluid

“…In all three endwall configurations studied the axisymmetric flow seen at low values of ⍀ and ⌬T z gives way above certain thresholds to a wave regime consisting of a number of stable eddy features which can be characterized in terms of their azimuthal wavenumber m. As ⍀ increases further, the flow becomes progressively more disordered and irregular, finally reaching a state akin to geostrophic turbulence. 18,32 These various flow regimes may be ordered with respect to two dimensionless parameters: the Taylor (), and Burger (S) numbers. The former parameter is defined as…”

Direct numerical simulation of transitions towards structural vacillation in an air-filled, rotating, baroclinic annulus

“…7 Such a sequence of transitions via structural vacillation seems to lead rapidly to the development of a complex, timedependent flow of relatively high attractor dimension, 8,20 well before the spatial flow pattern appears obviously disordered. Subsequent development within this so-called "transition zone" as ⍀ is further increased 6 leads to the gradual and progressive breakdown of the initially regular wave pattern into an increasingly disordered flow, ultimately leading to the emergence of a form of stably stratified "geostrophic turbulence." The latter is another important paradigm in geophysical fluid dynamics, with properties which may markedly differ from the well known homogeneous, isotropic turbulence in three dimensions, more closely resembling those of idealized two-dimensional turbulence under some circumstances.…”

“…Temporal spectra of mode m = 3 for Taylor numbers ͑a͒ Ta= 2 ϫ 10 6 and ͑b͒ 3.25ϫ 106 . The upper spectrum in each figure is of the cosine component of mode 3, while the lower spectrum in the same frame is of the amplitude of mode 3.…”

A Numerical Study of Tilted-Trough Vacillation Observed in a Differentially Heated Rotating Fluid Annulus

“…Although not a few experimental studies on this kind of vacillation have been done (Hide , 1953(Hide , , 1958 Pfeffer and Chiang, 1967;Spence and Fultz, 1977;Pfeffer et al, 1980aPfeffer et al, , 1980bBuzyna et al, 1984) , our knowledge is insufficient to understand its timedependent characteristics on the whole; one of the noticeable results concerning structural vacillation is the fluctuation in the radial distribution of temperature variance (Pfeffer et al, 1980a). In a recent paper (Ukaji and Tamaki , 1989) we made numerical simulations of a steady baroclinic wave by using a sectorial non-uniform grid system and compared the results with corresponding experimental ones.…”