Hostname: page-component-848d4c4894-pjpqr Total loading time: 0 Render date: 2024-07-07T15:19:58.751Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  20 April 2006

G. Buzyna ,
R. L. Pfeffer  and
R. Kung
G. Buzyna
Affiliation:
Florida State University, Tallahassee, FL 32306
R. L. Pfeffer
Affiliation:
Florida State University, Tallahassee, FL 32306
R. Kung
Affiliation:
Florida State University, Tallahassee, FL 32306
Get access Rights & Permissions [Opens in a new window]

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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 145 , August 1984 , pp. 377 - 403
Copyright
© 1984 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Andrews, D. G. & Hoskins, B. J. 1978 Energy spectra predicted by semi-geostrophic theories of frontogenesis. J. Atmos. Sci. 35, 509–512.Google Scholar
Charney, J. G. 1971 Geostrophic turbulence. J. Atmos. Sci. 28, 1087–1095.Google Scholar
Fenstermacher, P. R., Swinney, H. L. & Gollub, J. P. 1979 Dynamical instabilities and the transition to chaotic Taylor vortex flow. J. Fluid Mech. 94, 103–128.Google Scholar
Fowlis, W. W. & Pfeffer, R. L. 1969 Characteristics of amplitude vacillation in a rotating, differentially heated fluid determined by multi-probe technique. J. Atmos. Sci. 26, 100–108.Google Scholar
Gollub, J. P. & Benson, S. V. 1980 Many routes to turbulent convection. J. Fluid Mech. 100, 449–470.Google Scholar
Hide, R. & Mason, P. J. 1975 Sloping convection in a rotating fluid. Adv. Phys. 24, 47–100.Google Scholar
Hide, R., Mason, P. J. & Plumb, R. A. 1977 Thermal convection in a rotating fluid subject to a horizontal temperature gradient: spatial and temporal characteristics of fully developed baroclinic waves. J. Atmos. Sci. 34, 930–950.2.0.CO;2>CrossRefGoogle Scholar
Lindzen, R. S., Farrell, B. & Jacqmin, D. 1982 Vacillation due to wave interference: applications to the atmosphere and to annulus experiments. J. Atmos. Sci. 39, 14–23.Google Scholar
Moroz, I. M. & Brindley, J. 1982 An example of two-mode interaction in a three-layer model of baroclinic instability. Phys. Lett. 91A, 226–230.Google Scholar
Pfeffer, R., Buzyna, G. & Fowlis, W. W. 1974 Synoptic features and energetics of wave-amplitude vacillation in a rotating, differentially-heated fluid. J. Atmos. Sci. 31, 622–645.Google Scholar
Pfeffer, R. L., Buzyna, G. & Kung, R. 1980a Time-dependent modes of behavior of thermally driven rotating fluids. J. Atmos. Sci. 37, 2129–2149.Google Scholar
Pfeffer, R. L., Buzyna, G. & Kung, R. 1980b Relationships among eddy fluxes of heat, eddy temperature variances and basic-state temperature parameters in thermally driven rotating fluids. J. Atmos. Sci. 37, 2577–2599.Google Scholar
Rao, S. T. & Ketchum, C. B. 1975 Spectral characteristics of the baroclinic annulus waves. J. Atmos. Sci. 32, 698–711.Google Scholar
Rao, S. T. & Ketchum, C. B. 1976 Spectral properties of the baroclinic waves in an annulus with a rigid upper surface. J. Atmos. Sci. 33, 1067–1072.Google Scholar
Rhines, P. G. 1979 Geostrophic turbulence. Ann. Rev. Fluid Mech. 11, 401–410.Google Scholar
Shabbar, M. 1974 Inertial ranges in three-dimensional quasi-geostrophic turbulence. Boundary-Layer Met. 6, 413–421.Google Scholar
White, H. D. & Koschmieder, E. L. 1981 Convection in a rotating, laterally heated annulus. Pattern velocities and amplitude oscillations. Geophys. Astrophys. Fluid Dyn. 18, 301–320.Google Scholar