Abstract
Instabilities in the form of baroclinic waves occur in a rotating cylindrical annulus cooled from within. Flow visualisation studies and LDV-measurements of the radial velocity component were carried out in an annulus with an aspect ratio of 4.4. The flow undergoes transitions from the laminar stable state through baroclinic waves, both stable and time-varying, to an irregular state. Based on the time series of the radial velocity at fixed point in the rotating annulus, the attractors of the flow match previous results based on temperature measurements. The bifurcation diagram of extrema in the radial velocity shows the existence of low dimensional chaos at the transition from the axisymmetric flow to periodic baroclinic waves. This bifurcation scenario at low rotation rates is substantially different from the nonlinear behaviour of Taylor-Couette flow.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
P. Bernardet, A. Butet, M. Déqué: J. Atmos. Sci., 47, No 24, 3023–3043 (1990)
M. Bowden, H. F. Eden: J. Atmos. Sci, 22, 185–195 (1965)
F. H. Busse, C. R. Carrigan: J. Fluid Mech., 62, 579–592 (1972)
T. Buzug, G. Pfister: Phys. Rev. A, 45 (10), 7073–7098 (1992)
G. Buzyna, R. L. Pfeffer, R. Kung: J. FLuid Mech., 145, 377–403 (1984)
T. V. Davies: Phil. Trans. R. Soc. Lond. A, 249, 27–64 (1956)
E. T. Eady: Tellus, 1, 33–52 (1949)
C. Egbers, H. J. Rath: ‘LDV-measurements on wide gap instabilities in spherical Couette flow’. In: Developments in Laser Techniques and Applications to Fluid Mechanics, ed. by R. J. Adrian, D. F. G. Durao, F. Durst, M. V. Heitor, M. Maeda, J. H. Whitelaw (Springer, Berlin Heidelberg 1996), pp. 45–66
J. S. Fein, R. L. Pfeffer: J. Fluid Mech., 22, 541–558 (1976)
W. W. Fowlis, R. Hide: J. Atmos. Sci., 22, 541–558 (1965)
W.-G. Früh, P. L. Read: Phil. Trans. R. Soc. Lond. A, 355, 101–153 (1997)
J. Herrmann, F. H. Busse: Physics of Fluids, 10, No. 7, 1611–1620 (1998)
R. Hide: Phil. Trans. R. Soc. Lond. A, 250, 441–478 (1958)
R. Hide, P.-J. Mason: Phil. Trans. Roy. Soc. Lond. A, 268, 201–232 (1970)
R. Hide, P.-J. Mason: Adv. Physics, 24, No. 1, 47–100 (1975)
P. K. Kundu: Fluid Mechanics (Academic Press, San Diego 1990)
A. Lorenzen, G. E. A. Meier, M. Assenheimer, E.-A. M:uller: Experiments in Fluids, 8, 286–290 (1990)
O. Meincke, C. Egbers: Phys. Chem. Earth (B), 24, no. 5, 467–471 (1999)
O. Morita, M. Uryu: J. Atmos. Sci., 46, No. 15, 2349–2355
M. D. Mundt, N. H. Brummell, J. E. Hart: J. Fluid Mech., 291, 109–138 (1995)
J. Pedlosky: Geophysical Fluid Dynamics (Springer, New York 1987)
R. L. Pfeffer, G. Buzyna, R. Kung: J. Atmos. Sci., 37, 2129–2149 (1980)
R. L. Pfeffer, S. Applequist, R. Kung, C. Long, G. Buzyna: Theoret. Comput. Fluid Dynamics, 9, 253–267 (1997)
R. T. Pierrehumbert, K. L. Swanson: Annu. Rev. Fluid. Mech., 27, 419–467 (1995)
P. L. Read, M. J. Bell, D. W. Johnson, R, M. Small: J. Fluid Mech., 238, 599–632, (1992)
B. Sitte, C. Egbers: Phys. Chem. Earth (B), 24, No. 5, 473–476 (1999)
F. Takens: ‘Detecting strange attractors in turbulence’. In: Lecture Notes in Mathematics: Dynamical Systems and Turbulence, 898, ed. by D. Rand and L. S. Young (Springer, Berlin Heidelberg 1980), pp. 366–381
D. J. Tritton: Physical Fluid Dynamics, 2nd edition (Oxford University Press, Oxford 1988)
P. Wulf: VDIF ortschrittberichte Strömungstechnik: Untersuchungen zum laminarturbulenten Übergang im konzentrischen Kugelspalt, Band 333 (VDI-Verlag, Düsseldorf1997)
P. Wulf, C. Egbers, H. J. Rath: Phys. Fluids, 11, No. 6, 1359–1372 (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sitte, B., Egbers, C. (2000). Higher order dynamics of baroclinic waves. In: Egbers, C., Pfister, G. (eds) Physics of Rotating Fluids. Lecture Notes in Physics, vol 549. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45549-3_20
Download citation
DOI: https://doi.org/10.1007/3-540-45549-3_20
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67514-3
Online ISBN: 978-3-540-45549-3
eBook Packages: Springer Book Archive