Nonsteady stability of the flow around the circle in the Föppl model
Author:
Daniela Tordella
Journal:
Quart. Appl. Math. 53 (1995), 683-694
MSC:
Primary 76E99; Secondary 76C05
DOI:
https://doi.org/10.1090/qam/1359504
MathSciNet review:
MR1359504
Full-text PDF Free Access
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Abstract: The Föppl model for the incompressible flow about the circle is considered. The major feature of this model is the understanding of the convective mechanism that gives rise to the onset of the instability in the flow past the circle. Through this model the real flow is approximated by means of a potential field with two singular points, counter-rotating vortices, placed symmetrically behind the circle. This field configuration is topologically analogous to the actual steady field for Reynolds numbers below the critical value corresponding to the onset of the first instability. The intrinsic instability of the Föppl field to small perturbations may be described by a second-order linear dynamical system.
L. Föppl, Wirbelbewegung hinter einem Kreiszylinder, Munich Akad. Wiss., Sitzungsb. d. Math.-Phys. Kl. Jahrg., 1913
A. S. Grove, F. H. Shair, E. E. Petersen, and A. Acrivos, An experimental investigation of the steady separated flow past a circular cylinder, J. Fluid Mech. 19, 60–80 (1964)
J. M. Cimbala and K. T. Chen, The behaviour of a freely rotatable cylinder/splitter plate body at post-critical Reynolds numbers, Bull. Amer. Phys. Soc. 37, 1772 (1992)
S. Nocilla, Problemi insoliti di autovalori in meccanica non lineare, Rend. Mat. (4), Vol. 10, Serie VI, 1977
S. F. Shen, Some considerations of the laminar stability of incompressible time dependent basic flows, J. Aerospace Sci. 28, 397–417 (1961)
T. Von Karman and H. Rubach, Phys. Zeitschr., Jahrg., S. 49, 1912
L. D. Landau and E. M. Lifshitz, Fluid Mechanics, Pergamon Press, Oxford, 1987, p. 18
D. J. Tritton, Physical Fluid-Dynamics, Clarendon Press, Oxford, 1988, pp. 115, 116
E. Kamke, Differentialgleichungen, B. G. Teubner, Stuttgart, 1977, pp. 437–442
E. T. Whittaker and G. N. Watson, A course of modern analysis, Cambridge University Press, 1950, pp. 412–413
H. Kauderer, Nichtlineare Mechanik, Springer-Verlag, New York, 1958, pp. 503–511
E. Berger, Suppression of vortex shedding and turbulence behind oscillating cylinders, Phys. Fluids 10, 191–193 (1967)
O. H. Wehrmann, Reduction of velocity fluctuations in a Karman vortex street by a vibrating cylinder, Phys. Fluids 8, 547–761 (1965)
M. Shumm, E. Berger, and P. A. Monkewitz, Self-excited oscillations in the wake of two-dimensional bluff bodies and their control, submitted for publication, 1992
D. Oster and I. Wygnanski, The forced mixing layer between parallel streams, J. Fluid Mech. 123, 91–130 (1982)
C. H. Ho and P. Huerre, Perturbed free shear layer, Annual Rev. Fluid Mech. 16, 365–424 (1986)
D. Tordella and W. H. Christiansen, Spectral observation in a forced mixing layer, Vol. 27, 1989, pp. 1741–1743
D. Tordella and C. Cancelli, First instabilities in the wake past a circular cylinder. Comparison of transient regimes with Landau’s model, Meccanica 26, 75–83 (1991)
L. Föppl, Wirbelbewegung hinter einem Kreiszylinder, Munich Akad. Wiss., Sitzungsb. d. Math.-Phys. Kl. Jahrg., 1913
A. S. Grove, F. H. Shair, E. E. Petersen, and A. Acrivos, An experimental investigation of the steady separated flow past a circular cylinder, J. Fluid Mech. 19, 60–80 (1964)
J. M. Cimbala and K. T. Chen, The behaviour of a freely rotatable cylinder/splitter plate body at post-critical Reynolds numbers, Bull. Amer. Phys. Soc. 37, 1772 (1992)
S. Nocilla, Problemi insoliti di autovalori in meccanica non lineare, Rend. Mat. (4), Vol. 10, Serie VI, 1977
S. F. Shen, Some considerations of the laminar stability of incompressible time dependent basic flows, J. Aerospace Sci. 28, 397–417 (1961)
T. Von Karman and H. Rubach, Phys. Zeitschr., Jahrg., S. 49, 1912
L. D. Landau and E. M. Lifshitz, Fluid Mechanics, Pergamon Press, Oxford, 1987, p. 18
D. J. Tritton, Physical Fluid-Dynamics, Clarendon Press, Oxford, 1988, pp. 115, 116
E. Kamke, Differentialgleichungen, B. G. Teubner, Stuttgart, 1977, pp. 437–442
E. T. Whittaker and G. N. Watson, A course of modern analysis, Cambridge University Press, 1950, pp. 412–413
H. Kauderer, Nichtlineare Mechanik, Springer-Verlag, New York, 1958, pp. 503–511
E. Berger, Suppression of vortex shedding and turbulence behind oscillating cylinders, Phys. Fluids 10, 191–193 (1967)
O. H. Wehrmann, Reduction of velocity fluctuations in a Karman vortex street by a vibrating cylinder, Phys. Fluids 8, 547–761 (1965)
M. Shumm, E. Berger, and P. A. Monkewitz, Self-excited oscillations in the wake of two-dimensional bluff bodies and their control, submitted for publication, 1992
D. Oster and I. Wygnanski, The forced mixing layer between parallel streams, J. Fluid Mech. 123, 91–130 (1982)
C. H. Ho and P. Huerre, Perturbed free shear layer, Annual Rev. Fluid Mech. 16, 365–424 (1986)
D. Tordella and W. H. Christiansen, Spectral observation in a forced mixing layer, Vol. 27, 1989, pp. 1741–1743
D. Tordella and C. Cancelli, First instabilities in the wake past a circular cylinder. Comparison of transient regimes with Landau’s model, Meccanica 26, 75–83 (1991)
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© Copyright 1995
American Mathematical Society
