×
Dai, Rui-Xiu; Dong, Q.; Szeri, A. Z.

Flow between eccentric rotating cylinders: Bifurcation and stability. (English) Zbl 0764.76017

Int. J. Eng. Sci. 30, No. 10, 1323-1340 (1992).
The effect of cylinder eccentricity on Couette-Taylor transition is investigated here for flow between infinite rotating cylinders. The method of analysis is Fourier expansion of the conservation equations in the axial direction, followed by projection onto a polynomial subspace. Critical points of the solution, which are characterized by singularity of the Jacobian matrix, are located via parametric continuation.

Cited in 7 Documents

MSC:

76E05 Parallel shear flows in hydrodynamic stability
76U05 General theory of rotating fluids

Keywords:

Couette-Taylor transition; Fourier expansion; conservation equations; projection onto a polynomial subspace; singularity; Jacobian matrix; parametric continuation
Cite Review PDF
Full Text: DOI

References:

[1] Lin, C. C., The Theory of Hydrodynamic Stability (1967), Cambridge University Press · Zbl 0068.39202
[2] Coles, D., J. Fluid Mech., 21, 385-425 (1965) · Zbl 0134.21705
[3] Taylor, G. I., Phil. Trans. R. Soc. London, A223, 243-289 (1923) · JFM 49.0607.01
[4] Drazin, P. G.; Reid, W. H., Hydrodynamic Stability (1984), Cambridge University Press · Zbl 0449.76027
[5] Wilcock, D. F., Trans. ASME, 72, 825-834 (1950)
[6] Smith, M. I.; Fuller, D. D., Trans. ASME, 78, 467-474 (1956)
[7] DiPrima, R. C., Trans. ASLE, 6, 249-253 (1963)
[8] Vohr, J. H., J. Lub. Tech., 90, 285-296 (1968)
[9] DiPrima, R. C.; Stuart, J. T., J. Fluid Mech., 54, 393-415 (1972) · Zbl 0246.76038
[10] DiPrima, R. C.; Stuart, J. T., J. Fluid Mech, 67, 85-111 (1975) · Zbl 0297.76039
[11] Castle, P.; Mobbs, F. R., (Proc. Inst. Mech. Engrs, 182 (1968)), 41-52
[12] Mobbs, F. R.; Younes, M. A., J. Lub. Tech., 96, 127-134 (1974)
[13] Ritchie, G. S., J. Fluid Mech., 32, 131-144 (1968) · Zbl 0244.76021
[14] Versteegen, P. L.; Jankowski, D. F., Phys. Fluids, 12, 1138-1143 (1969)
[15] Frene, J.; Godet, M., J. Lub. Tech., 96, 135-140 (1974)
[16] Koschmieder, E. L., Phys. Fluids, 19, 1-4 (1976)
[17] Szeri, A. Z., J. Tribology, 109, 21-37 (1987)
[18] Weinstein, M., (Proc. R. Soc. London, A354 (1977)), 441-457 · Zbl 0361.76041
[19] Weinstein, M., (Proc. R. Soc. London, A354 (1977)), 459-489 · Zbl 0361.76042
[20] Frank, G.; Meyer-Spasche, R., Z. Angew. Math. Phys., 32, 710-720 (1981) · Zbl 0483.76055
[21] Marcus, P. S., J. Fluid Mech., 146, 45-64 (1984) · Zbl 0561.76037
[22] Marcus, P. S., J. Fluid Mech., 146, 65-113 (1984) · Zbl 0561.76038
[23] Cliffe, K. A.; Mullin, T., J. Fluid Mech., 153, 243-258 (1985) · Zbl 0584.76117
[24] Cliffe, K. A.; Spence, A., Numerical calculations of bifurcations in the finite Taylor problem, (Morton, K. W.; Baines, M. J., Numerical Methods for Fluid Dynamics (1986), Clarendon Press: Clarendon Press Oxford), 155-176 · Zbl 0633.35007
[25] Meyer-Spasche, R.; Keller, H. B., J. Comp. Phys., 35, 100-109 (1980) · Zbl 0425.76023
[26] Oikawa, M.; Karasndani, T.; Funakoshni, M., J. Phys. Soc. Japan, 58, 2355-2364 (1989)
[27] Oikawa, M.; Karasndani, T.; Funakoshni, M., J. Phys. Soc. Japan, 58, 2209-2210 (1989)
[28] Joseph, D. D., Stability of Fluid Motions I (1976), Springer: Springer Berlin · Zbl 0345.76022
[29] deBoor, C., A Practical Guide to Splines (1978), Springer: Springer Berlin · Zbl 0406.41003
[30] Ortega, J. M.; Rheinboldt, W. C., Iterative Solution of Non-Linear Equations in Several Variables (1970), Academic Press: Academic Press New York · Zbl 0241.65046
[31] Keller, H. B., Numerical solutions of bifurcation and non-linear eigenvalue problems, (Rabinowitz, P., Applications of Bifurcation Theory (1977), Academic Press: Academic Press New York) · Zbl 0581.65043
[32] Wood, W. W., J. Fluid Mech., 3, 159-175 (1957) · Zbl 0081.19304
[33] Schlichting, H., Boundary Layer Theory (1960), McGraw-Hill: McGraw-Hill New York · Zbl 0096.20105
[34] Donnelly, R. J.; Simon, N. J., J. Fluid Mech., 7, 171-175 (1960)
[35] Diprima, R. C.; Stuart, J. T., J. Lub. Tech., 94, 28-35 (1973)
[36] Kamal, M. M., J. Basic Engng, 88, 717-724 (1966)
[37] Andres, A. San; Szeri, A. Z., J. Appl. Mech., 51, 869-878 (1984)
[38] Benjamin, T. B., (Proc. R. Soc. London, A359 (1981)), 1-43
[39] Dai, R. X.; Szeri, A. Z., Int. J. Non-Linear Mech., 25, 45-60 (1990) · Zbl 0704.76061
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.