Mamun, Chowdhury K.; Tuckerman, Laurette S. Asymmetry and Hopf bifurcation in spherical Couette flow. (English) Zbl 0836.76033 Phys. Fluids 7, No. 1, 80-91 (1995). Summary: Spherical Couette flow is studied with a view to elucidating the transitions between various axisymmetric steady-state flow configurations. A stable, equatorially asymmetric state discovered recently consists of two Taylor vortices, one slightly larger than the other and straddling the equator. By adapting a pseudospectral time- stepping formulation to enable stable and unstable steady states to be computed (by Newton’s method) and linear stability analysis to be conducted (by Arnoldi’s method), the birucation-theoretic genesis of the asymmetric state is analyzed. It is found that the asymmetric branch originates from a pitchfork bifurcation; its stabilization, however, occurs via a subsequent subcritical Hopf bifurcation. Cited in 72 Documents MSC: 76E05 Parallel shear flows in hydrodynamic stability 76U05 General theory of rotating fluids Keywords:Taylor vortices; pseudospectral time-stepping formulation; Newton’s method; linear stability analysis; Arnoldi’s method; pitchfork bifurcation Software:NSPCG PDFBibTeX XMLCite \textit{C. K. Mamun} and \textit{L. S. Tuckerman}, Phys. Fluids 7, No. 1, 80--91 (1995; Zbl 0836.76033) Full Text: DOI Link References: [1] DOI: 10.1007/BF01174552 · doi:10.1007/BF01174552 [2] DOI: 10.1017/S0022112076002462 · doi:10.1017/S0022112076002462 [3] DOI: 10.1017/S0022112087003070 · Zbl 0645.76118 · doi:10.1017/S0022112087003070 [4] DOI: 10.1017/S0022112086000150 · Zbl 0601.76064 · doi:10.1017/S0022112086000150 [5] DOI: 10.1017/S0022112087003069 · Zbl 0645.76117 · doi:10.1017/S0022112087003069 [6] DOI: 10.1016/0021-9991(89)90238-6 · Zbl 0683.65026 · doi:10.1016/0021-9991(89)90238-6 [7] DOI: 10.1137/0613049 · Zbl 0754.65036 · doi:10.1137/0613049 [8] DOI: 10.1007/BF01061511 · Zbl 0666.65033 · doi:10.1007/BF01061511 [9] DOI: 10.1007/BF01065178 · Zbl 0677.65032 · doi:10.1007/BF01065178 [10] Arnoldi W. E., Q. Appl. Math. 9 pp 17– (1951) · Zbl 0042.12801 · doi:10.1090/qam/42792 [11] DOI: 10.1016/0024-3795(80)90169-X · Zbl 0456.65017 · doi:10.1016/0024-3795(80)90169-X [12] DOI: 10.1006/jcph.1994.1007 · Zbl 0792.76062 · doi:10.1006/jcph.1994.1007 [13] DOI: 10.1017/S0022112084001774 · Zbl 0561.76038 · doi:10.1017/S0022112084001774 [14] DOI: 10.1016/0167-2789(90)90113-4 · Zbl 0721.35008 · doi:10.1016/0167-2789(90)90113-4 [15] DOI: 10.1103/PhysRevLett.58.2212 · doi:10.1103/PhysRevLett.58.2212 [16] DOI: 10.1017/S0022112091003129 · Zbl 0850.76793 · doi:10.1017/S0022112091003129 [17] DOI: 10.1137/0515001 · Zbl 0543.34034 · doi:10.1137/0515001 [18] DOI: 10.1103/PhysRevA.42.4693 · doi:10.1103/PhysRevA.42.4693 [19] DOI: 10.1007/BF01032401 · doi:10.1007/BF01032401 [20] DOI: 10.1007/BF01032401 · doi:10.1007/BF01032401 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.