Global mode interaction and pattern selection in the wake of a disk: A weakly nonlinear expansion

Journal of Fluid Mechanics

Volumn 633, Issue , 2009, Pages 159-189

  Meliga, Philippe ^a   Chomaz, Jean Marc ^a,b   Sipp, Denis ^a  

^a ONERA   (France)

^b ECOLE POLYTECHNIQUE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); EIGENVALUES AND EIGENFUNCTIONS; EXPANSION; NONLINEAR EQUATIONS; REYNOLDS NUMBER; WAKES;

ADJOINT EIGENVALUE PROBLEM; AZIMUTHAL WAVENUMBERS; BIFURCATION SCENARIO; CRITICAL REYNOLDS NUMBER; HARMONICS GENERATION; NONLINEAR INTERACTIONS; RECIRCULATION BUBBLES; SYMMETRY PROPERTIES;

OSCILLATING FLOW;

ACCURACY ASSESSMENT; BIFURCATION; COMPUTER SIMULATION; EIGENVALUE; FLUID MECHANICS; HARMONIC ANALYSIS; NONLINEARITY; NUMERICAL MODEL; REYNOLDS NUMBER; STEADY FLOW; SYMMETRY; THEORETICAL STUDY; THRESHOLD; WAKE;

EID: 69649094769     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112009007290     Document Type: Article

References (28)

1. BARKLEY, D. 2006 Linear analysis of the cylinder wake mean flow. Europhys. Lett. 75, 750-756.
2. BARKLEY, D., GOMES, M. G. M. & HENDERSON, R. D. 2002 Three-dimensional instability in flow over a backward-facing step. J. Fluid Mech. 473, 167-190.
3. CHOMAZ, J.-M. 2005 Global instabilities in spatially developing flows: Non-normality and nonlinearity. Annu. Rev. Fluid. Mech. 37, 357-392.
4. CHOMAZ, J.-M., HUERRE, P. & REDEKOPP, L. G. 1990 The effect of nonlinearity and forcing on global modes. In Proceedings of the Conf. on New Trends in Nonlinear Dynamics and Pattern-Forming Phenomena: The Geometry of Nonequilibrium (ed. P. Coulet & P. Huerre), vol. 237, pp. 259-274. NATO ASI Series B, Plenum.
5. CHOSSAT, P. & IOOSS, G. 1994 The Couette-Taylor problem. Appl. Math. Sci. 102.
6. CRAWFORD, J. D., GOLUBITSKY, M. & LANGFORD, W. F. 1988 Modulated rotating waves in O(2) mode interactions. Dyn. Stab. Syst. 3, 159-175.
7. CRAWFORD, J. D. & KNOBLOCH, E. 1991 Symmetry, symmetry-breaking bifurcations in fluid dynamics. Annu. Rev. Fluid. Mech. 23, 341-387.
8. CROSS, M. C. 1986 Traveling and standing waves in binary-fluid convection in finite geometries. Phys. Rev. Lett. 57, 2935-2938.
9. DAVIS, T. A. 2004 A column pre-ordering strategy for the unsymmetric-pattern multifrontal method. ACM Trans. Math. Softw. 30 (2), 165-195.
10. DAVIS, T. A. & DUFF, I. S. 1997 An unsymmetric-pattern multifrontal method for sparse LU factorization. SIAM J. Matrix Anal. Appl. 18 (1), 140-158.
11. DING, Y. & KAWAHARA, M. 1999 Three-dimensional linear stability analysis of incompressible viscous flows using finite element method. Intl J. Numer. Methods Fluids 31, 451-479.
12. DUŠEK, J., LE GAL, P. & FRAUNIE, P. 1994 A numerical and theoretical study of the first Hopf bifurcation in a cylinder wake. J. Fluid Mech. 264, 59-80.
13. EHRENSTEIN, U. & GALLAIRE, F. 2005 On two-dimensional temporal modes in spatially evolving open flows: The flat-plate boundary layer. J. Fluid Mech. 536, 209-218.
14. FABRE, D., AUGUSTE, F. & MAGNAUDET, J. 2008 Bifurcations and symmetry breaking in the wake of axisymmetric bodies. Phys. Fluids 20 (5), 051702 1-4.
15. FRIEDRICHS, K. O. 1973 Spectral Theory of Operators in Hilbert Space. Springer.
16. GOLUBITSKY, M. & LANGFORD, W. 1988 Pattern formation and bistability in flow between counterrotating cylinders. Physica D 32, 362-392.
17. GOLUBITSKY, M. & STEWART, I. 1985 Hopf bifurcation in the presence of symmetry. Arch. Ration. Mech. Anal. 87, 107-165.
18. GOLUBITSKY, M., STEWART, I. & SCHAEFFER, D. 1988 Singularities and Groups in Bifurcation Theory Vol. II - Applied Mathematical Sciences Springer.
19. GUMOWSKI, K., MIEDZIK, J., GOUJON-DURAND, S., JENFFER, P. & WESFREID, J. E. 2008 Transition to a time-dependent state of fluid flow in the wake of a sphere. Phys. Rev. E 77, 055308, 1-4.
20. JACKSON, C. P. 1987 A finite-element study of the onset of vortex shedding in flow past variously shaped bodies. J. Fluid Mech. 182, 23-45.
21. NATARAJAN, R. & ACRIVOS, A. 1993 The instability of the steady flow past spheres and disks. J. Fluid Mech. 254, 323-344.
22. PIER, B. 2008 Local and global instabilities in the wake of a sphere. J. Fluid Mech. 603, 39-61.
23. PROVANSAL, M., MATHIS, C. & BOYER, L. 1987 Bénard von-Kármán instability: Transient and forced regimes. J. Fluid Mech. 182, 1-22.
24. SCHMID, P. J. & HENNINGSON, D. S. 2001 Stability and Transition in Shear Flows. Springer.
25. SIPP, D. & LEBEDEV, A. 2007 Global stability of base and mean flows: A general approach and its applications to cylinder and open cavity flows. J. Fluid Mech. 593, 333-358.
26. THOMPSON, M. C., LEWEKE, T. & PROVANSAL, M. 2001 Kinematics and dynamics of sphere wake transition. J. Fluid Struct. 15, 575-585.
27. ZEBIB, A. 1987 Stability of a viscous flow past a circular cylindar. J. Engng Math. 21, 155-165.
28. Zielinska, B. J. A., GOUJON-DURAND, S., DUŠEK, J. & WESFREID, J. E. 1997 Strongly nonlinear effect in unstable wakes. Phys. Rev. Lett. 79, 3893-3896.