Onset of shear layer instability in flow past a cylinder

Physics of Fluids

Volumn 20, Issue 5, 2008, Pages

  Mittal, Sanjay ^a   Kottaram, Jacob J ^a   Kumar, Bhaskar ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY KANPUR   (India)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; FINITE ELEMENT METHOD; INCOMPRESSIBLE FLOW; PERTURBATION TECHNIQUES; REYNOLDS NUMBER; VORTEX SHEDDING; WAKES;

GLOBAL STABILITY ANALYSIS; SHEAR LAYER;

CONFINED FLOW;

COMPUTATIONAL FLUID DYNAMICS; CONFINED FLOW; FINITE ELEMENT METHOD; INCOMPRESSIBLE FLOW; PERTURBATION TECHNIQUES; REYNOLDS NUMBER; VORTEX SHEDDING; WAKES;

EID: 44649171046     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2909587     Document Type: Article

References (36)

1. C. H. K. Williamson, "Vortex dynamics in the cylinder wake," Annu. Rev. Fluid Mech. ARVFA30066-418910.1146/annurev.fluid.28.1.477 28, 477 (1996).
2. A. Roshko, "Perspectives on bluff body aerodynamics," J. Wind. Eng. Ind. Aerodyn. JWEAD60167-610510.1016/0167-6105(93)90007-B 49, 79 (1993).
3. H. Bénard, "Formation de centres de giration á l'arriére d'un obstacle en mouvement," Acad. Sci., Paris, C. R. COREAF0001-4036 147, 839842 (1908).
4. T. von Kármán, "Über den mechanismus des widerstandes, den ein bewegter körper in einer flüssigkeit erfährt," Nachr. Ges. Wiss. Goettingen, Math.-Phys. Kl. NWGAAN0369-6650 12, 509 (1911).
5. C. P. Jackson, "A finite-element study of the onset of vortex shedding in flow past variously shaped bodies," J. Fluid Mech. JFLSA70022-112010.1017/S0022112087002234 182, 23 (1987).
6. M. S. Bloor, "The transition to turbulence in the wake of a circular cylinder," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112064000726 19, 290 (1964).
7. J. H. Gerrard, "The wakes of cylindrical bluff bodies at low Reynolds number," Philos. Trans. R. Soc. London, Ser. A PTRMAD0962-8428 288, 351 (1978).
8. M. F. Unal and D. Rockwell, "On the vortex formation from a cylinder. Part 1: The initial instability," J. Fluid Mech. JFLSA70022-112010.1017/S0022112088001429 190, 491 (1988).
9. A. Prasad and C. H. K. Williamson, "The instability of the shear layer separating from a bluff body," J. Fluid Mech. JFLSA70022-112010.1017/S0022112096004326 333, 375 (1997).
10. S. Rajagopalan and R. A. Antonia, "Flow around a circular cylinder: Structure of the near wake shear layer," Exp. Fluids EXFLDU0723-486410.1007/s00348-004-0913-0 38, 393 (2005).
11. S. Mittal and B. Kumar, "A stabilized finite element method for global analysis of convective instabilities in nonparallel flows," Phys. Fluids PHFLE61070-663110.1063/1.2759977 19, 088105 (2007).
12. S. Mittal, "Instability of the separated shear layer in flow past a cylinder: Forced excitation," Int. J. Numer. Methods Fluids IJNFDW0271-209110.1002/fld.1548 56, 687 (2007).
13. D. Barkley, "Linear analysis of the cylinder wake mean flow," Europhys. Lett. EULEEJ0295-507510.1209/epl/i2006-10168-7 75, 750 (2006).
14. S. Mittal, "Global linear stability analysis of time-averaged flows," Int. J. Numer. Methods Fluids IJNFDW0271-2091 (in press).
15. T. E. Tezduyar, S. Mittal, S. E. Ray, and R. Shih, "Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements," Comput. Methods Appl. Mech. Eng. CMMECC0045-782510.1016/0045-7825(92)90141-6 95, 221 (1992).
16. X. Yang and A. Zebib, "Absolute and convective instability of a cylinder wake," Phys. Fluids A PFADEB0899-821310.1063/1.857362 1, 689 (1989).
17. P. A. Monkewitz, "The absolute and convective nature of instability in two-dimensional wakes at low Reynolds numbers," Phys. Fluids PFLDAS0031-917110.1063/1.866720 31, 999 (1988).
18. R. T. Pierrehumbert, "Local and global baroclinic instability of zonally varying flow," J. Atmos. Sci. JAHSAK0022-4928 41, 21412162 (1985).
19. P. Huerre, J. M. Chomaz, and L. G. Redekopp, "Bifurcations to local and global modes in spatially developing flows," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.60.25 60, 25 (1988).
20. K. A. Cliffe, K. H. Winters, and C. P. Jackson, The Prediction of Instabilities Using Bifurcation Theory (Wiley, New York, 1986).
21. M. Morzynski and F. Thiele, "Numerical stability analysis of a flow about a cylinder," Z. Angew. Math. Mech. ZAMMAX0044-2267 71, T424 (1991).
22. M. Morzynski, K. Afanasiev, and F. Thiele, "Solution of the eigenvalue problems resulting from global non-parallel flow stability analysis," Comput. Methods Appl. Mech. Eng. CMMECC0045-782510.1016/ S0045-7825(98)00183-2 169, 161 (1999).
23. Y. Ding and M. Kawahara, "Three dimensional linear stability analysis of incompressible viscous flows using the finite element method," Int. J. Numer. Methods Fluids IJNFDW0271-209110.1002/ (SICI)1097-0363(19990930)31:2<451::AID-FLD885 31, 451 (1999).
24. S. Mittal and B. Kumar, "Flow past a rotating cylinder," J. Fluid Mech. JFLSA70022-112010.1017/S0022112002002938 476, 303 (2003).
25. T. J. R. Hughes and A. N. Brooks, in Finite Element Methods for Convection Dominated Flows, edited by T. J. R. Hughes (ASME, New York, 1979), Vol. 34, pp. 19-35.
26. A. N. Brooks and T. J. R. Hughes, "Streamline upwind/ Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations," Comput. Methods Appl. Mech. Eng. CMMECC0045-782510.1016/ 0045-7825(82)90071-8 32, 199 (1982).
27. T. J. R. Hughes, L. P. Franca, and M. Balestra, "A new finite element formulation for computational fluid dynamics, V. Circumventing the Babuška-Brezzi condition, a stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations," Comput. Methods Appl. Mech. Eng. CMMECC0045-782510.1016/0045-7825(86)90025-3 59, 85 (1986).
28. S. Mittal, "On the performance of high aspect-ratio elements for incompressible flows," Comput. Methods Appl. Mech. Eng. CMMECC0045-782510.1016/S0045-7825(99)00152-8 188, 269 (2000).
29. Y. Saad and M. Schultz, "GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems," SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. SIJCD40196-5204 7, 856 (1986).
30. G. W. Stewart, Topics in Numerical Analysis II, edited by J. H. H. Miller (Academic, London, 1975), pp. 169-185.
31. B. Fornberg, "Steady incompressible flow past a row of circular cylinders," J. Fluid Mech. JFLSA70022-112010.1017/S0022112091002215 225, 655 (1991).
32. J. S. B. Gajjar and N. Azzam, "Numerical solution of the Navier-Stokes equations for the flow in a cylinder cascade," J. Fluid Mech. JFLSA70022-1120 520, 51 (2004).
33. I. P. Castro, "The stability of laminar symmetric separated wakes," J. Fluid Mech.JFLSA70022-1120 532, 389 (2005).
34. A. G. Kravchenko, P. Moin, and K. Shariff, "B-Spline method and zonal grids for simulations of complex turbulent flows," J. Comput. Phys. JCTPAH0021-999110.1006/jcph.1999.6217 151, 757 (1999).
35. H. Persillon and M. Braza, "Physical analysis of the transition to turbulence in the wake of a circular cylinder by three-dimensional Navier-Stokes simulation," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112098001116 365, 23 (1998).
36. C. H. K. Williamson, "Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low Reynolds numbers," J. Fluid Mech.JFLSA70022-112010.1017/S0022112089002429 206, 579 (1989).