The critical layer in pipe flow at high Reynolds number

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 367, Issue 1888, 2009, Pages 561-576

  Viswanath, D ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Critical layer; GMRES hookstep; Pipe flow; Travelling waves

Indexed keywords

PIPE FLOW; REYNOLDS NUMBER; WAVE TRANSMISSION;

ARNOLDI; CRITICAL LAYER; EIGENVALUES; GMRES HOOKSTEP; LOWER BRANCHES; TRAVELLING WAVES;

PIPE;

EID: 58149121621     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2008.0225     Document Type: Article

References (21)

1. Brown, P. & Saad. Y. 1990 Hybrid Krylov methods for nonlinear systems of equations. SIAM J. Sci. Stat Comput. 11, 450-481. (doi:10.1137/0911026)
2. Dennis, J. & Schuabel, R. 1996 Numerical methods for unconstrained optimization and nonlinear equations. Philadelphia, PA: SIAM.
3. Eckhardt, B., Schneider, T., Hof, B. & Westerweel, J. 2007 Turbulence transition in pipe flow. Annu. Rev. Fluid Mech. 39, 447-468. (doi:10.1146/annurev.fiuid.39.050905.110308)
4. Faisst, H. & Eckhardt, B. 2003 Traveling waves in pipe flow, Phys. Rev. Lett. 91, 224 502. (doi:10. 1103/PhysRevLett.91.224502)
5. Faisst. H. & Eckhardt, B. 2004 Sensitive dependence on initial conditions in transition to turbulence in pipe flow. J. Fluid Mech. 504, 343-352. (doi:10.1017/S0022112004008134)
6. Golub. G. & van Loan, C. 1996 Matrix computations, 3rd edn. Baltimore, MD: Johns Hopkins University Press.
7. Hof, B., van Doorne, C, Westerweel, J., Nieuwstadt, F. T. M., Faisst, H., Eckhardt, B., Wedin, H, Kerswell, R. R. & Waleffe, F. 2004 Experimental observation of nonlinear traveling waves in turbulent pipe flows. Science 305, 1594-1598. (doi:10.1126/science.1100393)
8. Luksan, L. & Vlcek, J. 1997 Truncated trust region methods based on preconditioned iterative subalgorithms for large sparse systems of nonlinear equations. J. Optim. Theory Appl. 95, 637-658. (doi: 10.1023/A: 1022678023392)
9. Peixinho, J. & Mullin, T. 2006 Decay of turbulence in pipe flow. Phys. Rev. Lett. 96, 094 501. (doi:10.1103/PhysRevLett. 96.094501)
10. Pringle, C. & Kerswell, R. 2007 Asymmetric, helical, and mirror-symmetric traveling waves in pipe flow. Phys. Rev. Lett. 99, 074 502. (doi:10.1103/PhysRevLett.99.074502)
11. Sancheź, J., Net, M., Garćia-Archilla, B. & Simó, C. 2004 Newton Krylov continuation of periodic orbits for Navier-Stokes flows. J. Comput. Phys. 201, 13-33. (doi:10.1016/j.jcp.2004.04.018)
12. Schneider, T., Eckhardt, B. & Vollrner, J. 2007a Statistical analysis of coherent structures in transitional pipe flow. Phys. Rev. E 75, 066 313. (doi:10.1103/PhysRevE.75.066313)
13. Schneider, T., Eckhardt, B. & Yorke, J. 20076 Turbulence transition and edge of chaos in pipe flow. Phys. Rev. Lett. 99, 034 502. (doi:10.1103/PhysRcvLctt.99.034502)
14. Trefethen, L. & Bau, D. 1997 Numerical linear algebra. Philadelphia, PA: SIAM.
15. Viswanath, D. 2007 Recurrent motions within plane Couette turbulence. J. Fluid Mech. 580, 339-358. (doi:10.1017/S0022112007005459)
16. Viswanath, D. 2008 The dynamics of transition to turbulence in plane Couette flow. In Mathematics and computation, a contemporary view. The Abel Symposium 2006. Abel Symposia, vol. 3. Berlin, Germany: Springer.
17. Waleffe, F. 2003 Homotopy of exact coherent structures in plane shear flows. Phys. Fluids 15, 1517-1534. (doi:10.1063/1.1566753)
18. Wang, J., Gibson. J. & Waleffe, F. 2007 Lower branch coherent states in shear flows: transition and control. Phys. Rev. Lett. 98, 204-501. (doi:10.1103/PhysRevLett.98.204501)
19. Wedin, H. & Kerswell, R. 2004 Exact coherent structures in pipe flow: travelling wave solutions. J. Fluid Mech. 508, 333-371. (doi:10.1017/S0022112004009346)
20. Willis, A. P. & Kerswell, R. R. 2008 Coherent structures in localised and global pipe turbulence. Phys. Rev. Lett. 100, 124501.
21. Wynn, P. 1956 On a procrustean technique for the numerical transformation of slowly convergent sequences and series. Proc. Carnb. Philos. Soc. 52, 663-671.