An optimal path to transition in a duct

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

Volumn 367, Issue 1888, 2009, Pages 529-544

  Biau, Damien ^a,b   Bottaro, Alessandro ^b  

^a LEA   (France)

^b UNIVERSITY OF GENOA   (Italy)

Author keywords

Duct flow; Minimal defects; Optimal perturbations; Transition to turbulence

Indexed keywords

DEFECTS; DUCTS; FLUID DYNAMICS; GROUNDWATER FLOW; LAMINAR FLOW; MATHEMATICAL MODELS; NAVIER STOKES EQUATIONS; REYNOLDS NUMBER; VORTEX FLOW; WAVE TRANSMISSION;

BASE FLOWS; DUCT FLOW; EDGE STATES; LONGITUDINAL VORTICES; MINIMAL DEFECTS; NON-LINEAR RESPONSES; NUMERICAL SIMULATIONS; OPTIMAL DISTURBANCES; OPTIMAL PATHS; OPTIMAL PERTURBATIONS; OPTIMAL SOLUTIONS; OPTIMIZATION PROCEDURES; QUADRATIC INTERACTIONS; SIMILAR CASES; SQUARE CROSS SECTIONS; TRANSITION TO TURBULENCE; TRAVELLING WAVES; TURBULENT TRANSITIONS; UNSTABLE MEAN FLOWS; UNSTABLE SOLUTIONS; VARIATIONAL APPROACHES;

TURBULENCE;

EID: 58149139535     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2008.0191     Document Type: Article

References (27)

1. Ben-Dov, G. & Cohen, J. 2007a Critical Reynolds number for a natural transition to turbulence in pipe flows. Phys. Rev. Lett. 98, 064 503. (doi:10.1103/Phys RevLett.98.064503)
2. Ben-Dov, G. & Cohen, J. 2007b Instability of optimal non-axisymmetric base-flow deviations in pipe Poiseuille flow. J. Fluid Mech. 588, 189-215. (doi: 10.1017/S0022112007007446)
3. Biau, D. & Bottaro, A. 2004 Transient growth and minimal defects: two possible initial paths of transition to turbulence in plane shear flows. Phys. Fluids 16, 3515-3529. (doi:10.1063/1.1775194)
4. Biau, D., Soueid, H. & Bottaro, A. 2008 Transition to turbulence in duct flow. J. Fluid Mech. 596, 113-442. (doi:10.1017/ S0022112007009536)
5. Bottaro, A., Corbett, P. & Luchini, P. 2003 The effect of base flow variation on flow stability. J. Fluid Mech. 476, 293-302. (doi:10.1017/S002211200200318X)
6. Butler, K. & Farrell, B. 1992 Three-dimensional optimal perturbations in viscous shear flow. Phys. Fluids A 4, 1637-1650. (doi:10.1063/1.858386)
7. Cherhabili, A. & Ehrcnstcin, U. 1997 Finite-amplitude equilibrium states in plane Couette flow. J. Fluid Mech. 342, 159-177. (doi:10.1017/S0022112097005661)
8. Clever, R. M. & Busse, F. H. 1992 Three-dimensional convection in a horizontal fluid layer subjected to a constant shear. J. Fluid Mech. 234, 511-527. (doi:10.1017/S0022112092000892)
9. Duguet, Y., Willis, A. P. & Kerswell, R. R. 2008 Transition in pipe flow: the saddle structure on the boundary of turbulence, J. Fluid Mech. 613, 255-274. (doi:10.1017/S0022112008003248)
10. Eckhardt, B., Schneider, T. M., Hof, B. & Westerweel, J. 2007 Turbulence transition in pipe flow. Annu. Rev. Fluid Mech. 39, 447-468. (doi:10.1146/annurcv.fluid.39.050905.110308)
11. Faisst, H. & Eckhardt, B. 2003 Traveling waves in pipe flow. Phys. Rev. Lett. 91, 224-502. (doi:10. 1103/PhysRevLett.91.224502)
12. Gill, A. 1965 On the behaviour of small disturbances to Poiseuille flow in a circular pipe. J. Fluid Mech. 21, 145-172. (doi:10.1017/S0022112065000101)
13. Hamilton, J. M., Kim, J. & Waleffe, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317-348. (doi:10.1017/S0022112095000978)
14. Jackson, D. & Launder, B. 2007 Osborne Reynolds and the publication of his paper on turbulent flow. Annu. Rev. Fluid Mech. 39, 19-35. (doi:10.1146/annurev.fluid.39.050905.110241)
15. Kawahara, G. & Kida, S. 2001 Periodic motion embedded in plane Couette turbulence: regeneration cycle and burst. J. Fluid Mech. 449, 291-300. (doi: 10.1017/S0022112001006243)
16. Nagata, M. 1990 Three-dimensional finite amplitude solutions in plane Couette flow. J. Fluid Mech. 217, 519-527. (doi:10.1017/ S0022112090000829)
17. Pringle, C. & Kerswell, R. 2007 Asymmetric, helical and mirror-symmetric travelling waves in pipe flow. Phys. Rev. Lett. 99, 74-502. (doi:10.1103/PhysRevLett.99.074502)
18. Reynolds, O. 1883 An experimental investigation of the circumstances which determine whether the motion of water in parallel channels shall be direct or sinuous and the law of resistance in parallel channels. Phil. Trans. R. Soc. 174, 935-982. (doi:10.1098/rstl.1883.0029)
19. Reynolds, O. 1895 On the dynamical theory of incompressible viscous fluids and the determination of the criterion. Phil. Trans. R. Soc. 186, 123-164. (doi:10.1098/rsta.1895.0004)
20. Ruelle, D. & Takens, F. 1971 On the nature of turbulence. Commun. Math. Phys. 20, 167-192. (doi:10.1007/BF01646553)
21. Schneider, T. M., Eckhardt, B. & Yorke, J. A. 2007 Turbulence transition and the edge of chaos in pipe flow. Phys. Rev. Lett. 99, 034-502. (doi:10.1103/PhysRevLett.99.034502)
22. Tatsumi, T. & Yoshimura. T. 1990 Stability of the laminar flow in a rectangular duct. J. Fluid Mech. 212, 437-449. (doi:10.1017/S002211209000204X)
23. Toh, S. & Itano, T. 2003 A periodic-like solution in channel flow. J. Fluid Mech. 481, 67-76. (doi:10.1017/S0022112003003768)
24. Trefethen, L., Trefethen, A., Reddy, S. & Driscoll, T. 1993 Hydrodynamic stability without eigenvalues. Science 261, 578-584. (doi:10.1126/scicncc.261.5121.578)
25. Uhlmann. M., Pinelli, A., Kawahara, G. & Sekimoto, A. 2007 Marginally turbulent flow in a square duct. J. Fluid Mech. 588, 153-162. (doi:10.1017/S0022112007007604)
26. Waleffe, F. 1997 On a self-sustaining process in shear flows. Phys. Fluids 9, 883-900. (doi: 10.1063/1.869185)
27. Wedin, H. & Kerswell, R. R. 2004 Exact coherent structures in pipe flow: travelling wave solutions. J. Fluid Mech. 508, 333-371. (doi:10.1017/S0022112004009346)