Threshold and decay properties of transient isolated turbulent band in plane Couette flow

doi:10.1007/s10483-019-2531-6

Applied Mathematics and Mechanics (English Edition) ›› 2019, Vol. 40 ›› Issue (10): 1449-1456.doi: https://doi.org/10.1007/s10483-019-2531-6

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Threshold and decay properties of transient isolated turbulent band in plane Couette flow

Jianzhou LU¹, Jianjun TAO¹, Weitao ZHOU¹, Xiangming XIONG²

1. CAPT-HEDPS, SKLTCS, Collaborative Innovation Center of IFSA, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, China;
2. The Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, U.S.A

Received:2019-05-10 Revised:2019-05-28 Online:2019-10-01 Published:2019-09-17
Contact: Jianjun TAO E-mail:jjtao@pku.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 91752203, 11490553, and 11602148)

Abstract

Abstract: By direct numerical simulations of the plane Couette flow (PCF) in a large computational domain, it is shown that an isolated turbulent band decays monotonically at low Reynolds numbers but experiences transient growth before the eventual relaminarization at moderate Reynolds numbers. The lower bound Reynolds number of the transient-growth regime is determined as 286. The width, length, and tilt angle of the isolated band structure are defined based on the disturbance kinetic energy in the mid-plane, and the geometric characteristics of the band can be described with a tilted rectangle. It is illustrated that before its eventual fragmentation, the isolated turbulent band decays in a style of longitudinal contraction, where the center, width, and tilt angle of the band keep almost constant but the band length contracts with a statistically constant velocity.

Key words: plane Couette flow (PCF), subcritical transition, turbulent band

2010 MSC Number:

Jianzhou LU, Jianjun TAO, Weitao ZHOU, Xiangming XIONG. Threshold and decay properties of transient isolated turbulent band in plane Couette flow. Applied Mathematics and Mechanics (English Edition), 2019, 40(10): 1449-1456.

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References

[1] REYNOLDS, O. An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels. Proceedings of the Royal Society of London, 35, 84-99(1883)
[2] DRAZIN, P. G. and REID, W. H. Hydrodynamic Stability, Cambridge University Press, Cambridge (2004)
[3] LEUTHEUSSER, H. J. and CHU, V. H. Experiments on plane Couette flow. Journal of the Hydraulics Division, American Society of Civil Engineers, 97, 1269-1284(1971)
[4] LUNDBLADH, A. and JOHANSSON, A. V. Direct simulation of turbulent spots in plane Couette flow. Journal of Fluid Mechanics, 229, 499-516(1991)
[5] TILLMARK, N. and ALFREDSSON, P. H. Experiments on transition in plane Couette flow. Journal of Fluid Mechanics, 235, 89-102(1992)
[6] DAVIAUD, F., HEGSETH, J., and BERGÉ, P. Subcritical transition to turbulence in plane Couette flow. Physical Review Letters, 69, 2511-2514(1992)
[7] DAUCHOT, O. and DAVIAUD, F. Finite-amplitude perturbation in plane Couette flow. Europhysics Letters, 28, 225-230(1994)
[8] BOTTIN, S., DAVIAUD, F., MANNEVILLE, P., and DAUCHOT, O. Discontinuous transition to spatiotemporal intermittency in plane Couette flow. Europhysics Letters, 43, 171-176(1998)
[9] BOTTIN, S. and CHATÉ, H. Statistical analysis of the transition to turbulence in plane Couette flow. The European Physical Journal B, 6, 143-155(1998)
[10] DAUCHOT, O. and DAVIAUD, F. Finite amplitude perturbation and spots growth mechanism in plane Couette flow. Physics of Fluids, 7, 335-343(1995)
[11] BOTTIN, S., DAUCHOT, O., and DAVIAUD, F. Intermittency in a locally forced plane Couette flow. Physical Review Letters, 79, 4377-4380(1997)
[12] BOTTIN, S., DAUCHOT, O., DAVIAUD, F., and MANNEVILLE, P. Experimental evidence of streamwise vortices as finite amplitude solutions in transitional plane Couette flow. Physics of Fluids, 10, 2597-2607(1998)
[13] PRIGENT, A., GREGOIRÉ, G., CHATÉ, H., DAUCHOT, O., and VAN SAARLOS, W. Largescale finite-wavelength modulation within turbulent shear flows. Physical Review Letters, 89, 014501(2002)
[14] PRIGENT, A., GRÉGOIRE, G., CHATÉ, H., and DAUCHOT, O. Long-wavelength modulation of turbulent shear flows. Physica D, 174, 100-113(2003)
[15] BARKLEY, D. and TUCKERMAN, L. S. Computational study of turbulent laminar patterns in Couette flow. Physical Review Letters, 94, 014502(2005)
[16] TUCKERMAN, L. and BARKLEY, D. Patterns and dynamics in transional plane Couette flow. Physics of Fluids, 23, 041301(2011)
[17] SHI, L., AVILA, M., and HOF, B. Scale invariance at the onset of turbulence in Couette flow. Physical Review Letters, 110, 204502(2013)
[18] DUGUET, Y., SCHLATTER, P., and HENNINGSON, D. S. Formation of turbulent patterns near the onset of transition in plane Couette flow. Journal of Fluid Mechanics, 650, 119-129(2010)
[19] LEMOULT, G., SHI, L., AVILA, K., JALIKOP, S. V., AVILA, M., and HOF, B. Directed percolation phase transition to sustained turbulence in Couette flow. Nature Physics, 12, 254-258(2016)
[20] CHANTRY, M., TUCKERMAN, L., and BARKLEY, D. Universal continuous transition to turbulence in a planar shear flow. Journal of Fluid Mechanics, 824, R1(2017)
[21] MANNEVILLE, P. On the decay of turbulence in plane Couette flow. Fluid Dynamics Research, 43, 065501(2011)
[22] ROLLAND, J. Mechanical and statistical study of the laminar hole formation in transitional plane Couette flow. The European Physical Journal B, 88, 66(2015)
[23] MANNEVILLE, P. Understanding the sub-critical transition to turbulence in wall flows. PRAMANA-Journal of Pyhiscs, 70, 1009-1021(2008)
[24] ECKHARDT, B. A critical point for turbulence. Science, 333, 165-166(2011)
[25] TAO, J. J., CHEN, S. Y., and SU, W. D. Local Reynolds number and thresholds of transition in shear flows. Science China-Physics, Mechanics and Astronomy, 56, 263-269(2013)
[26] TAO, J. J. and XIONG, X. M. The unified transition stages in linearly stable shear flows. Proceedings of the 14th Asian Congress of Fluid Mechanics, Hanoi and Halong, Vietnam (2013)
[27] XIONG, X. M., TAO, J. J., CHEN, S. Y., and BRANDT, L. Turbulent bands in plane-Poiseuille flow at moderate Reynolds numbers. Physics of Fluids, 27, 041702(2015)
[28] LU, J. Z. and TAO, J. J. Spatio-temporal evolution of isolated turbulent bands in channel flows. Proceedings of the 24th International Congress of Theoretical and Applied Mechanics, Montreal, Canada (2016)
[29] CHEVALIER, M., SCHLATTER, P., LUNDBLADH, A., and HENNINGSON, D. S. SIMSON-A Pseudo-Spectral Solver for Incompressible Boundary Layer Flows, Technical Report, No. TRITAMEK 2007:07, Stockholm, Sweden (2007)
[30] TAO, J. J., ECKHARDT, B., and XIONG, X. M. Extended localized structures and the onset of turbulence in channel flow. Physical Review Fluids, 3, 011902(R) (2018)

Threshold and decay properties of transient isolated turbulent band in plane Couette flow

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