Subcritical transition in channel flows and localized turbulence

TAO Jianjun

doi:10.7638/kqdlxxb-2019.0159

English Version Journal Login

您当前的位置：

首页 >

文章列表页 >

Subcritical transition in channel flows and localized turbulence

更新时间：2026-05-28

- Subcritical transition in channel flows and localized turbulence
- Vol. 38, Issue 1, Pages: 128-136(2020)
- 作者机构：
  
  北京大学工学院力学与工程科学系, 湍流与复杂系统国家重点实验室,北京,100871
- 作者简介：
- 基金信息：
- DOI：10.7638/kqdlxxb-2019.0159
  CLC： V211.3
- Published：2020
- 稿件说明：
移动端阅览
陶建军. 槽流的亚临界转捩与局地湍流[J]. 空气动力学学报, 2020, 38(1): 128-136.

TAO Jianjun. Subcritical transition in channel flows and localized turbulence[J]. 2020, 38(1): 128-136.
陶建军. 槽流的亚临界转捩与局地湍流[J]. 空气动力学学报, 2020, 38(1): 128-136. DOI： 10.7638/kqdlxxb-2019.0159.

TAO Jianjun. Subcritical transition in channel flows and localized turbulence[J]. 2020, 38(1): 128-136. DOI： 10.7638/kqdlxxb-2019.0159.

摘要

在中低雷诺数时，处于线性稳定的槽道流若受到强扰动可发生亚临界转捩变为湍流。近年人们对该类转捩机理的研究取得重要进展。对于平板泊肃叶流，亚临界转捩之初是稀疏湍流态，其特征结构是远间隔的包含小尺度涡和高低速条带的大尺度的湍流带，可倾斜伸长。该阶段的湍流占比有上限但并非雷诺数的单值函数。随着雷诺数的增加转捩进入平衡局地湍流态，即存在统计定常态，其湍流占比是雷诺数单值函数，可由定向逾渗模型描述。进一步增加雷诺数，湍流带的分裂愈发频繁，最终流场会布满湍流带，在更高的雷诺数时变为均匀湍流。论文概述了为比拟亚临界转捩过程所提出的动力学模型，以及为定量表征管流、平板库艾特流和平板泊肃叶流转捩过程的相似性所提出的局地稳定性参数，并在最后对槽道流亚临界转捩研究的发展做了简要展望。

Abstract

Triggered by strong disturbances

linearly stable channel flows may turn to be turbulent at moderate Reynolds numbers

and encouraging progresses have been made on the study of these subcritical transitions in the past two decades. For plane-Poiseuille flow

the initial stage of the transition is a sparse turbulent state

where large-scale oblique turbulent bands are composed of small-scale vortices and high and low speed streaks

separated by large laminar regions

and are able to extend obliquely. At this stage

the turbulence fraction has an upper bound

but is not a single-valued function of the Reynolds number. With the increase of the Reynolds number

the equilibrium localized turbulence state is reached

i.e. when the channel domain is large enough the flow is statistically steady and its turbulent fraction is a single-valued function of the Reynolds number and can be described by the Directed Percolation model. When the Reynolds number is increased further

band split occurs more frequently and the turbulent bands spread to the whole flow domain eventually

and the flow turns to be uniform turbulence at higher Reynolds numbers. The dynamic models proposed for the subcritical transitions are summarized

and the local stability parameters to quantitatively characterize the similarity among the transitions of pipe flow

plane-Couette flow

and plane-Poiseuille flow are surveyed. Finally

the development of the study on the subcritical transitions in channel flows is prospected.

关键词

Keywords

references

ZHOU H, ZHAO G F. Hydrodynamic stability[M]. Beijing:National Defence Industry Press, 2004.

BUSSE F H. The sequence-of-bifurcations approach towards understanding turbulent fluid flow[J]. Surveys in Geophysics, 2003, 24:269-288.

SCHMID P J, HENNINGSON D S. Stability and transition in shear flows[M]. New York, NY:Springer(2001).

MESEGUER A, TREFETHEN L N. Linearized pipe flow to Reynolds numbers 10 7 [J ] . J Comp Phys, 2003, 186:178-197.

MANNEVILLE P. Laminar-turbulent patterning in transitional flows[J]. Entropy, 2017, 19:316.

TUCKERMAN L S, CHANTRY M, BARKLEY D. Patterns in wall-bounded shear flows[J]. Annu Rev Fluid Mech, 2020, 52:343-367.

PFENNINGER W. Transition experiments in the inlet length of tubes at high Reynolds numbers[M]//LACHMANN G, In Boundary Layer and Flow Control: Its Principles and Application, 2: 970-980. New York, NY: Pergamon(1961).

PEIXINHO J, MULLIN T. Finite-amplitude thresholds for transition in pipe flow[J]. J Fluid Mech, 2007, 582:169-178.

WU X, LEIB S J, GOLDSTEIN M E. On the nonlinear evolution of a pair of oblique Tollmien-Schlichting waves in boundary layers[J]. J Fluid Mech, 1997, 340:361-394.

WU X. Nonlinear theories for shear flow instabilities:physical insights and practical implications[J]. Annu Rev Fluid Mech, 2019, 51:451-485.

FU S, WANG L. RANS modeling of high-speed aerodynamic flow transition with consideration of stability theory[J]. Progress in Aerospace Sciences, 2013, 58:36-59.

LEE C B, WU J Z. Transition in wall-bounded flows[J]. Appl Mech Rev, 2008, 61:030802.

FAISST H, ECKHARDT B. Traveling waves in pipe flow[J]. Phys Rev Lett, 2003, 91:224502.

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[J]. Proc. R. Soc. London 1883, 35:84-99.

WYGNANSKI I J, CHAMPAGNE F H. On transition in a pipe. Part 1. The origin of puffs and slugs and the flow in a turbulent slug[J]. J Fluid Mech, 1973, 59(2):281-335

WYGNANSKI I, SOKOLOV M, FRIEDMAN D. On transition in a pipe. Part 2. The equilibrium puff[J]. J Fluid Mech, 1975, 69(2):283-304

HOF B, DELOZAR A, KUIK D J, et al. Repeller or attractor? Selecting the dynamical model for the onset of turbulence in pipe flow[J]. Phys Rev Lett, 2008, 101:214501.

AVILA K, MOXEY D, DE LOZAR A, et al. The onset of turbulence in pipe flow[J]. Science, 2011, 333:192-196.

ECKHARDT B, SCHNEIDER T M, HOF B, et al. Turbulence transition in pipe flow[J]. Annu Rev Fluid Mech, 2007, 39:447-468.

MULLIN T. Experimental studies of transition to turbulence in a pipe[J]. Annu Rev Fluid Mech, 2011, 43:1-24.

HOF B, DOORNE C W H, WESTERWEEL J, et al. Experimental observation of nonlinear traveling waves in turbulent pipe flow[J]. Science, 2004, 305:1594-1598.

HOF B, De LOZAR A, AVILA M, et al. Eliminating turbulence in spatially intermittent flows[J]. Science, 2010, 327:1491-1494.

ECKHARDT B. A critical point for turbulence[J]. Science, 2011, 333:165-166.

HOF B, WESTERWEEL J, SCHNEIDER T M, et al. Finite lifetime of turbulence in shear flows[J]. Nature Physics, 2006, 443:59-62.

BARKLEY D, SONG B, MUKUND V. et al. The rise of fully turbulent flow[J]. Nature Physics, 2015, 526:550-553.

JOSEPH D D, CARMI S. Stability of Poiseuille flow in pipes, annuli, and channels[J]. Quarterly of Applied Mathematics, 1969, 26:575-599.

BUSSE F H. Bounds on the transport of mass and momentum by turbulent flow between parallel plates[J]. Zeitschrift für angewandte Mathematik und Physik ZAMP 1969, 20(1):1-14.

JOSEPH D D. Nonlinear stability of the Boussinesq equations by the method of energy[J]. Archive for Rational Mechanics and Analysis, 1966, 22(3):163-184.

XIONG X, TAO J. Lower bound for transient growth of inclined buoyancy layer[J]. Appl Math Mech (Engl Ed), 2017, 38:779-796.

BUTLER K M, FARRELL B F. Three-dimensional optimal perturbations in viscous shear flow[J]. Physics of Fluids A, 1992, 4(8):1637-1650.

TREFETHEN L N, TREFETHEN A E, REDDY S C, et al. Hydrodynamic stability without eigenvalues[J]. Science, 1993, 261:578-584.

REDDY S C, HENNINGSON D S. Energy growth in viscous channel flows[J]. J Fluid Mech, 1993, 252:209-238.

NAGATA M. Three-dimensional finite-amplitude solutions in plane Couette flow:bifurcation from infinity[J]. J Fluid Mech, 1990, 217:519-527.

CLEVER R M, BUSSE F H. Three-dimensional convection in a horizontal fluid layer subjected to a constant shear[J]. J Fluid Mech, 1992, 234:511-527.

WALEFFE F. Three-dimensional coherent states in plane shear flows[J]. Phys Rev Lett, 1998, 81:4140-4143.

WEDIN H, KERSWELL R R. Exact coherent structures in pipe flow:travelling wave solutions[J]. J Fluid Mech, 2004, 508:333-371.

KAWAHARA G, KIDA S. Periodic motion embedded in plane Couette turbulence:regeneration cycle and burst[J]. J Fluid Mech, 2001, 449:291-300.

GIBSON J F, HALCROW J, CVITANOVIC P. Visualizing the geometry of state space in plane Couette flow[J]. J Fluid Mech, 2008, 611:107-130.

SCHNEIDER T M, MARINC D, ECKHARDT B. Localized edge states nucleate turbulence in extended plane Couette cells[J]. J Fluid Mech, 2010, 646:441-451.

ZAMMERT S, ECKHARDT B. Streamwise and doubly-localised periodic orbits in plane Poiseuille flow[J]. J Fluid Mech, 2014, 761:348-359.

KAWAHARA G, UHLMANN M, VAN VEEN L. The significance of simple invariant solutions in turbulent flows[J]. Annu Rev Fluid Mech, 2012, 44:203-225.

DAVIES S J, WHITE C M. An experimental study of the flow of water in pipes of rectangular section[C]//Proceedings of the Royal Society of London, Series A: Mathematical, Physical and Engineering Sciences, 1928, 119(781): 92-107.

PATEL V C, HEAD M R. Some observations on skin friction and velocity profiles in fully developed pipe and channel flows[J]. J Fluid Mech, 1969, 38(1):181-201.

NISHIOKA M, ASAI M. Some observations of the subcritical transition in plane Poiseuille flow[J]. J Fluid Mech, 1985, 150:441-450.

CARLSON D R, WIDNALL S E, PEETERS M F. A flow-visualization study of transition in plane Poiseuille flow[J]. J Fluid Mech, 1982, 121:487-505.

HENNINGSON D, SPALART P, KIM J. Numerical simulations of turbulent spots in plane Poiseuille and boundary-layer flow[J]. Phys Fluids, 1987, 30(10):2914-2917.

HENNINGSON D S, ALFREDSSON P H. The wave structure of turbulent spots in plane Poiseuille flow[J]. J Fluid Mech, 1987, 178:405-421.

LI F, WIDNALL S E. Wave patterns in plane Poiseuille flow created by concentrated disturbances[J]. J Fluid Mech, 1989, 208:639-656.

HENNINGSON D S, KIM J. On turbulent spots in plane Poiseuille flow[J]. J Fluid Mech, 1991, 228:183-205.

HENNINGSON D S, JOHANSSON A V, ALFREDSSON P H. Turbulent spots in channel flows[J]. J Eng Math, 1994, 28:21-42.

ALAVYOON F, HENNINGSON D S, ALFREDSSON P H. Turbulent spots in plane Poiseuille flow-flow visualization[J]. Phys Fluids, 1986, 29(4):1328-1331.

TSUKAHARA T, SEKI Y, KAWAMURA H, et al. DNS of turbulent channel flow at very low Reynolds numbers[C]//Proceedings of the 4th International Symposium on Turbulence and Shear Flow Phenomena, Williamsburg, 27-29 June 2005(unpublished), pp. 935-940, arXiv: 1406. 0248[physics. flu-dyn].

TSUKAHARA T, IWAMOTO K, KAWAMURA H, et al. DNS of heat transfer in a transitional channel flow accompanied by a turbulent puff-like structure[C]//Turbulent, Heat and Mass Transfer 5, 2006, Sept, 25-29, Dubrovnik, Croatia.

TSUKAHARA T, KAWAGUCHI Y, KAWAMURA H, et al. Turbulence stripe in transitional channel flow with/without system rotation[C]//Proceedings of the IUTAM Symposium on Laminar-Turbulent Transition, 2009, Stockholm, Sweden.

HASHIMOTO S, HASOBE A, TSUKAHARA T, et al. An experimental study on turbulent-stripe structure in transitional channel flow[C]//Turbulence, heat and Mass Transfer 6, 2009, 14-18 September, Rome, Italy.

AIDA H, TSUKAHARA T, KAWAGUCHI Y. Development of a turbulent spot into stripe pattern in plane Poiseuille flow[C]//Proceedings of Seventh International Symposium on Turbulence Shear Flow Phenomena, 2011, July, 28-31, Ottawa, Canada.

TSUKAHARA T, ISHIDA T, DUGUET Y. Turbulent-spot development in constant-mass-flux channel flow[C ] //14 th European Turbulence Conference 2013, Sept. 1-4, Lyon, France.

TAO J, CHEN S Y, SU W D. Universal threshold of the transition to localized turbulence in shear flows[J]. Theor Appl Mech Lett, 2011, 1(5):052002.

TUCKERMAN L. Turbulent-laminar banded patterns in plane Poiseuille flow[C ] //23 rd ICTAM, 2012, Aug. 19-24, Beijing, China.

TUCKERMAN L S, BARKLEY D. Patterns and dynamics in transitional plane Couette flow[J]. Phys Fluids, 2011, 23:041301.

TAO J, XIONG X. The unified transition stages in linearly stable shear flows[C]//Proc 14th Asian Congress of Fluid Mechanics, 2013, Oct. 15-19, Hanoi and Halong, Vietnam.

TSUKAHARA T, ISHIDA T. The lower bound of subcritical transition in plane Poiseuille flow[C]//Euromech Colloquium EC565, 2014, May 6-9, Cargese, France.

TUCKERMAN L S, KREILOS T, SCHROBSDORFF H, et al. Turbulent-laminar patterns in plane Poiseuille flow[J]. Phys Fluids, 2014, 26(11):114103.

XIONG X, TAO J, CHEN S Y, et al. Turbulent bands in plane-Poiseuille flow at moderate Reynolds numbers[J]. Phys Fluids, 2015, 27(4):041702.

TAO J J, ECKHARDT B, XIONG X M. Extended localized structures and the onset of turbulence in channel flow[J]. Phys Rev Fluids, 2018, 3(1):011902(R).

SHIMIZU M, KANAZAWA T, KAWAHARA G. Exponential growth of lifetime of localized turbulence with its extent in channel flow[J]. Fluid Dyn Res, 2019, 51:011404.

BARKLEY D. Simplifying the complexity of pipe flow[J]. Phys Rev E, 2011, 84:016309.

BARKLEY D. Modeling the transition to turbulence in shear flows[J]. J Phys:Conf Ser, 2011, 38:032001.

SONG B F, BARKLEY D, HOF B, et al. Speed and structure of turbulent fronts in pipe flow[J]. J Fluid Mech, 2017, 813:1045-1059.

BARKLEY D. Theoretical perspective on the route to turbulence in a pipe[J]. J Fluid Mech, 2016, 803:P1.

FARANDA D, LUCARINI V, MANNEVILLE P, et al. On using extreme values to detect global stability thresholds in multi-stable systems:The case of transitional plane Couette flow[J]. Chaos, Solitons Fractals, 2014, 64:26-35.

SHIH H Y, HSIEH T L, GOLDENFELD N. Ecological collapse and the emergence of travelling waves at the onset of shear turbulence[J]. Nature Phys, 2016, 12:245-248.

POMEAU Y. Front motion, meta stability and subcritical bifurcations in hydrodynamics[J]. Physica D, 1986, 23:3-11.

SIPOS M, GOLDENFELD N. Directed percolation describes lifetime and growth of turbulent puffs and slugs[J]. Phys Rev E, 2011, 84:035304(R).

LEMOULT G, SHI L, AVILA K, et al. Directed percolation phase transition to sustained turbulence in Couette flow[J]. Nature Phys, 2016, 12(3):254-258.

CHANTRY M, TUCKERMAN L S, BARKLEY D. Universal continuous transition to turbulence in a planar shear flow[J]. J Fluid Mech, 2017, 824:R1.

SANO M, TAMAI K. A universal transition to turbulence in channel flow[J]. Nature Phys, 2016, 12(3):249-253.

ECKHARDT B. Turbulence transition in pipe flow:some open questions[J]. Nonlinearity, 2008, 21:T1-T11.

TAO J J, CHEN S Y, SU W D. Local Reynolds number and thresholds of transition in shear flows[J]. Sci China-Phys Mech Astron, 2013, 56(2):263-269.

ALFREDSSON P H, MATSUBARA M. Free-stream turbulence, streaky structures and transition in boundary layer flows[R]. AIAA 2000-2534, 2000.

MANNEVILLE P, PRIGENT A, DAUCHOT O. Banded turbulence in Taylor-Couette and plane Couette flow[C]//APS/DFD meeting. Bull Am Phys Soc, 2001, 46: 35.

RYANN W, JOHNSON M M. Transition from laminar to turbulent flow in pipes[J]. AIChE J, 1959, 5:433-435.

HANKS R W. The laminar-turbulent transition for flow in pipes, concentric annuli, and parallel plates[J]. AIChE J, 1963, 9:45-48.

DOU H S. Mechanism of flow instability and transition to turbulence[J]. International J Non-Linear Mechanics, 2006, 41:512-517.

DOU H S, KHOO B C, YEO K S. Instability of Taylor-Couette flow between concentric rotating cylinders[J]. Inter J of Thermal Science, 2008, 47:1422-1435.

LU J Z, TAO J J, ZHOU W T, et al. Threshold and decay properties of transient isolated turbulent band in plane Couette flow[J]. Appl Math Mech, 2019, 40(10):1449-1456.

LIU J S, XIAO Y, LI M G, et al. Measurement of localized turbulent structures in a plane Poiseuille flow[C]//Reynolds number effect: implications on understanding and control turbulence, Mar, 28-30, 2019, Shenzhen, China.

XIAO X K, SONG B F. The growth mechanism of turbulent bands in channel flow at low Reynolds numbers[J]. J Fluid Mech, 2020, 883:R1.

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

Numerical and experimental study on aerodynamic design for the rear wing of an electric sports car

An Ac-criteria-based optimal input design method

Numerical simulation on gust responses of high aspect ratio aircraft

Impact of inter-wing spacing on aerodynamic noise in multi-flapping wing configurations

Dynamic ablation morphology measurement of thermal protection materials using structured light vision

Related Author

No data

Related Institution

No data

AI问答

⁰