2 45 : ,, (coherent structure).,,,,. :,,., 2. Liepmann (1979),.,,, 5% 9%, (Gad-el-hak 2).,., (Kravchenko et al. 1993),.,. Hussain (1986). Ro

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1 , 215, 45 : 2154, 184,,.,,,.,,,.,,.,, : O357.5 : A DOI: 1.652/ : ; : ; : xucx@tsinghua.edu.cn :.., 215, 45: 2154 Xu C X. Coherent structures and drag-reduction mechanism in wall turbulence. Advances in Mechanics, 215, 45: 2154 c 215

2 2 45 : ,, (coherent structure).,,,,. :,,., 2. Liepmann (1979),.,,, 5% 9%, (Gad-el-hak 2).,., (Kravchenko et al. 1993),.,. Hussain (1986). Robinson (1991),, ( ).,, (PIV) (direct numerical simulation, DNS),,., Marusic (21c) 3 : (1), 1δ ν (δ ν = ν/u τ, ν, u τ ); (2) δ( ) (large scale motion, LSM); (3) 1δ (very large scale motion, VLSM) (superstructure)(,, ).,,.

3 : 3,,. 2 (Marusic & Adrian 213): (extrinsic scale) (intrinsic scale)., ;,.,, ν u τ = τ w /ρ, τ w., δ ν = ν/u τ u τ, +, y + = y/δ ν, U + = U/u τ., δ ( δ H R), u τ, u τ., (Marusic & Adrian, 213). y + = y/δ ν = u τ y/ν, y + y,. y +,, 1. y + < 5, ; y + > 5, U. (y + < 5) (5 < y + < 3). y /yu τ /ν y δ

4 4 45 : 2154,,, ;,. 3 < y + <.15δ +,,. y + >.15δ +,. (Pope 2), y/δ <.1 u τ y +, U + = f w (y + ),, y/δ <.1. y + = (y/δ)δ +, δ + = u τ δ/ν = Re τ ( ),, y + > 5 y/δ <.1,,,..,,,, y + = 3,, Nagib (27) 2 < y + <.12δ +, McKeon (24) 6 < y + <.12δ +, Jiménez Moser (27), 3 < y + <.45δ +., (Marusic & Adrian 213): (y + < 4), (4 < y + < 1), (3 < y + < δ + ),,. 3,., 2, y v 2δ z w x u 2

5 : 5 y,, (Pope 2) µ du ( dy ρ u v = τ w 1 y ) δ (1). C f = τ w /ρu 2 m, U m, (1), C f ( 29) C f = 3 3 Re m δ 2 Um 2 (δ y) u v dy (2) Re m = U m δ/ν. 1, ; 2, δ, 2., µ du dr ρ u v r = τ w δ C f = 4 Re m + 4 δ 3 U 2 m δ u r u z. C x (3) r 2 u ru z dr (4),, µ U y ρ u v = τ w + ρ y C x dy (5) = U U/ x + V U/ y., Fukagata (22) (5), C f = 2 ) (1 δ 2 Re δ δ 2 U 2 δ (δ y) u v dy 1 δ 2 U 2 δ (δ y) 2 C x dy (6), δ, Re = U δ/ν.,,.,,, C f = 1 Re 1 δu 2 δ u v dy 1 δu 2 δ (δ y)c x dy (7) :,. Fukagata (22) ( FIK ), Deng (214) (2)

6 6 45 : 2154., Deck (214) (6), 5%,.,., , , Kline Stanford, (burst) (Kline et al. 1967). 3,,. Robinson (1991), 8 : (ejection) (sweep) (pocket) (back). 3., y + < 3,, 1 δ ν,,, 8δ ν 12δ ν (Kim et al. 1987). y + < 6,, 4. (Jeong & Hussain 1995, Chakraborty et al. 25). Jeong (1997) Re τ = 18,, 2δ ν, (2 3)δ ν, (.6.8)U (U ), 9 4., y + = 2,, y + = 5,, 15δ ν (Kim et al. 1987).

1987). y + < 6,, 4. (Jeong & Hussain 1995, Chakraborty et al. 25).

7 许春晓 : 壁湍流相干结构和减阻控制机理研究 7 b a ᅲ偠 y+/ ᅲ偠 y+/. c d 䅵ㅫ y+/. 䅵ㅫ y+/ 图3 壁湍流中的条带结构. (a), (b) 边界层氢气泡流动显示实验 (Kline et al. 1967); (c), (d) 槽道湍流直接数值模拟, Reτ = 395. 黑色: u < ; 白色: u > x+ z 图4 壁湍流中的流向涡结构 (Jeong et al. 1997). 俯视图: < y + < 6 内 λ2 =.3 等值面 (直接数值模拟槽道湍流, Reτ = 18) 流向涡和条带的空间位置存在密切的对应关系, 流向涡总是位于条带附近, 每根条带上有数个流向涡, 其流向平均间距约为 3δν (Jime nez & Kawahara 213). 条件统计表明, 低速条带位于正负成对的流向涡之间, 而流向涡两侧分别为高速流体和低速流体, 如图 5 所示. 在流向涡的上洗侧, 低速流体被带离壁面, 称为上抛 (ejection), 而在其下洗侧, 高速流体被带向壁面, 称为下扫 (sweep), 上抛和下扫合称为猝发 (bursting). 在 (u, v ) 的相平面上, 上抛和下扫分别位于第 2 和第 4 象限, 因此在象限分析中也将其分别称为 Q2 和 Q4 事件. 这种高速流体的下扫和低速流体的上抛所构成的猝发过

3 等值面 (直接数值模拟槽道湍流, Reτ = 18) 流向涡和条带的空间位置存在密切的对应关系, 流向涡总是位于条带附近, 每根条带上有数个流向涡, 其流向平均间距约为 3δν (Jime nez & Kawahara 213).

8 8 45 : 2154 uϕ< vϕ> uϕ> vϕ< 5,, 2 ;, 7%, 3% ,. Hamilton (1995) (Couette),,,. 3 : (1) ; (2) ; (3), 6. Jiménez (1999) (Poiseuille), y + > 6,, 2 < y + < 6. Jiménez (25),.,, (Jiménez & Moin 1991).,,,,, T + = T u 2 τ /ν 4, T + 6.,, 1/3, T + 1. (self-suataining process, SSP), :,,.

9 : 9 x 6 (Hamilton et al. 1995), (lift-up).. N S,,,,,. Bulter Farrell (1992, 1993),,,,. del Álamo & Jiménez (26) Cossu (29),,..,. Schoppa Hussain (22) :.., Brooke & Hanratty (1993) Bernard (1993). Smith Walker (1994), (Kelvin Helmholtz),. Zhou (1999),,,.,.., Robinson (1991),,, ; Kawahara (23),,

10 1 45 : Schoppa Hussain (22),, : (streak transient growth, STG),., 3 : (1) (ω x ) ; (2) ( u / x) ; (3) u / x ω x., (Jiménez & Kawahara 213).,,.,. Nagata (199) Couette 1, Waleffe (1998, 23).,,, ;.,. Nagata (199),, Kawahara Kida (21) Couette, :. Poiseuille (Toh & Itano, 23) Hagen-Poiseuille (Duguet et al., 28).,,. Jiménez (25),,., < y + < 1, (Marusic & Adrian 213). Theodorsen (1952), Ω, Λ,., (Head & Bandyopadhyay 1981, Robinson, 1991).

,,, ;.,. Nagata (199),, Kawahara Kida (21) Couette, :.

11 : 11.,, (Meinhart & Adrian 1995, Adrian et al. 2, Christensen & Adrian 21, Gao et al. 211).. Kim (1987) 1,. Chacin (1996),,, Theodorsen (1952). Adrian Liu (22). Wu Moin (29), Re τ = 46 (Re θ = 94),,,,,., (Adrian 27),., Adrian (27), 7.,,,,., Q2, Q4, Q2 Q4., : Q2 Q2/Q4., 5 1,. Zhou (1999). Q2,, Re τ = 18,, 8. (PHV), 1δ ν,, (DHV) (SHV).,,,,,., 2,,. (THV), 8.

Wu Moin (29), Re τ = 46 (Re θ = 94),,,,,., (Adrian 27),., Adrian (27), 7.,,,,., Q2, Q4, Q2 Q4.

12 力 12 学进第 45 卷 : 2154 展发卡涡包的迁移速度, 发现二次涡和下游涡与主发卡涡的迁移速度类似, 约为槽道中心平均速度的 87% (Uc+ = 15.7), 涡包结构的弥散速度很小, 约为槽道中心平均速度的 3.5%. 这种发卡涡的自生是一种非线性过程, 要求定义初始涡的 Q2 事件具有足够的强度, 该阈值约为 (u, v) = (1.5σu, 1.5σv ). Adrian (27) 认为任何时刻的壁湍流均是由不同尺度的涡包所构成的层级组成, 如图 9 所示, 发卡涡在不同的发展阶段, 其迁移速度也不一样, 一般来讲, 发卡涡包越远离壁面尺度越大, 其向下游的迁移速度越快. a 偏 Q4 ߛሖ y Q2 x 乜㝓 u z b y x u 图7 (a) 发卡涡结构示意图; (b) 流向法向截面上发卡涡的标志 (Adrian 27) DHV PHV t+/ C SHV y+ y+ QSV C THV 图8 发卡涡包形成过程 (Zhou et al. 1999) C5 C1 z+ C2 C3

Adrian (27) 认为任何时刻的壁湍流均是由不同尺度的涡包所构成的层级组成, 如图 9 所示, 发卡涡在不同的发展阶段, 其迁移速度也不一样, 一般来讲, 发卡涡包越远离壁面尺度越大, 其向下游的迁移速度越快.

13 : 13 γ U c2 U c3 U c1 <U c2 <U c3 U c1 9 (Adrian, 27).,,. Ganapathisubramani (23) PIV Re τ = 1 6 (Re θ = 2 5),,, y + = 92 15, u v 28% 25%, 4.% 4.5%.., (Adrian 27).,, (2 4)δ v, 5 1, (1 4 )δ v., y,, Townsend,.,. (Zhou et al. 1999). Smith Walker (1994), Kelvin Helmholtz. Zhou (1999) ( ),., Skote (22), varicose, sinuous. Chernoray (26), sinuous varicose

14 14 45 : (Wang et al. 214),,,. Sharma McKeon (213) N S,,,, / Kim Adrian (1999) k x E uu, k x E uu 2, (bimodal),,.. Balakumar Adrian (27), (Λ LSM Λ VLSM ) (y), 1., Λ LSM y, y/δ.5, (2 3)δ, y., Λ VLSM y, y/δ.5, Λ VLSM 2R (13 15)h,, y/δ.2, Λ VLSM (6 8)δ., Balakumar Adrian (27) 3δ. Hutchins Marusic (27a), 2 16 VLSM Λ max δ LSM y δ 1 (Balakumar & Adrian 27)

15 : 15, 11, 1δ.., (6δ). Monty (29), 3R. Monty (29) (Re τ 3 ), 3. 3,, Λ VLSM, Λ VLSM, VLSM.,,, del Álamo Jiménez (29),, k x E uu, k 1 x (Townsend 1976).,,, (Lee & Sung 211) / /,,, (inactive) (Townsend 1976). Guala (26) /, 4 < Re τ < 8, λ x > 3R 65% 5% 6% ; λ x > 1R 35%. Balakumar Adrian (27) /, Re τ = 531, 96, 1 584, Re τ = ,, λ x > 3H u u 45%, u v 4% ;, 65% 5%. /. y δ x δ HW rake 2 11, y/δ =.15, Re τ = (Hutchins & Marusic 27)

2 / /,,, (inactive) (Townsend 1976). Guala (26) /, 4 < Re τ < 8, λ x > 3R 65% 5% 6% ; λ x > 1R 35%.

16 16 45 : 2154,. (Hutchins & Marusic 27b).,. 12,, (y + = 15 ), u u, ;,,, (Marusic et al. 21a). Jiménez (28),,. Hutchins (27). 13,, :,, ;,,. Mathis (29), Marusic (21b) Mathis (211), Agostini Leschziner (214) /. /. Adrian (27), (2 4)δ ν, 5 1, (1 4 )δ ν, a 2 u 2 Uτ Re τ =5 Re τ =2 8 Re τ =3 9 Re τ =7 3 Re τ =13 6 Re τ =19 b 2 u 2 Uτ λx<δ λx δ Re τ z z 12 (a) ; (b) Re τ = 3 9, 7 3, 19 (Marusic et al. 21a)

/. Adrian (27), (2 4)δ ν, 5 1, (1 4 )δ ν, a 2 u 2 Uτ 8 6 4 Re τ =5 Re τ =2 8 Re τ =3 9 Re τ =7 3 Re τ =13 6 Re τ

17 a u : b 1 c d tu δ u(λ x >73) u(λ x <73) u(λ x < t 13 y + = 15, Re τ = 73 (Hutchins & Marusic et al. 27b),. Lee Sung (211) 57 Re θ 2 56,,, /,,. Baltzer (213) Re τ = 685, /,, 3 : λ x <.2R, R λ x 2R, λ x > 3R, R λ x 2R, (roll cell).,. Flores (26),,. Pujals (29),, Hutchins (27b). Flores (21) Hwang (211),.,,,,.,

18 18 45 : 2154, ( Smits McKeon Adrian Metzger ) ( Schlatter ONERA Deck ) ( Marusic ),.,,, (Re τ ),, (Wang et al. 214, 214). 5,,., (passive control) (active control), (predetermined control) (reactive control).,, ( ) ( ) ( ) ( ),,,. 5.1 ( 6),, Choi (1994), :,,,. 14, y d. Choi (1994) Re τ y + d = 18, = 15, 25%,., 3,. Choi (1994) Hammond (1998),

, (passive control) (active control), (predetermined control) (reactive control).

19 : 19 y SV y c y d z 14 (Chung et al. 211) y wϕ n s vϕ wϕ vϕ z uϕ s 15 (Deng & Xu, 212) y + d y + d < 2, ; > 2,, ; y + = 15, 25%., Chung (211) y + d > 2,,,,.,., Kim (211),. Deng Xu (212). (x, n, s), 15, ω x ω x t + U ω x x = Ω u s x, u s, v w ; Ω,. Ω u s/ x ω x.,, u s, ω x. v y + = 2, y + d < 2 (8)

20 2 45 : 2154 v, v, y + d > 2, v, ω x,., Deng Xu (212), Deng (214),, Re τ = 18 25% 34%,,, Gad-el-Hak Blackwelder (1989),,. Schoppa Hussain (1998), Sinuous,, 2% 5%. Roy (26),,,, ;. Lim Kim (24),, Re τ = 18, y + < 2,, ; y + > 2,.,. Jung (1992),, Re τ = 18 4%,, (Quadrio 211).,. Choi (22),. 16,,,, ;, Stokes,,,., Choi (22) Stokes,.

21 : 21 a uϕ> Q>1,ω x>uϕ< y =5 y =1 y = b 3 -p (a) ; (b) 5.1.3,,. Kang (28),,,,, 6% 35%.,,,. Kim (28),, 18%, ; 61%,,.,. 5.2,,. 6, 3,, ( v/ z)(du/dy) ; :, U(y, z),, Schoppa Hussain (22) ( ), N S ;,. Kim Lim (2). N S v ω y, Fourier

22 22 45 : 2154 d ˆvˆω = L os dt y L c L sq ˆvˆω + y N v N ωy (9), L os L sq Orr Sommerfeld Squire, L c = ik z (du/dy) ( ( v/ z)(du/dy)), N v N ωy.,,,,,. Lee (1997) N S,,,,. Lee (1998) N S,,,.,,,, N S,.,,,,.,., (Kim 23, Kim & Bewley, 211). Kim (23) N S,, (linear quadratic regulator, LQR),, LQR., ( (9) L c ) LQR,,.,,, Lee (21) N S, (linear quadratic gaussian, LQG), 2%.,.,,,, (Re τ 1 2 ), (Re τ

23 : ),. 5.3,,,., Re τ = 18 Re τ = 72, 25% 18% (Iwamoto et al. 22, Chang et al. 22); Re τ = 18 Re τ = 1,, 4% 28% (Touber & Leschziner, 212, Agostini et al. 214)., Choi (22) 1 Re τ 4, Re.2, Touber Leschziner (212) Agostini et al. (214) (Re τ = 5 1 ),,. 3, Re τ 2,, (y + < 6),?. Iwamoto (25),,.. (214) Re τ = 1 -y(1-y)<uϕvϕ> Re τ =18 Re τ =55 Re τ =95 Re τ =2 y = y 17

24 24 45 : 2154,,,,,.,,,.,,. 6, :,,,.,.,.,,,,,.,,,,,. ( , , ) [ ]. : (Deng B Q Research on mechanism of drag-reduction control based on coherent structures in wall-turbulence. [PhD Thesis]. Beijing: School of Aerospace Engineering, Tsinghua University) , , (Zheng XJ Study on high-reynolds-number wall turbulence in wind-blown sand environment. 8th National Conference on Fluid Mechanics, September 19-21, Lanzhou)., : (Zhu K Q, Xu C X. 29. Viscous Fluid Mechanics. Beijing: Higher Education Press).

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3 45 : 2154 Coherent structures and drag-reduction mechanism in wall turbulence XU Chunxiao Department of Engineering Mechanics, Tsinghua University, Beijing 184, China Abstract The discovery of

30 3 45 : 2154 Coherent structures and drag-reduction mechanism in wall turbulence XU Chunxiao Department of Engineering Mechanics, Tsinghua University, Beijing 184, China Abstract The discovery of coherent structures in turbulent shear flows is one of the most important advances in turbulence research of the last century. These large-scale structures play important role in the physics of wall turbulence, and suggest a new direction for turbulence control. High skin friction in wall-bounded turbulent flows is closely associated with the coherent structures in the near-wall region. The control strategy based on the near-wall physics successfully achieves drag reduction, yet becomes less effective as the Reynolds number increases. It was discovered recently that large-scale coherent motions exist in the outer layer of the high-reynolds number wall turbulence. These motions have important influence on turbulence in the near-wall region and the skin friction, and bring new challenges to the control of turbulent flow at high Reynolds number. In the present paper, we briefly review the research history on coherent structures in wall turbulence, and mainly focus on discussing the near-wall coherent structures and their control mechanism, the recent research developments on the large-scale motions in the outer region of high-reynolds number wall turbulence, and the key issues concerning the drag-reduction control of the high-reynolds number turbulent flows. Keywords wall turbulence, coherent structure, drag-reduction control,,,, ,.,. SCI (29) 2 (2) (1996, 1997). Received: 3 January 215; accepted: 16 February 215; online: 1 April xucx@tsinghua.edu.cn Cite as: Xu C X. Coherent structures and drag-reduction mechanism in wall turbulence. Advances in Mechanics, 215, 45: 2154 c 215 Advances in Mechanics.

2 ( 自然科学版 ) 第 20 卷波 ). 这种压缩波空气必然有一部分要绕流到车身两端的环状空间中, 形成与列车运行方向相反的空气流动. 在列车尾部, 会产生低于大气压的空气流

2 ( 自然科学版 ) 第 20 卷波 ). 这种压缩波空气必然有一部分要绕流到车身两端的环状空间中, 形成与列车运行方向相反的空气流动. 在列车尾部, 会产生低于大气压的空气流第 20 卷第 3 期 2014 年 6 月 ( 自然科学版 ) JOURNAL OF SHANGHAI UNIVERSITY (NATURAL SCIENCE) Vol. 20 No. 3 June 2014 DOI: 10.3969/j.issn.1007-2861.2013.07.031 基于 FLUENT 测轨道交通隧道中电波折射率结构常数张永