The turbulent flow originating from the interaction between two parallel streams with different velocities is studied by means of direct numerical simulation. Rather than the more common temporal evolving layer, a spatially evolving configuration, with perturbed laminar inlet conditions is considered. The streamwise evolution and the self-similar state of turbulence statistics are reported and compared to results available in the literature. The characteristics of the transitional region agree with those observed in other simulations and experiments of mixing layers originating from laminar inlets. The present results indicate that the transitional region depends strongly on the inlet flow. Conversely, the self-similar state of turbulent kinetic energy and dissipation agrees quantitatively with those in a temporal mixing layer developing from turbulent initial conditions [M. M. Rogers and R. D. Moser, “Direct simulation of a self-similar turbulent mixing layer,” Phys. Fluids 6, 903 (1994)]. The statistical features of turbulence in the self-similar region have been analysed in terms of longitudinal velocity structure functions, and scaling exponents are estimated by applying the extended self-similarity concept. In the small scale range (60 < r/η < 250), the scaling exponents display the universal anomalous scaling observed in homogeneous isotropic turbulence. The hypothesis of isotropy recovery holds in the turbulent mixing layer despite the presence of strong shear and large-scale structures, independently of the means of turbulence generation. At larger scales (r/η > 400), the mean shear and large coherent structures result in a significant deviation from predictions based on homogeneous isotropic turbulence theory. In this second scaling range, the numerical values of the exponents agree quantitatively with those reported for a variety of other flows characterized by strong shear, such as boundary layers, as well as channel and wake flows.
REFERENCES
1.
M. M.
Rogers
and R. D.
Moser
, “Direct simulation of a self-similar turbulent mixing layer
,” Phys. Fluids
6
, 903
(1994
).2.
A.
Michalke
, “On spatially growing disturbances in an inviscid shear layer
,” J. Fluid Mech.
23
(03
), 521
–544
(1965
).3.
A.
Michalke
, “On the inviscid instability of the hyperbolic tangent velocity profile
,” J. Fluid Mech.
19
(04
), 543
–556
(1964
).4.
G. L.
Brown
and A.
Roshko
, “On density effects and large structure in turbulent mixing layers
,” J. Fluid Mech.
64
(04
), 775
–816
(1974
).5.
P. E.
Dimotakis
, “The mixing transition in turbulent flows
,” J. Fluid Mech.
409
, 69
–98
(2000
).6.
J.
Bell
and R.
Mehta
, “Development of a two-stream mixing layer from tripped and untripped boundary layers
,” AIAA J.
28
(12
), 2034
–2042
(1990
).7.
M. M.
Rogers
and R. D.
Moser
, “The three-dimensional evolution of a plane mixing layer: the Kelvin–Helmholtz rollup
,” J. Fluid Mech.
243
, 183
–226
(1992
).8.
R. D.
Moser
and M. M.
Rogers
, “Mixing transition and the cascade to small scales in a plane mixing layer
,” Phys. Fluids
3
, 1128
(1991
).9.
R. D.
Moser
and M. M.
Rogers
, “The three-dimensional evolution of a plane mixing layer: pairing and transition to turbulence
,” J. Fluid Mech.
247
, 275
–320
(1993
).10.
S.
Laizet
, S.
Lardeau
, and E.
Lamballais
, “Direct numerical simulation of a mixing layer downstream a thick splitter plate
,” Phys. Fluids
22
, 015104
(2010
).11.
N. D.
Sandham
and R. D.
Sandberg
, “Direct numerical simulation of the early development of a turbulent mixing layer downstream of a splitter plate
,” J. Turbul.
10
(1
), 1
–17
(2009
).12.
E.
Balaras
, U.
Piomelli
, and J. M.
Wallace
, “Self-similar states in turbulent mixing layers
,” J. Fluid Mech.
446
, 1
–24
(2001
).13.
M. M.
Koochesfahani
and P. E.
Dimotakis
, “Mixing and chemical reactions in a turbulent liquid mixing layer
,” J. Fluid Mech.
170
, 83
–112
(1986
).14.
P. E.
Dimotakis
, “Turbulent free shear layer mixing and combustion
,” High Speed Flight Propul Syst.
137
, 265
–340
(1991
).15.
P. E.
Dimotakis
and G. L.
Brown
, “The mixing layer at high Reynolds number: Large-structure dynamics and entrainment
,” J. Fluid Mech.
78
(3
), 535
–560
(1976
).16.
J. H.
Konrad
, “An experimental investigation of mixing in two-dimensional turbulent shear flows with application to diffusion-limited chemical reactions
,” Ph.D. dissertation (California Institute of Technology
, 1977
).17.
S. M.
Masutani
and C. T.
Bowman
, “The structure of a chemically reacting plane mixing layer
,” J. Fluid Mech.
172
, 93
–126
(1986
).18.
N. T.
Clemens
and M. G.
Mungal
, “Large-scale structure and entrainment in the supersonic mixing layer
,” J. Fluid Mech.
284
, 171
–216
(1995
).19.
P. S.
Karasso
and M. G.
Mungal
, “Scalar mixing and reaction in plane liquid shear layers
,” J. Fluid Mech.
323
, 23
–63
(1996
).20.
J. C.
Lasheras
and H.
Choi
, “Three-dimensional instability of a plane free shear layer: An experimental study of the formation and evolution of streamwise vortices
,” J. Fluid Mech.
189
, 53
–86
(1988
).21.
A. N.
Kolmogorov
, “The local structure of turbulence in incompressible viscous fluid for very large Reynolds
,” C. R. Acad. Sci. URSS
30
, 301
(1941
).22.
A. N.
Kolmogorov
, “Energy dissipation in locally isotropic turbulence
,” C. R. Acad. Sci. URSS
32
, 16
(1941
).23.
U.
Frisch
, Turbulence: The Legacy of A. N. Kolmogorov
(Cambridge University Press
, 1995
).24.
Y.
Wang
, M.
Tanahashi
, and T.
Miyauchi
, “Coherent fine scale eddies in turbulence transition of spatially-developing mixing layer
,” Int. J. Heat Fluid Flow
28
(6
), 1280
–1290
(2007
).25.
Z. S.
She
, E.
Jackson
, and S. A.
Orszag
, “Intermittent vortex structures in homogeneous isotropic turbulence
,” Nature (London)
344
(6263
), 226
–228
(1990
).26.
A.
Vincent
and M.
Meneguzzi
, “The spatial structure and statistical properties of homogeneous turbulence
,” J. Fluid Mech.
225
, 1
–20
(1991
).27.
P.
Gualtieri
, C. M.
Casciola
, R.
Benzi
, G.
Amati
, and R.
Piva
, “Scaling laws and intermittency in homogeneous shear flow
,” Phys. Fluids
14
, 583
(2002
).28.
H.
Fujisaka
, Y.
Nakayama
, T.
Watanabe
, and S.
Grossmann
, “Scaling hypothesis leading to generalized extended self-similarity in turbulence
,” Phys. Rev. E
65
(4
), 046307
(2002
).29.
C. M.
Casciola
, R.
Benzi
, P.
Gualtieri
, B.
Jacob
, and R.
Piva
, “Double scaling and intermittency in shear dominated flows
,” Phys. Rev. E
65
(1
), 015301
(2001
).30.
C. M.
Casciola
, P.
Gualtieri
, B.
Jacob
, and R.
Piva
, “Scaling properties in the production range of shear dominated flows
,” Phys. Rev. Lett.
95
(2
), 024503
(2005
).31.
X. Q.
Jiang
, H.
Gong
, J. K.
Liu
, M. D.
Zhou
, and Z. S.
She
, “Hierarchical structures in a turbulent free shear flow
,” J. Fluid Mech.
569
, 259
–286
(2006
).32.
G.
Ruiz-Chavarria
, S.
Ciliberto
, C.
Baudet
, and E.
Leveque
, “Scaling properties of the streamwise component of velocity in a turbulent boundary layer
,” Physica D
141
(3–4
), 183
–198
(2000
).33.
R.
Benzi
, G.
Amati
, C. M.
Casciola
, F.
Toschi
, and R.
Piva
, “Intermittency and scaling laws for wall bounded turbulence
,” Phys. Fluids
11
, 1284
(1999
).34.
M.
Onorato
, R.
Camussi
, and G.
Iuso
, “Small scale intermittency and bursting in a turbulent channel flow
,” Phys. Rev. E
61
(2
), 1447
–1454
(2000
).35.
C. M.
Casciola
, P.
Gualtieri
, R.
Benzi
, and R.
Piva
, “Scale-by-scale budget and similarity laws for shear turbulence
,” J. Fluid Mech.
476
, 105
–114
(2003
).36.
A. N.
Kolmogorov
, “A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number
,” J. Fluid Mech.
13
(1
), 82
–85
(1962
).37.
F.
Toschi
, E.
Leveque
, and G.
Ruiz-Chavarria
, “Shear effects in nonhomogeneous turbulence
,” Phys. Rev. Lett.
85
(7
), 1436
–1439
(2000
).38.
F.
Toschi
, G.
Amati
, S.
Succi
, R.
Benzi
, and R.
Piva
, “Intermittency and structure functions in channel flow turbulence
,” Phys. Rev. Lett.
82
(25
), 5044
–5047
(1999
).39.
E.
Gaudin
, B.
Protas
, S.
Goujon-Durand
, J.
Wojciechowski
, and J. E.
Wesfreid
, “Spatial properties of velocity structure functions in turbulent wake flows
,” Phys. Rev. E
57
(1
), 9
–12
(1998
).40.
R.
Benzi
, M V
Struglia
, and R.
Tripiccione
, “Extended self-similarity in numerical simulations of three-dimensional anisotropic turbulence
,” Phys. Rev. E
53
(6
), 5565
–5568
(1996
).41.
O.
Desjardins
, G.
Blanquart
, G.
Balarac
, and H.
Pitsch
, “High order conservative finite difference scheme for variable density low Mach number turbulent flows
,” J. Comput. Phys.
227
(15
), 7125
–7159
(2008
).42.
J.
Kim
and P.
Moin
, “Application of a fractional-step method to incompressible Navier-Stokes equations
,” J. Comput. Phys.
59
(2
), 308
–323
(1985
).43.
R.
Falgout
, J.
Jones
, and U.
Yang
, “The design and implementation of hypre, a library of parallel high performance preconditioners
,” in Numerical Solution of Partial Differential Equations on Parallel Computers
(Springer
, 2006
), pp. 267
–294
.44.
M. A.
Ol'shanskii
and V. M.
Staroverov
, “On simulation of outflow boundary conditions in finite difference calculations for incompressible fluid
,” Int. J. Numer. Methods Fluid
33
(4
), 499
–534
(2000
).45.
X.
Wu
and P.
Moin
, “Direct numerical simulation of turbulence in a nominally zero-pressure-gradient flat-plate boundary layer
,” J. Fluid Mech.
630
(1
), 5
–41
(2009
).46.
D.
Wallace
and L. G.
Redekopp
, “Linear instability characteristics of wake-shear layers
,” Phys. Fluids
4
, 189
(1992
).47.
48.
T. T.
Clark
and Y.
Zhou
, “Self-similarity of two flows induced by instabilities
,” Phys. Rev. E
68
(6
), 066305
(2003
).49.
F. K.
Browand
and P. D.
Weidman
, “Large scales in the developing mixing layer
,” J. Fluid Mech.
76
(1
), 127
–144
(1976
).50.
51.
A. N.
Kolmogorov
, “On degeneration of isotropic turbulence in an incompressible viscous liquid
,” C. R. Acad. Sci. URSS
31
, 538
(1941
).52.
F.
Anselmet
, Y.
Gagne
, E. J.
Hopfinger
, and R. A.
Antonia
, “High-order velocity structure functions in turbulent shear flows
,” J. Fluid Mech.
140
, 63
–89
(1984
).53.
A.
Arneodo
, C.
Baudet
, F.
Belin
, R.
Benzi
, B.
Castaing
, B.
Chabaud
, R.
Chavarria
, S.
Ciliberto
, R.
Camussi
, F.
Chilla
, et al, “Structure functions in turbulence, in various flow configurations, at Reynolds number between 30 and 5000, using extended self-similarity
,” Europhys. Lett.
34
, 411
(1996
).54.
R.
Benzi
, S.
Ciliberto
, C.
Baudet
, and G. R.
Chavarria
, “On the scaling of three-dimensional homogeneous and isotropic turbulence
,” Physica D
80
(4
), 385
–398
(1995
).55.
T.
Watanabe
and T.
Gotoh
, “Statistics of a passive scalar in homogeneous turbulence
,” New J. Phys.
6
, 40
(2004
).56.
V. S.
Lâvov
, A.
Pomyalov
, and I.
Procaccia
, “Temporal surrogates of spatial turbulent statistics: The Taylor hypothesis revisited
,” Phys. Rev. E
60
(4
), 4175
(1999
).57.
R. A.
Antonia
and P.
Burattini
, “Approach to the 4/5 law in homogeneous isotropic turbulence
,” J. Fluid Mech.
550
, 175
–184
(2006
).58.
R. A.
Antonia
, R. J.
Smalley
, T.
Zhou
, F.
Anselmet
, and L.
Danaila
, “Similarity of energy structure functions in decaying homogeneous isotropic turbulence
,” J. Fluid Mech.
487
, 245
–269
(2003
).59.
S.
Kurien
and K. R.
Sreenivasan
, “Anisotropic scaling contributions to high-order structure functions in high-Reynolds-number turbulence
,” Phys. Rev. E
62
(2
), 2206
–2212
(2000
).60.
G. K.
Batchelor
, “Pressure fluctuations in isotropic turbulence
,” in MPCPC
(Cambridge University Press
, 1951
), Vol. 47
, pp. 359
–374
.61.
J.
Meyers
and C.
Meneveau
, “A functional form for the energy spectrum parametrizing bottleneck and intermittency effects
,” Phys. Fluids
20
, 065109
(2008
).62.
R.
Benzi
, S.
Ciliberto
, R.
Tripiccione
, C.
Baudet
, F.
Massaioli
, and S.
Succi
, “Extended self-similarity in turbulent flows
,” Phys. Rev. E
48
(1
), 29
–32
(1993
).63.
D.
Segel
, V.
L’vov
, and I.
Procaccia
, “Extended self-similarity in turbulent systems: an analytically soluble example
,” Phys. Rev. Lett.
76
(11
), 1828
–1831
(1996
).64.
S.
Grossmann
, D.
Lohse
, and A.
Reeh
, “Application of extended self-similarity in turbulence
,” Phys. Rev. E
56
(5
), 5473
(1997
).© 2012 American Institute of Physics.
2012
American Institute of Physics
You do not currently have access to this content.
