Di Savino, Silvio

Ducasse, Lauris

Iovieno, Michele

Tordella, Daniela

DI SAVINO, SILVIO

IOVIENO, MICHELE

DUCASSE, LAURIS

TORDELLA, Daniela

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

04 August 2020POLITECNICO DI TORINORepository ISTITUZIONALEDimensionality influence on the passive scalar transport observed through numerical experiments on turbulenceshearless mixings. / Di Savino S.; Iovieno M.; Ducasse L.; Tordella D.. - STAMPA. - (2011), pp. 15-16. ((Interventopresentato al convegno Third International Conference ‘Turbulent Mixing and Beyond' tenutosi a Trieste nel 21-28agosto 2011.OriginalDimensionality influence on the passive scalar transport observed through numerical experiments onturbulence shearless mixings.Publisher:PublishedDOI:Terms of use:openAccessPublisher copyright(Article begins on next page)This article is made available under terms and conditions as specified in the  corresponding bibliographic description inthe repositoryAvailability:This version is available at: 11583/2446975 since:The Abdus Salam International Centre for Theoretical PhysicsDimensionality influence on the passive scalar transport observedthrough experiments on the turbulunce shearless mixingS.Di Savino, M. Iovieno, L.Ducasse, D.Tordella,Dipartimento di Ingegneria Aeronautica e Spaziale, Politecnico di Torino,Corso Duca degli Abruzzi 24, 10129 Torino, ItalyThe transport of a passive substance by a turbulent flow is important in many naturaland engineering contexts, e.g. turbulent mixing, combustion, pollution dispersal. Theevolution of the scalar concentration is not only a footprint of the organized velocitystructures, but the scalar statistics are in part decoupled from those in the velocityfield, showing an intrinsic intermittency, with large fluctuations on small scales whichdominate high moments [1, 2].We would like to present new results concerning the passive scalar turbulent trans-port in two and three dimensions in a simple, but not trivial, inhomogeneous flow, seefig.1. The dimensionality of the field induces differences in the transport characteristicvelocity, length scales, and temporal scaling, although qualitative similarity is retainedin the general trend and in the shape of the the scalar flux and moment distributions.We go one step beyond the homogeneous isotropic turbulence and consider the sim-plest inhomogeneous and shearfree turbulent Navier-Stokes motion: the system whereone energetic turbulent isotropic field is left to convectively diffuse into a low energyone. In this system the region where the two turbulences interact is associated to a highintermittent thin layer - where the energy flux is maximum - that propagates into thelow energy region [4, 5]. The very presence of the interaction zone offers the way tocarry out independent numerical measurements of the (long-term temporal) time de-pendent turbulent diffusivity. By means of Eulerian one-point statistics, we observedthe turbulent energy interaction width and the passive scalar variance width. Spec-tra, probability density function, flux, variance, velocity derivative statistics have beenobtained, a few of them are presented in this abstract.In synthesis, we have seen that the diffusion in 2D is faster then in 3D. In particularthe time scaling of the growth of the interaction width is superdiffusive in 2D (∆ ∼t0.68), while it is very slightly subdiffusive in 3D (∆ ∼ t0.46), see fig.2. The timeevolution of these interaction widths are equal to that observed for self-diffusion of thevelocity field with the same dimensionality (that is, in the absence of the passive scalar,the turbulent diffusion associated to the mean flow of turbulent energy induced by thepresence of a turbulent energy gradient, see again fig.2 and [4, 5, 8]). This seems toindicate that the passive scalar field follows the fluctuation velocity field. However,if we remove the turbulent energy gradient, the interaction widths remain unchanged,either in the 2D or 3D case. And this send back, on the one hand, to the decouplingof the velocity-scalar fields, and, on the other, to a possible universal growth of theturbulent diffusion layer across an interface. The presence of the turbulent energygradient is instead felt on the distribution across the layer of local statistical quantities,as the skewness and kurtosis, see fig.3 (left and central parts, respectively). Thesedepart from symmetry/antisymmetry with respect to the interface, respectively, whenthe energy gradient is absent. It should be noted that the passive scalar fields, differentlyfrom the velocity fields, present two intermittency layers released by the interface inopposite directions. In fig. 3, passive scalar and velocity spectra are shown on the right.In two dimensions, the passive scalar decay in the inertial range is less than that of thevelocity field, while in three dimensions, the difference is very mild. The intermittencyon the scalar fluctuations is not only limited to large scales but spreads also to the small12Dmixing3DmixingFigure 1: Visualization of the scalar field. The high turbulent energy velocity field ison the left of each image. The three different instants correspond from left to rightto t/τ = 1, 5, 10, respectively. The 3D simulation has an initial Rλ equal to 150 inthe high energy isotropic region and 60 in the low energy region. [Full time history:2D-movie, 3D-movie ]scale fluctuations, as can be seen in the derivative skewness and kurtosis in fig.4, wheretwo distinct regions of high kurtosis can be observed at both edges of the mixing layer.The results are obtained from direct numerical simulations of the diffusion of thepassive scalar across the interface which separates the two isotropic decaying turbulentfields with different kinetic energy. The size of the computational domain is 4pi×(2pi)2(discretized with 1200×6002 grid points) in the 3D simulations and (2pi)2 (discretizedwith 10242 grid points) in the 2D simulations [6, 7]. For details on the numericaltechnique, see [4, 5].2PSfrag replacementsxE1E2High EnergyLow Energy2Mixing LayersL=2 L02Dmixing10-110010110210-1 100 101 102t/τ∆/lkinetic energyscalar with E1/E2 = 1scalar with E1/E2 = 6.60.68-0.08-0.06-0.04-0.02 0 0.02-3 -2 -1  0  1  2  3(x − xc)/∆θu′ θ′t/τ1510203Dmixing10010-1 100 101t/τ∆/lkinetic energyscalar with E1/E2 = 1scalar with E1/E2 = 6.6kinetic energy, lab.exp.scalar, lab.exp.0.46-0.08-0.06-0.04-0.02 0 0.02-3 -2 -1  0  1  2  3(x − xc)/∆θu′ θ′12.557.51012.5t/τFigure 2: Left: Scheme of the numerical domain. Center and Right: Interaction layerthickness, normalized with the initial integral scale `, and scalar flow u′θ′. The scalarlayer thickness ∆θ is defined as the distance between the points where θ is equal to0.25 and 0.75. The energy layer thickness is defined as the distance between the pointswhere the normalized turbulent kinetic energy (E−E2)/(E1−E2) is equal to 0.25 and0.75 as in [5]. Experimental data are from the wind tunnel experiments by Veeravalliand Warhaft [3] with E1/E2 = 7.2Dmixing-8-6-4-2 0 2 4 6 8-3 -2 -1  0  1  2  3(x − xc)/∆θS θt/τ151020 0 10 20 30 40 50 60 70 80-3 -2 -1  0  1  2  3(x − xc)/∆θKθt/τ15102010-410-310-210-1100101100 101 102 103kE θ(k)k1.4,E u(k)k30.45151020t/τEu k3, t/τ = 103Dmixing-8-6-4-2 0 2 4 6 8-3 -2 -1  0  1  2  3(x − xc)/∆θS θ12.557.51012.5t/τ 0 10 20 30 40 50 60 70 80 90-3 -2 -1  0  1  2  3(x − xc)/∆θKθ12.557.51012.5t/τ10-510-410-310-210-1100100 101 102 103kE θ(k)k5/3,E u(k)k5/30.10.51.12.65.57.5t/τEu k5/3, t/τ = 5.5Figure 3: Scalar skewness and kurtosis distributions across the interaction layer(the full lines correspond to the case where the turbulent energy gradient is present,E1/E2 = 6.6, and the dashed lines to the case where E1/E2 = 1) and compensatedone-dimensional scalar (full lines) and velocity (black dotted lines) spectra in the cen-tre of the mixing layer. The spectra refer to simulations where the turbulent energygradient is present.32Dmixing-1 0 1 2 3 4 5 6-3 -2 -1  0  1  2  3(x − xc)/∆θS ∂θ′/∂xt/τ151020 0 5 10 15 20 25 30 35 40 45 50-3 -2 -1  0  1  2  3(x − xc)/∆θK∂θ′/∂xt/τ1510203Dmixing-1 0 1 2 3 4 5 6-3 -2 -1  0  1  2  3(x − xc)/∆θS ∂θ′/∂x12.557.51012.5t/τ 0 10 20 30 40 50 60 70 80-3 -2 -1  0  1  2  3(x − xc)/∆θK∂θ′/∂x12.557.51012.5t/τFigure 4: Scalar derivative in the inhomogenoeus direction statistics across the mixinglayer.4References[1] Shraiman, B.I., Siggia, E.D.: Scalar turbulence. Nature 405(6787): 639–646, 2000.[2] Warhaft, Z.: Passive scalar in turbulent flows. Ann. Rev. Fluid Mech. 32: 203–240,2000.[3] Veeravalli, S., Warhaft Z.: Thermal dispersion from a line source in the shearlessturbulence mixing layer. J. Fluid Mech. 216:35–70, 1990.[4] Tordella, D., Iovieno, M.: Numerical experiments on the intermediate asymptotisof the shear-free turbulent transport and diffusion. J. Fluid Mech. 549: 429–441,2006.[5] Tordella, D., Iovieno, M., Bailey P.R.: Sufficient condition for Gaussian departurein turbulence. Phys. Rev. E 77: 016309/1-11, 2008.[6] Tordella, D., Iovieno M., Ducasse L.: Diffusion of a passive scalar across a turbu-lent energy step DSFD-10, Roma, July 2010.[7] Tordella, D., Iovieno M., Ducasse L.: Passive scalar diffusion through a turbulentenergy gradient. EFMC-10, Bad Reichenhall, September 2010.[8] Tordella, D., Iovieno M.: Small scale anisotropy in the turbulent shearless mixing.Under revision for Phys. Rev. Lett., 2011.5

English

Dimensionality influence on the passive scalar transport observed through numerical experiments on turbulence shearless mixings.

PORTO Publications Open Repository TOrino

Politecnico di Torino
Porto Institutional Repository
[Proceeding] Dimensionality influence on the passive scalar transport
observed through numerical experiments on turbulence shearless mixings
Original Citation:
Di Savino S., Iovieno M., Ducasse L., Tordella D. (2011). Dimensionality influence on the passive
scalar transport observed through numerical experiments on turbulence shearless mixings. In:
Third International Conference ‘Turbulent Mixing and Beyond’, Trieste, 21-28 agosto 2011. pp. 15-
16
Availability:
This version is available at : http://porto.polito.it/2446975/ since: October 2011
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(Article begins on next page)
Dimensionality influence on the passive scalar transport observed
through experiments on the turbulunce shearless mixing
S.Di Savino, M. Iovieno, L.Ducasse, D.Tordella,
Dipartimento di Ingegneria Aeronautica e Spaziale, Politecnico di Torino,
Corso Duca degli Abruzzi 24, 10129 Torino, Italy
The transport of a passive substance by a turbulent flow is important in many natural
and engineering contexts, e.g. turbulent mixing, combustion, pollution dispersal. The
evolution of the scalar concentration is not only a footprint of the organized velocity
structures, but the scalar statistics are in part decoupled from those in the velocity
field, showing an intrinsic intermittency, with large fluctuations on small scales which
dominate high moments [1, 2].
We would like to present new results concerning the passive scalar turbulent trans-
port in two and three dimensions in a simple, but not trivial, inhomogeneous flow, see
fig.1. The dimensionality of the field induces differences in the transport characteristic
velocity, length scales, and temporal scaling, although qualitative similarity is retained
in the general trend and in the shape of the the scalar flux and moment distributions.
We go one step beyond the homogeneous isotropic turbulence and consider the sim-
plest inhomogeneous and shearfree turbulent Navier-Stokes motion: the system where
one energetic turbulent isotropic field is left to convectively diffuse into a low energy
one. In this system the region where the two turbulences interact is associated to a high
intermittent thin layer - where the energy flux is maximum - that propagates into the
low energy region [4, 5]. The very presence of the interaction zone offers the way to
carry out independent numerical measurements of the (long-term temporal) time de-
pendent turbulent diffusivity. By means of Eulerian one-point statistics, we observed
the turbulent energy interaction width and the passive scalar variance width. Spec-
tra, probability density function, flux, variance, velocity derivative statistics have been
obtained, a few of them are presented in this abstract.
In synthesis, we have seen that the diffusion in 2D is faster then in 3D. In particular
the time scaling of the growth of the interaction width is superdiffusive in 2D (∆ ∼
t0.68), while it is very slightly subdiffusive in 3D (∆ ∼ t0.46), see fig.2. The time
evolution of these interaction widths are equal to that observed for self-diffusion of the
velocity field with the same dimensionality (that is, in the absence of the passive scalar,
the turbulent diffusion associated to the mean flow of turbulent energy induced by the
presence of a turbulent energy gradient, see again fig.2 and [4, 5, 8]). This seems to
indicate that the passive scalar field follows the fluctuation velocity field. However,
if we remove the turbulent energy gradient, the interaction widths remain unchanged,
either in the 2D or 3D case. And this send back, on the one hand, to the decoupling
of the velocity-scalar fields, and, on the other, to a possible universal growth of the
turbulent diffusion layer across an interface. The presence of the turbulent energy
gradient is instead felt on the distribution across the layer of local statistical quantities,
as the skewness and kurtosis, see fig.3 (left and central parts, respectively). These
depart from symmetry/antisymmetry with respect to the interface, respectively, when
the energy gradient is absent. It should be noted that the passive scalar fields, differently
from the velocity fields, present two intermittency layers released by the interface in
opposite directions. In fig. 3, passive scalar and velocity spectra are shown on the right.
In two dimensions, the passive scalar decay in the inertial range is less than that of the
velocity field, while in three dimensions, the difference is very mild. The intermittency
on the scalar fluctuations is not only limited to large scales but spreads also to the small
1
2D
m
ix
in
g
3D
m
ix
in
g
Figure 1: Visualization of the scalar field. The high turbulent energy velocity field is
on the left of each image. The three different instants correspond from left to right
to t/τ = 1, 5, 10, respectively. The 3D simulation has an initial Rλ equal to 150 in
the high energy isotropic region and 60 in the low energy region. [Full time history:
2D-movie, 3D-movie ]
scale fluctuations, as can be seen in the derivative skewness and kurtosis in fig.4, where
two distinct regions of high kurtosis can be observed at both edges of the mixing layer.
The results are obtained from direct numerical simulations of the diffusion of the
passive scalar across the interface which separates the two isotropic decaying turbulent
fields with different kinetic energy. The size of the computational domain is 4pi×(2pi)2
(discretized with 1200×6002 grid points) in the 3D simulations and (2pi)2 (discretized
with 10242 grid points) in the 2D simulations [6, 7]. For details on the numerical
technique, see [4, 5].
2
PSfrag replacements
x
E
1
E
2
High Energy
Low Energy
2
Mixing Layers
L=2 L0
2D
m
ix
in
g
10-1
100
101
102
10-1 100 101 102
t/τ
∆
/l
kinetic energy
scalar with E1/E2 = 1
scalar with E1/E2 = 6.6
0.68
-0.08
-0.06
-0.04
-0.02
 0
 0.02
-3 -2 -1  0  1  2  3
(x − xc)/∆θ
u
′ θ
′
t/τ
1
5
10
20
3D
m
ix
in
g
100
10-1 100 101
t/τ
∆
/l
kinetic energy
scalar with E1/E2 = 1
scalar with E1/E2 = 6.6
kinetic energy, lab.exp.
scalar, lab.exp.
0.46
-0.08
-0.06
-0.04
-0.02
 0
 0.02
-3 -2 -1  0  1  2  3
(x − xc)/∆θ
u
′ θ
′
1
2.5
5
7.5
10
12.5
t/τ
Figure 2: Left: Scheme of the numerical domain. Center and Right: Interaction layer
thickness, normalized with the initial integral scale `, and scalar flow u′θ′. The scalar
layer thickness ∆θ is defined as the distance between the points where θ is equal to
0.25 and 0.75. The energy layer thickness is defined as the distance between the points
where the normalized turbulent kinetic energy (E−E2)/(E1−E2) is equal to 0.25 and
0.75 as in [5]. Experimental data are from the wind tunnel experiments by Veeravalli
and Warhaft [3] with E1/E2 = 7.
2D
m
ix
in
g
-8
-6
-4
-2
 0
 2
 4
 6
 8
-3 -2 -1  0  1  2  3
(x − xc)/∆θ
S θ
t/τ
1
5
10
20
 0
 10
 20
 30
 40
 50
 60
 70
 80
-3 -2 -1  0  1  2  3
(x − xc)/∆θ
K
θ
t/τ
1
5
10
20
10-4
10-3
10-2
10-1
100
101
100 101 102 103
k
E θ
(k)
k1
.4
,
E u
(k)
k3
0.45
1
5
10
20
t/τ
Eu k3, t/τ = 10
3D
m
ix
in
g
-8
-6
-4
-2
 0
 2
 4
 6
 8
-3 -2 -1  0  1  2  3
(x − xc)/∆θ
S θ
1
2.5
5
7.5
10
12.5
t/τ
 0
 10
 20
 30
 40
 50
 60
 70
 80
 90
-3 -2 -1  0  1  2  3
(x − xc)/∆θ
K
θ
1
2.5
5
7.5
10
12.5
t/τ
10-5
10-4
10-3
10-2
10-1
100
100 101 102 103
k
E θ
(k)
k5
/3
,
E u
(k)
k5
/3
0.1
0.5
1.1
2.6
5.5
7.5
t/τ
Eu k5/3, t/τ = 5.5
Figure 3: Scalar skewness and kurtosis distributions across the interaction layer
(the full lines correspond to the case where the turbulent energy gradient is present,
E1/E2 = 6.6, and the dashed lines to the case where E1/E2 = 1) and compensated
one-dimensional scalar (full lines) and velocity (black dotted lines) spectra in the cen-
tre of the mixing layer. The spectra refer to simulations where the turbulent energy
gradient is present.
3
2D
m
ix
in
g
-1
 0
 1
 2
 3
 4
 5
 6
-3 -2 -1  0  1  2  3
(x − xc)/∆θ
S ∂
θ′
/∂
x
t/τ
1
5
10
20
 0
 5
 10
 15
 20
 25
 30
 35
 40
 45
 50
-3 -2 -1  0  1  2  3
(x − xc)/∆θ
K
∂
θ′
/∂
x
t/τ
1
5
10
20
3D
m
ix
in
g
-1
 0
 1
 2
 3
 4
 5
 6
-3 -2 -1  0  1  2  3
(x − xc)/∆θ
S ∂
θ′
/∂
x
1
2.5
5
7.5
10
12.5
t/τ
 0
 10
 20
 30
 40
 50
 60
 70
 80
-3 -2 -1  0  1  2  3
(x − xc)/∆θ
K
∂
θ′
/∂
x
1
2.5
5
7.5
10
12.5
t/τ
Figure 4: Scalar derivative in the inhomogenoeus direction statistics across the mixing
layer.
4
References
[1] Shraiman, B.I., Siggia, E.D.: Scalar turbulence. Nature 405(6787): 639–646, 2000.
[2] Warhaft, Z.: Passive scalar in turbulent flows. Ann. Rev. Fluid Mech. 32: 203–240,
2000.
[3] Veeravalli, S., Warhaft Z.: Thermal dispersion from a line source in the shearless
turbulence mixing layer. J. Fluid Mech. 216:35–70, 1990.
[4] Tordella, D., Iovieno, M.: Numerical experiments on the intermediate asymptotis
of the shear-free turbulent transport and diffusion. J. Fluid Mech. 549: 429–441,
2006.
[5] Tordella, D., Iovieno, M., Bailey P.R.: Sufficient condition for Gaussian departure
in turbulence. Phys. Rev. E 77: 016309/1-11, 2008.
[6] Tordella, D., Iovieno M., Ducasse L.: Diffusion of a passive scalar across a turbu-
lent energy step DSFD-10, Roma, July 2010.
[7] Tordella, D., Iovieno M., Ducasse L.: Passive scalar diffusion through a turbulent
energy gradient. EFMC-10, Bad Reichenhall, September 2010.
[8] Tordella, D., Iovieno M.: Small scale anisotropy in the turbulent shearless mixing.
Under revision for Phys. Rev. Lett., 2011.
5


Dimensionality influence on the passive scalar transport observed through numerical experiments on turbulence shearless mixings

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Dimensionality influence on the passive scalar transport observed through numerical experiments on turbulence shearless mixings

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