We study the physics of the turbulent/non-turbulent interface (TNTI) of an isolated turbulent region in dilute polymer solutions and Newtonian fluids. We designed an experimental setup of a turbulent patch growing in water/dilute polymer solutions, without mean shear and far from the walls. The observations from the experiments are complemented and expanded by simulations performed using a localised homogeneous forcing to generate the turbulent front and the Finitely Extensible Elastic model with the Peterlin closure model for the polymer stress. The comparison, which shows that when Newtonian and viscoelastic TNTIs are fed by the same energy they behave in similar manner both in the experiments and in the simulations, permits to extend the applicability, on a qualitative basis, of single relaxation time polymer models also to turbulent/non-turbulent interfaces. From the detailed analysis offered by the numerical results, the alterations in the dynamics between strain and vorticity help understanding the mechanics of the polymer action on the TNTI without mean shear. The reduced vorticity stretching and increased vorticity compression terms are found to be due to the modified degrees of alignment between vorticity, polymer conformation tensor, and rate-of-strain tensor eigenvectors observed especially near the interface. These alignments at the smallest scales of the non-Newtonian turbulent flow lead to a reduced production of enstrophy and consequently to a reduced entrainment, which in this problem are seen as reduced advancement of a turbulent region.

1.
C. B.
da Silva
,
J. C. R.
Hunt
,
I.
Eames
, and
J.
Westerweel
, “
Interfacial layers between regions of different turbulence intensity
,”
Annu. Rev. Fluid Mech.
46
,
567
590
(
2014
).
2.
S.
Corrsin
and
A. L.
Kistler
, “
The free-stream boundaries of turbulent flows
,” NACA TN-3133, TR-1244,
1955
.
3.
M.
Wolf
,
M.
Holzner
,
B.
Lüthi
,
D.
Krug
,
W.
Kinzelbach
, and
A.
Tsinober
, “
Effects of mean shear on the local turbulent entrainment process
,”
J. Fluid Mech.
731
,
95
116
(
2013
).
4.
E.
De Angelis
,
C. M.
Casciola
,
R.
Benzi
, and
R.
Piva
, “
Homogeneous isotropic turbulence in dilute polymers
,”
J. Fluid Mech.
531
,
1
10
(
2005
).
5.
A. M.
Crawford
,
N.
Mordant
,
H.
Xu
, and
E.
Bodenschatz
, “
Fluid acceleration in the bulk of turbulent dilute polymer solutions
,”
New J. Phys.
10
,
123015
(
2008
).
6.
J.
Jovanovic
,
M.
Pashtrapanska
,
B.
Frohnapfel
,
F.
Durst
,
J.
Koskinen
, and
K.
Koskinen
, “
On the mechanism responsible for turbulent drag reduction by dilute addition of high polymers: Theory, experiments, simulations, and predictions
,”
ASME J. Fluids Eng.
128
,
118
130
(
2005
).
7.
Y.
Dubief
,
C. M.
White
,
V. E.
Terrapon
,
E. S. G.
Shaqfeh
,
P.
Moin
, and
S. K.
Lele
, “
On the coherent drag-reducing and turbulence-enhancing behaviour of polymers in wall flows
,”
J. Fluid Mech.
514
,
271
280
(
2004
).
8.
A.
Liberzon
,
M.
Guala
,
B.
Lüthi
,
W.
Kinzelbach
, and
A.
Tsinober
, “
Turbulence in dilute polymer solutions
,”
Phys. Fluids
17
,
031707
(
2005
).
9.
J.
Davoudi
and
J.
Schumacher
, “
Stretching of polymers around the Kolmogorov scale in a turbulent shear flow
,”
Phys. Fluids
18
,
025103
(
2006
).
10.
D.
Vincenzi
,
P.
Perlekar
,
L.
Biferale
, and
F.
Toschi
, “
Impact of the Peterlin approximation on polymer dynamics in turbulent flows
,”
Phys. Rev. E
92
,
053004
(
2015
).
11.
P. C.
Valente
,
C. B.
da Silva
, and
F. T.
Pinho
, “
The effect of viscoelasticity on the turbulent kinetic energy cascade
,”
J. Fluid Mech.
760
,
39
62
(
2014
).
12.
F.
Bagheri
,
D.
Mitra
,
P.
Perlekar
, and
L.
Brandt
, “
Statistics of polymer extensions in turbulent channel flow
,”
Phys. Rev. E
86
,
056314
(
2012
).
13.
P.
Perlekar
,
D.
Mitra
, and
R.
Pandit
, “
Direct numerical simulations of statistically steady, homogeneous, isotropic fluid turbulence with polymer additives
,”
Phys. Rev. E
82
,
066313
(
2010
).
14.
A.
Liberzon
,
M.
Holzner
,
B.
Lüthi
,
M.
Guala
, and
W.
Kinzelbach
, “
On turbulent entrainment and dissipation in dilute polymer solutions
,”
Phys. Fluids
21
,
035107
(
2009
).
15.
M. D.
Graham
, “
Fluid dynamics of dissolved polymer molecules in confined geometries
,”
Annu. Rev. Fluid Mech.
43
,
273
298
(
2011
).
16.
I.
Ghosh
,
G. H.
McKinley
,
R. A.
Brown
, and
R. C.
Armstrong
, “
Deficiencies of FENE dumbbell models in describing the rapid stretching of dilute polymer solutions
,”
J. Rheol.
45
,
721
758
(
2001
).
17.
C. M.
Casciola
and
E.
De Angelis
, “
Energy transfer in turbulent polymer solutions
,”
J. Fluid Mech.
581
,
419
(
2007
).
18.
G.
Khujadze
and
M.
Oberlack
, “
DNS of vibrating grid turbulence
,” in
Sixth International Symposium on Turbulence and Shear Flow Phenomena, Seoul, Korea, 22-24 June 2009
(
Springer
,
2009
), pp.
215
219
.
19.
A. A.
Draad
,
G.
Kuiken
, and
F.
Nieuwstadt
, “
Laminar–turbulent transition in pipe flow for Newtonian and non-Newtonian fluids
,”
J. Fluid Mech.
377
,
267
312
(
1998
).
20.
R. G.
Owens
and
T. N.
Phillips
,
Computational Rheology
(
World Scientific
,
2002
).
21.
M.
Baevsky
and
A.
Liberzon
, Temporal evolution of vorticity component ωz in a cross-section of a axisymmetric turbulent patch measured with particle image velocimetry, https://goo.gl/QY6DJ9.
22.
V.
Dallas
,
J. C.
Vassilicos
, and
G. F.
Hewitt
, “
Strong polymer-turbulence interactions in viscoelastic turbulent channel flow
,”
Phys. Rev. E
82
,
066303
(
2010
).
23.
M.
Zhang
,
I.
Lashgari
,
T. A.
Zaki
, and
L.
Brandt
, “
Linear stability analysis of channel flow of viscoelastic Oldroyd-B and FENE-P fluids
,”
J. Fluid Mech.
737
,
249
279
(
2013
).
24.
Y.
Hasegawa
,
M.
Quadrio
, and
B.
Frohnapfel
, “
Numerical simulation of turbulent duct flows with constant power input
,”
J. Fluid Mech.
750
,
191
209
(
2014
).
25.
Y.
Dubief
and
S.
Lele
, “
Direct numerical simulation of polymer flow
,”
Center Turbul. Res.: Annu. Res. Briefs
2001
,
197
208
.
26.
T.
Min
,
J.
Yul Yoo
,
H.
Choi
, and
D. D.
Joseph
, “
Drag reduction by polymer additives in a turbulent channel flow
,”
J. Fluid Mech.
486
,
213
238
(
2003
).
27.
A.
Tsinober
,
An Informal Conceptual Introduction to Turbulence
(
Springer
,
2009
), Vol. 483.
28.
B.
Lüthi
,
A.
Tsinober
, and
W.
Kinzelbach
, “
Lagrangian measurement of vorticity dynamics in turbulent flow
,”
J. Fluid Mech.
528
,
87
118
(
2005
).
29.
T.
Watanabe
and
T.
Gotoh
, “
Coil-stretch transition in an ensemble of polymers in isotropic turbulence
,”
Phys. Rev. E
81
,
066301
(
2010
).
30.
C. B.
da Silva
and
J. C.
Pereira
, “
Invariants of the velocity-gradient, rate-of-strain, and rate-of-rotation tensors across the turbulent/nonturbulent interface in jets
,”
Phys. Fluids
20
,
055101
(
2008
).
31.
M.
Gampert
,
K.
Kleinheinz
,
N.
Peters
, and
H.
Pitsch
, “
Experimental and numerical study of the scalar turbulent/non-turbulent interface layer in a jet flow
,”
Flow, Turbul. Combust.
92
,
429
449
(
2014
).
32.
A.
Tsinober
, “
Turbulent drag reduction versus structure of turbulence
,” in
Structure of Turbuelnce and Drag Reduction: IUTAM Symposium
, edited by
A.
Gyr
(
Springer
,
1990
), pp.
313
334
.
33.
G.
Elsinga
and
I.
Marusic
, “
Universal aspects of small-scale motions in turbulence
,”
J. Fluid Mech.
662
,
514
539
(
2010
).
You do not currently have access to this content.