Direct numerical simulations of turbulent Taylor-Couette flow are performed up to inner cylinder Reynolds numbers of Rei = 105 for a radius ratio of η = ri/ro = 0.714 between the inner and outer cylinders. With increasing Rei, the flow undergoes transitions between three different regimes: (i) a flow dominated by large coherent structures, (ii) an intermediate transitional regime, and (iii) a flow with developed turbulence. In the first regime the large-scale rolls completely drive the meridional flow, while in the second one the coherent structures recover only on average. The presence of a mean flow allows for the coexistence of laminar and turbulent boundary layer dynamics. In the third regime, the mean flow effects fade away and the flow becomes dominated by plumes. The effect of the local driving on the azimuthal and angular velocity profiles is quantified, in particular, we show when and where those profiles develop.

1.
F. H.
Busse
, “
Viewpoint: The twins of turbulence research
,”
Physics
5
,
4
(
2012
).
2.
B.
Eckhardt
,
T.
Schneider
,
B.
Hof
, and
J.
Westerweel
, “
Turbulence transition in pipe flow
,”
Annu. Rev. Fluid Mech.
39
,
447
468
(
2007
).
3.
R. H.
Kraichnan
, “
Turbulent thermal convection at arbritrary Prandtl number
,”
Phys. Fluids
5
,
1374
1389
(
1962
).
4.
P. E.
Roche
,
G.
Gauthier
,
R.
Kaiser
, and
J.
Salort
, “
On the triggering of the ultimate regime of convection
,”
New J. Phys.
12
,
085014
(
2010
).
5.
X.
He
,
D.
Funfschilling
,
H.
Nobach
,
E.
Bodenschatz
, and
G.
Ahlers
, “
Transition to the ultimate state of turbulent Rayleigh-Bénard convection
,”
Phys. Rev. Lett.
108
,
024502
(
2012
).
6.
G. S.
Lewis
and
H. L.
Swinney
, “
Velocity structure functions, scaling, and transitions in high-Reynolds-number Couette-Taylor flow
,”
Phys. Rev. E
59
,
5457
5467
(
1999
).
7.
D. P. M.
van Gils
,
S. G.
Huisman
,
S.
Grossmann
,
C.
Sun
, and
D.
Lohse
, “
Optimal Taylor-Couette turbulence
,”
J. Fluid Mech.
706
,
118
149
(
2012
).
8.
S. G.
Huisman
,
D. P. M.
van Gils
,
S.
Grossmann
,
C.
Sun
, and
D.
Lohse
, “
Ultimate turbulent Taylor-Couette flow
,”
Phys. Rev. Lett.
108
,
024501
(
2012
).
9.
S.
Grossmann
and
D.
Lohse
, “
Multiple scaling in the ultimate regime of thermal convection
,”
Phys. Fluids
23
,
045108
(
2011
).
10.
S.
Grossmann
and
D.
Lohse
, “
Logarithmic temperature profiles in the ultimate regime of thermal convection
,”
Phys. Fluids
24
,
125103
(
2012
).
11.
L.
Prandtl
, “
Bericht über Untersuchungen zur ausgebildeten Turbulenz
,”
Z. Angew. Math. Mech.
5
,
136
139
(
1925
).
12.
T.
von Karman
, “
Mechanische Ähnlichkeit und turbulenz
,” in
Proceedings of the 3rd International Congress Applied Mechanic, Stockholm, Sweden
(
Weidmannsche
,
Berlin
,
1930
), pp.
85
105
.
13.
A. A.
Townsend
,
The Structure of Turbulent Shear Flow
(
Cambridge University Press
,
Cambridge, England
,
1976
).
14.
T.
Wei
and
W.
Willmarth
, “
Reynolds-number effects effects on the structure of a turbulent channel flow
,”
J. Fluid Mech.
204
,
57
95
(
1989
).
15.
H. T.
Kim
,
P.
Moin
, and
R.
Moser
, “
Turbulence statistics in fully developed channel flow at low Reynolds number
,”
J. Fluid Mech.
177
,
133
160
(
1971
).
16.
A. J.
Smits
,
B. J.
McKeon
, and
I.
Marusic
, “
High-reynolds number wall turbulence
,”
Ann. Rev. Fluid. Mech.
43
,
353
375
(
2011
).
17.
J.
Jimenez
, “
Cascades in wall-bounded turbulence
,”
Ann. Rev. Fluid. Mech.
44
,
27
45
(
2011
).
18.
R.
van Hout
and
J.
Katz
, “
Measurements of mean flow and turbulence characteristics in high-Reynolds number counter-rotating Taylor-Couette flow
,”
Phys. Fluids
23
,
105102
(
2011
).
19.
S. G.
Huisman
,
S.
Scharnowski
,
C.
Cierpka
,
C.
Kähler
,
D.
Lohse
, and
C.
Sun
, “
Logarithmic boundary layers in strong Taylor-Couette turbulence
,”
Phys. Rev. Lett.
110
,
264501
(
2013
).
20.
S.
Grossmann
,
D.
Lohse
, and
C.
Sun
, “
Velocity profiles in strongly turbulent Taylor-Couette flow
,” Phys. Fluids (to be published); preprint arXiv:1310.6196 (
2013
).
21.
G.
Ahlers
,
E.
Bodenschatz
,
D.
Funfschilling
,
S.
Grossmann
,
X.
He
,
D.
Lohse
,
R.
Stevens
, and
R.
Verzicco
, “
Logarithmic temperature profiles in turbulent Rayleigh-Bénard convection
,”
Phys. Rev. Lett.
109
,
114501
(
2012
).
22.
H.
Schlichting
,
Boundary Layer Theory
, 7th ed. (
McGraw Hill Book Company
,
1979
).
23.
R.
Verzicco
and
P.
Orlandi
, “
A finite-difference scheme for three-dimensional incompressible flow in cylindrical coordinates
,”
J. Comput. Phys.
123
,
402
413
(
1996
).
24.
P.
Ashwin
and
J.
King
, “
A study of particle paths in non-axisymmetric Taylor-Couette flows
,”
J. Fluid Mech.
338
,
341
362
(
1997
).
25.
J.
Antonijoan
and
F.
Marques
, “
Non-linear spirals in the Taylor-Couette problem
,”
Phys. Fluids
10
,
829
(
1998
).
26.
R.
Ostilla
,
R. J. A. M.
Stevens
,
S.
Grossmann
,
R.
Verzicco
, and
D.
Lohse
, “
Optimal Taylor-Couette flow: Direct numerical simulations
,”
J. Fluid Mech.
719
,
14
46
(
2013
).
27.
H.
Brauckmann
and
B.
Eckhardt
, “
Direct numerical simulations of local and global torque in Taylor-Couette flow up to Re = 30.000
,”
J. Fluid Mech.
718
,
398
427
(
2013
).
28.
R. C. A.
van der Veen
,
S. G.
Huisman
, and
C.
Sun
, “
Twente turbulent Taylor-Couette data
,” Personal communication (
2013
).
29.
L. D.
Landau
and
E. M.
Lifshitz
,
Fluid Mechanics
(
Pergamon Press
,
Oxford
,
1987
).
30.
C. D.
Andereck
,
S. S.
Liu
, and
H. L.
Swinney
, “
Flow regimes in a circular Couette system with independently rotating cylinders
,”
J. Fluid Mech.
164
,
155
(
1986
).
31.
S.
Dong
, “
Direct numerical simulation of turbulent Taylor-Couette flow
,”
J. Fluid Mech.
587
,
373
393
(
2007
).
You do not currently have access to this content.