Research on the von Kármán boundary layer extends back almost 100 years but remains a topic of active study, which continues to reveal new results; it is only now that fully nonlinear direct numerical simulations (DNS) have been conducted of the flow to compare with theoretical and experimental results. The von Kármán boundary layer, or rotating-disk boundary layer, provides, in some senses, a simple three-dimensional boundary-layer model with which to compare other more complex flow configurations but we will show that in fact the rotating-disk boundary layer itself exhibits a wealth of complex instability behaviors that are not yet fully understood.

References

1.
von Kármán
,
T.
,
1921
, “
Über Laminare und Turbulente Reibung
,”
Z. Angew. Math. Mech.
,
1
(4), pp.
233
252
.10.1002/zamm.19210010401
2.
Bödewadt
,
U. T.
,
1940
, “
Die Drehströmung über Festem Grund
,”
Z. Angew. Math. Mech.
,
20
(5), pp.
241
253
.10.1002/zamm.19400200502
3.
Ekman
,
V. W.
,
1905
, “
On the Influence of the Earth’s Rotation on Ocean Currents
,”
Ark. Mat. Astron. Fys.
,
2
(
11
), pp.
1
53
.
4.
Alfredsson
,
P. H.
,
Imayama
,
S.
,
Lingwood
,
R. J.
,
Örlü
,
R.
, and
Segalini
,
A.
,
2013
, “
Turbulent Boundary Layers Over Flat Plates and Rotating Disks—The Legacy of Von Kármán: A Stockholm Perspective
,”
Eur. J. Mech. B Fluids
,
40
, pp.
17
29
.10.1016/j.euromechflu.2013.01.001
5.
Imayama
,
S.
,
Alfredsson
,
P. H.
, and
Lingwood
,
R. J.
,
2014
, “
On the Laminar-Turbulent Transition of the Rotating-Disk Flow: The Role of Absolute Instability
,”
J. Fluid Mech.
,
745
, pp.
132
163
.10.1017/jfm.2014.80
6.
Lingwood
,
R. J.
,
1995
, “
Stability and Transition of the Boundary Layer on a Rotating Disk
,” Ph.D. thesis,
University of Cambridge
,
Cambridge, UK
.
7.
Gray
,
W.
,
1952
, “
The Nature of the Boundary Layer at the Nose of a Swept Back Wing
,” Min. Aviation, Lond. (unpublished).
8.
Gregory
,
N.
,
Stuart
,
J. T.
, and
Walker
,
W. S.
,
1955
, “
On the Stability of Three-Dimensional Boundary Layers With Application to the Flow due to a Rotating Disk
,”
Philos. Trans. R. Soc. London
,
248
, pp.
155
199
.10.1098/rsta.1955.0013
9.
Theodorsen
,
T.
, and
Regier
,
A. A.
,
1944
, “
Experiments on Drag of Revolving Disks, Cylinders and Streamline Rods at High Speeds
,” NACA Report No. 793.
10.
Smith
,
N. H.
,
1947
, “
Exploratory Investigation of Laminar-Boundary-Layer Oscillations on a Rotating Disk
,” NACA Report No. TN 1227.
11.
Pfenninger
,
W.
, and
Reed
,
V. D.
,
1966
, “
Laminar-Flow Research and Experiments
,”
Astronaut. Aeronaut.
,
4
, pp.
44
50
.
12.
Wazzan
,
A.
,
Okamura
,
T. T.
, and
Smith
,
A. M. O.
,
1968
, “
The Stability of Water Flow Over Heated and Cooled Flat Plates
,”
ASME J. Heat Transfer
,
90
(1), pp.
109
114
.10.1115/1.3597439
13.
Cebeci
,
T.
, and
Stewartson
,
K.
,
1980
, “
Stability and Transition in Three-Dimensional Flows
,”
AIAA J.
,
18
, pp.
398
405
.
14.
Mack
,
L.
,
1981
, “
Compressible Boundary-Layer Stability Calculations for Swept-Back Wings With Suction
,”
AIAA J.
,
20
(3), pp.
363
369
.10.2514/3.51080
15.
Kohama
,
Y.
,
1987
, “
Some Expectation on the Mechanism of Cross-Flow Instability in a Swept Wing Flow
,”
Acta Mech.
,
66
(1–4), pp.
21
38
.10.1007/BF01184283
16.
Cebeci
,
T.
, and
Chen
,
H. H.
,
1992
, “
Numerical-Method for Predicting Transition in 3-Dimensional Flows by Spatial Amplification Theory
,”
AIAA J.
,
30
(8), pp.
1972
1979
.10.2514/3.11168
17.
Lin
,
R. S.
, and
Reed
,
H. L.
,
1993
, “
Effect of Curvature on Stationary Cross-Flow Instability of a 3-Dimensional Boundary Layer
,”
AIAA J.
,
31
(9), pp.
1611
1617
.10.2514/3.11822
18.
Malik
,
M.
,
1994
, “
The Neutral Curve for Stationary Disturbances in Rotating Disk Flow
,”
J. Fluid Mech.
,
164
, pp.
275
287
.10.1017/S0022112086002550
19.
Zandbergen
,
P. J.
, and
Dijkstra
,
D.
,
1987
, “
Von Kármán Swirling Flows
,”
Ann. Rev. Fluid Mech.
,
19
, pp.
465
491
.10.1146/annurev.fl.19.010187.002341
20.
Johnston
,
J. P.
, and
Flack
,
K. A.
,
1996
, “
Review—Advances in Three-Dimensional Turbulent Boundary Layers With Emphasis on Wall-Layer Regions
,”
ASME J. Fluids Eng.
,
118
(2), pp.
219
232
.10.1115/1.2817367
21.
Launder
,
B.
,
Poncet
,
S.
, and
Serre
,
E.
,
2010
, “
Laminar, Transitional, and Turbulent Flows in Rotor-Stator Systems
,”
Ann. Rev. Fluid Mech.
,
42
, pp.
229
248
.10.1146/annurev-fluid-121108-145514
22.
Kohama
,
Y.
,
1984
, “
Study on Boundary Layer Transition of a Rotating Disk
,”
Acta Mech.
,
50
(3–4), pp.
193
199
.10.1007/BF01170959
23.
Wilkinson
,
S. P.
, and
Malik
,
M. R.
,
1985
, “
Stability Experiments in the Flow Over a Rotating Disk
,”
AIAA J.
,
23
(4), pp.
588
595
.10.2514/3.8955
24.
Mack
,
L.
,
1985
, “
The Wave Pattern Produced by a Point Source on a Rotating Disk
,”
AIAA
Paper No. 85–0490. 10.2514/6.1985-0490
25.
Kobayashi
,
R.
,
Kohama
,
Y.
, and
Takamadate
,
C.
,
1980
, “
Spiral Vortices in Boundary Layer Transition Regime on a Rotating Disk
,”
Acta Mech.
,
35
(1–2), pp.
71
82
.10.1007/BF01190058
26.
Malik
,
M. R.
,
Wilkinson
,
S. P.
, and
Orszag
,
S. A.
,
1981
, “
Instability and Transition in Rotating Disk Flow
,”
AIAA J.
,
19
(9), pp.
1131
1138
.10.2514/3.7849
27.
Faller
,
A. J.
,
1991
, “
Instability and Transition of Disturbed Flow Over a Rotating Disk
,”
J. Fluid Mech.
,
230
, pp.
245
269
.10.1017/S0022112091000782
28.
Lilly
,
D.
,
1966
, “
On the Instability of Ekman Boundary Flow
,”
J. Atmos. Sci.
,
23
(5), pp.
481
494
.10.1175/1520-0469(1966)023<0481:OTIOEB>2.0.CO;2
29.
Faller
,
A. J.
, and
Kaylor
,
R. E.
,
1966
, “
A Numerical Study of the Instability of the Laminar Ekman Boundary Layer
,”
J. Atmos. Sci.
,
23
(5), pp.
466
480
.10.1175/1520-0469(1966)023<0466:ANSOTI>2.0.CO;2
30.
Tatro
,
P.
, and
Mollö-Christensen
,
E.
,
1967
, “
Experiments on Ekman Layer Instability
,”
J. Fluid Mech.
,
28
(3), pp.
531
543
.10.1017/S0022112067002289
31.
Bassom
,
A. P.
, and
Gajjar
,
J. S. B.
,
1988
, “
Non-Stationary Cross-Flow Vortices in Three-Dimensional Boundary-Layer Flow
,”
Proc. R. Soc. London
,
417
, pp.
179
212
.10.1098/rspa.1988.0056
32.
Balakumar
,
P.
, and
Malik
,
M. R.
,
1990
, “
Traveling Disturbances in Rotating-Disk Flow
,”
Theor. Comput. Fluid. Dyn.
,
2
, pp.
125
137
.
33.
Bassom
,
A. P.
, and
Hall
,
P.
,
1991
, “
Concerning the Interaction of Non-Stationary Crossflow Vortices in a Three-Dimensional Boundary Layer
,”
Q. J. Mech. Appl. Math.
,
44
(
1
), pp.
147
172
.10.1093/qjmam/44.1.147
34.
Lingwood
,
R. J.
,
1995
, “
Absolute Instability of the Boundary Layer on a Rotating Disk
,”
J. Fluid Mech.
,
299
, pp.
17
33
.10.1017/S0022112095003405
35.
Imayama
,
S.
,
Lingwood
,
R. J.
, and
Alfredsson
,
P. H.
,
2014
, “
The Turbulent Rotating-Disk Boundary Layer
,”
Eur. J. Mech. B/Fluids
,
48
, pp.
245
253
.10.1016/j.euromechflu.2014.03.009
36.
Lingwood
,
R. J.
,
1997
, “
Absolute Instability of the Ekman Layer and Related Rotating Flows
,”
J. Fluid Mech.
,
331
, pp.
405
428
.10.1017/S0022112096004144
37.
Lingwood
,
R. J.
,
1997
, “
On the Application of the Briggs’ and Steepest-Descent Methods to a Boundary-Layer Flow
,”
Stud. Appl. Math.
,
98
(3), pp.
213
254
.10.1111/1467-9590.00048
38.
Briggs
,
R. J.
,
1964
,
Electron-Stream Interaction With Plasmas
,
MIT Press
, Cambridge, MA, Chap. 2.
39.
Betchov
,
R.
, and
Criminale
,
W. O.
,
1968
, “
Spatial Instability of the Inviscid Jet and Wake
,”
Phys. Fluids.
,
9
(2), pp.
359
362
.10.1063/1.1761679
40.
Koch
,
W.
,
1985
, “
Local Instability Characteristics and Frequency Determination of Self-Excited Wake Flows
,”
J. Sound Vib.
,
99
(1), pp.
53
83
.10.1016/0022-460X(85)90445-6
41.
Brazier-Smith
,
P. R.
, and
Scott
,
J. F.
,
1984
, “
Stability of Fluid Flow in the Presence of a Compliant Surface
,”
Wave Motion.
,
6
(6), pp.
547
560
.10.1016/0165-2125(84)90045-3
42.
Heurre
,
P.
, and
Monkewitz
,
P. A.
,
1985
, “
Absolute and Convective Instabilities in Free Shear Layers
,”
J. Fluid Mech.
,
159
, pp.
151
168
.10.1017/S0022112085003147
43.
Dagenhart
,
J. R.
, and
Saric
,
W. S.
,
1999
, “
Crossflow Stability and Transition Experiments in Swept-Wing Flow
,” Report No. NASA/TP-1999-209344.
44.
Lingwood
,
R. J.
,
1997
, “
On the Impulse Response for Swept Boundary-Layer Flows
,”
J. Fluid Mech.
,
344
, pp.
317
334
.10.1017/S0022112097006149
45.
Ryzhov
,
O. S.
, and
Terent’ev
,
E. D.
,
1998
, “
Streamwise Absolute Instability of a Three-Dimensional Boundary Layer at High Reynolds Numbers
,”
J. Fluid Mech.
,
373
, pp.
111
153
.10.1017/S0022112098002456
46.
Taylor
,
M. J.
, and
Peake
,
N.
,
1998
, “
The Long-Time Behaviour of Incompressible Swept-Wing Boundary Layers Subject to Impulsive Forcing
,”
J. Fluid Mech.
,
355
, pp.
359
381
.10.1017/S002211209700788X
47.
Heurre
,
P.
,
2000
, “
Open Shear Flow Instabilities
,”
Perspectives in Fluid Dynamics
,
G. K.
Batchelor
,
H. K.
Moffatt
, and
M. G.
Worster
, eds.,
Cambridge University Press
, Cambridge, pp.
159
229
.
48.
Chomaz
,
J.-M.
,
Huerre
,
P.
, and
Redekopp
,
L. G.
,
1991
, “
A Frequency Selection Criterion in Spatially Developing Flows
,”
Stud. Appl. Math.
,
84
, pp.
119
144
.
49.
Le Dizès
,
S.
, and
Huerre
,
P.
,
1996
, “
Linear Global Modes in Spatially Developing Media
,”
Philos. Trans. R. Soc. A.
,
354
, pp.
169
212
.
50.
Couairon
,
A.
, and
Chomaz
,
J.-M.
,
1996
, “
Global Instability in Fully Nonlinear Systems
,”
Phys. Rev. Lett.
,
77
, pp.
4015
4018
.10.1103/PhysRevLett.77.4015
51.
Couairon
,
A.
, and
Chomaz
,
J.-M.
,
1997
, “
Absolute and Convective Instabilities, Front Velocities and Global Modes in Nonlinear Systems
,”
Physica D
,
108
(3), pp.
236
276
.10.1016/S0167-2789(97)00045-6
52.
Couairon
,
A.
, and
Chomaz
,
J.-M.
,
1997
, “
Pattern Selection in the Presence of a Cross Flow
,”
Phys. Rev. Lett.
,
79
, pp.
2666
2669
.10.1103/PhysRevLett.79.2666
53.
Couairon
,
A.
, and
Chomaz
,
J.-M.
,
1999
, “
Fully Nonlinear Global Modes in Slowly Varying Flows
,”
Phys. Fluids
,
11
(12), pp.
3688
3703
.10.1063/1.870232
54.
Couairon
,
A.
, and
Chomaz
,
J.-M.
,
1999
, “
Primary and Secondary Nonlinear Global Instability
,”
Physica D
,
132
(4), pp.
428
456
.10.1016/S0167-2789(99)00062-7
55.
Pier
,
B.
, and
Huerre
,
P.
,
1996
, “
Fully Nonlinear Global Modes in Spatially Developing Media
,”
Physica D
,
97
(1–3), pp.
206
222
.10.1016/0167-2789(96)00152-2
56.
Pier
,
B.
,
Huerre
,
P.
,
Chomaz
,
J.-M.
, and
Couairon
,
A.
,
1998
, “
Steep Nonlinear Global Modes in Spatially Developing Media
,”
Phys. Fluids
,
10
(10), pp.
2433
2435
.10.1063/1.869784
57.
Pier
,
B.
,
2001
, “
Nonlinear Synchronization in Open Flows
,”
J. Fluid Struct.
,
15
(3–4), pp.
471
480
.10.1006/jfls.2000.0349
58.
Monkewitz
,
P. A.
,
Huerre
,
P.
, and
Chomaz
,
J.-M.
,
1993
, “
Global Linear Stability Analysis of Weakly Non-Parallel Shear Flows
,”
J. Fluid Mech.
,
251
, pp.
1
20
.10.1017/S0022112093003313
59.
Pier
,
B.
, and
Huerre
,
P.
,
2001
, “
Nonlinear Self-Sustained Structures and Fronts in Spatially Developing Wake Flows
,”
J. Fluid Mech.
,
435
, pp.
145
174
.
60.
Pier
,
B.
,
2002
, “
On the Frequency Selection of Finite-Amplitude Vortex Shedding in the Cylinder Wake
,”
J. Fluid Mech.
,
458
, pp.
407
417
.
61.
Lingwood
,
R. J.
,
1996
, “
An Experimental Study of Absolute Instability of the Rotating-Disk Boundary-Layer Flow
,”
J. Fluid Mech.
,
314
, pp.
373
405
.10.1017/S0022112096000365
62.
Healey
,
J. J.
,
2004
, “
On the Relation Between the Viscous and Inviscid Absolute Instabilities of the Rotating-Disk Boundary Layer
,”
J. Fluid Mech.
,
511
, pp.
179
199
.10.1017/S0022112004009565
63.
Healey
,
J. J.
,
2006
, “
Inviscid Long-Wave Theory for the Absolute Instability of the Rotating-Disc Boundary Layer
,”
Proc. R. Soc. London A
,
462
, pp.
1467
1482
.10.1098/rspa.2005.1634
64.
Healey
,
J. J.
,
2006
, “
A New Convective Instability of the Rotating Disk Boundary Layer With Growth Normal to the Disk
,”
J. Fluid Mech.
,
560
, pp.
279
310
.10.1017/S0022112006000504
65.
Davies
,
C.
, and
Carpenter
,
P. W.
,
2003
, “
Global Behaviour Corresponding to the Absolute Instability of the Rotating-Disc Boundary Layer
,”
J. Fluid Mech.
,
486
, pp.
287
329
.10.1017/S0022112003004701
66.
Spalart
,
P. R.
,
1991
, “
On the Cross-Flow Instability Near a Rotating Disk
,”
R. Aero. Soc., Proc. Boundary Layer Transition Control
,
22
, pp.
1
13
.
67.
Malik
,
M. R.
, and
Balakumar
,
P.
,
1992
, “
Nonparallel Stability of Rotating Disk Flow Using PSE
,”
Instability, Transition and Turbulence
,
M. Y.
Hussaini
,
A.
Kumar
, and
C. L.
Streett
, eds.,
Springer
, New York, pp.
168
180
.10.1007/978-1-4612-2956-8_17
68.
Davies
,
C.
,
Thomas
,
C.
, and
Carpenter
,
P. W.
,
2007
, “
Global Stability of the Rotating-Disk Boundary Layer
,”
J. Eng. Math.
,
57
(3), pp.
219
236
.10.1007/s10665-006-9112-8
69.
Huerre
,
P.
, and
Monkewitz
,
P. A.
,
1990
, “
Local and Global Instabilities in Spatially Developing Flows
,”
Annu. Rev. Fluid Mech.
,
22
, pp.
473
537
.10.1146/annurev.fl.22.010190.002353
70.
Pier
,
B.
,
2003
, “
Finite-Amplitude Crossflow Vortices, Secondary Instability and Transition in the Rotating-Disk Boundary Layer
,”
J. Fluid Mech.
,
487
, pp.
315
343
.10.1017/S0022112003004981
71.
Pier
,
B.
,
2007
, “
Primary Crossflow Vortices, Secondary Absolute Instabilities and Their Control in the Rotating-Disk Boundary Layer
,”
J. Eng. Math.
,
57
(3), pp.
237
251
.10.1007/s10665-006-9095-5
72.
Corke
,
T. C.
,
Matlis
,
E. H.
, and
Othman
,
H.
,
2007
, “
Transition to Turbulence in Rotating-Disk Boundary Layers—Convective and Absolute Instabilities
,”
J. Eng. Math.
,
57
(3), pp.
253
272
.10.1007/s10665-006-9099-1
73.
Corke
,
T. C.
, and
Knasiak
,
K. F.
,
1998
, “
Stationary Travelling Cross-Flow Mode Interactions on a Rotating Disk
,”
J. Fluid Mech.
,
355
, pp.
285
315
.10.1017/S0022112097007738
74.
Othman
,
H.
, and
Corke
,
T. C.
,
2006
, “
Experimental Investigation of Absolute Instability of a Rotating-Disk Boundary Layer
,”
J. Fluid Mech.
,
565
, pp.
63
94
.10.1017/S0022112006001546
75.
Healey
,
J. J.
,
2007
, “
Instabilities of Flows due to Rotating Disks: Preface
,”
J. Eng. Math.
,
57
(3), pp.
199
204
.10.1007/s10665-006-9132-4
76.
Healey
,
J. J.
,
2010
, “
Model for Unstable Global Modes in the Rotating-Disk Boundary Layer
,”
J. Fluid Mech.
,
663
, pp.
148
159
.10.1017/S0022112010003836
77.
Pier
,
B.
,
2013
, “
Transition Near the Edge of a Rotating Disk
,”
J. Fluid Mech.
,
737
, pp.
R1 1
9
.10.1017/jfm.2013.578
78.
Imayama
,
S.
,
Alfredsson
,
P. H.
, and
Lingwood
,
R. J.
,
2013
, “
An Experimental Study of Edge Effects on Rotating-Disk Transition
,”
J. Fluid Mech.
,
716
, pp.
638
657
.10.1017/jfm.2012.564
79.
Siddiqui
,
M. E.
,
Mukund
,
V.
,
Scott
,
J.
, and
Pier
,
B.
,
2013
, “
Experimental Characterization of Transition Region in Rotating-Disk Boundary Layer
,”
Phys. Fluids
,
25
(3), p.
034102
.10.1063/1.4798435
80.
Imayama
,
S.
,
Alfredsson
,
P. H.
, and
Lingwood
,
R. J.
,
2012
, “
A New Way to Describe the Transition Characteristics of a Rotating-Disk Boundary-Layer Flow
,”
Phys. Fluids
,
24
(3), p.
031701
.10.1063/1.3696020
81.
Viaud
,
B.
,
Serre
,
E.
, and
Chomaz
,
J.-M.
,
2008
, “
The Elephant Mode Between Two Rotating Disks
,”
J. Fluid Mech.
,
598
, pp.
451
464
.10.1017/S0022112007009962
82.
Viaud
,
B.
,
Serre
,
E.
, and
Chomaz
,
J.-M.
,
2011
, “
Transition to Turbulence Through Steep Global-Modes Cascade in an Open Rotating Cavity
,”
J. Fluid Mech.
,
688
, pp.
493
506
.10.1017/jfm.2011.393
83.
Appelquist
,
E.
,
Schlatter
,
P.
,
Alfredsson
,
P. H.
, and
Lingwood
,
R. J.
, “
Global Linear Instability of the Rotating-Disk Flow Investigated Through Simulations
,”
J. Fluid Mech.
(in press).
84.
Thomas
,
C.
, and
Davies
,
C.
,
2010
, “
The Effects of Mass Transfer on the Global Stability of the Rotating-Disk Boundary Layer
,”
J. Fluid Mech.
,
663
, pp.
401
433
.10.1017/S0022112010003563
85.
Thomas
,
C.
, and
Davies
,
C.
,
2013
, “
Global Stability of the Rotating-Disc Boundary Layer With an Axial Magnetic Field
,”
J. Fluid Mech.
,
724
, pp.
510
526
.10.1017/jfm.2013.162
86.
Appelquist
,
E.
,
Schlatter
,
P.
,
Alfredsson
,
P. H.
, and
Lingwood
,
R. J.
,
2014
, “
Investigation of the Global Instability of the Rotating-Disk Boundary Layer
,”
Proceedings of the IUTAM ABCM Symposium on Laminar Turbulent Transition
,
Rio de Janeiro
,
Brazil
, Elsevier.
87.
Lingwood
,
R. J.
,
1997
, “
On the Effects of Suction and Injection on the Absolute Instability of the Rotating-Disk Boundary Layer
,”
Phys. Fluids
,
9
(5), pp.
1317
1328
.10.1063/1.869246
88.
Davies
,
C.
, and
Thomas
,
C.
,
2010
, “
Disturbance Evolution in Rotating-Disk Boundary Layers: Competition Between Absolute Instability and Global Stability
,” Proceedings of the Seventh
IUTAM
Symposium on Laminar-Turbulent Transition
,
P.
Schlatter
, and
D. S.
Henningson
, eds.,
Stockholm
,
Sweden, Springer
, Dordrecht, Heidelberg, London, New York, Vol. 18, pp.
135
140
.10.1007/978-90-481-3723-7_20
89.
Hussain
,
Z.
,
Garrett
,
S. J.
, and
Stephen
,
S. O.
,
2011
, “
The Instability of the Boundary Layer Over a Disk Rotating in an Enforced Axial Flow
,”
Phys. Fluids
,
23
(11), p.
114108
.10.1063/1.3662133
90.
Lingwood
,
R. J.
, and
Garrett
,
S. J.
,
2011
, “
The Effects of Surface Mass Flux on the Instability of the BEK System of Rotating Boundary-Layer Flows
,”
Eur. J. Mech. B-Fluid.
,
30
(3), pp.
299
310
.10.1016/j.euromechflu.2011.02.003
91.
Cooper
,
A. J.
, and
Carpenter
,
P. W.
,
1997
, “
The Stability of Rotating-Disc Boundary-Layer Flow Over a Compliant Wall. Part 2. Absolute Instability
,”
J. Fluid Mech.
,
350
, pp.
261
270
.10.1017/S0022112097006964
92.
Carpenter
,
P. W.
, and
Thomas
,
P. J.
,
2007
, “
Flow Over Compliant Rotating Disks
,”
J. Eng. Math.
,
57
(3), pp.
303
315
.10.1007/s10665-006-9089-3
93.
Thomas
,
P. J.
, and
Zoueshtiagh
,
F.
,
2007
, “
Rotating-Disk-Type Flow Over Loose Boundaries
,”
J. Eng. Math.
,
57
(3), pp.
317
332
.10.1007/s10665-006-9090-x
94.
Garrett
,
S. J.
, and
Peake
,
N.
,
2007
, “
On the Global Linear Stability of the Boundary Layer on Rotating Bodies
,”
Adv. Turbul. XI
,
117
, pp.
550
552
.10.1007/978-3-540-72604-3
95.
Garrett
,
S. J.
, and
Peake
,
N.
,
2002
, “
The Stability and Transition of the Boundary Layer on a Rotating Sphere
,”
J. Fluid Mech.
,
456
, pp.
199
218
.10.1017/S0022112001007571
96.
Garrett
,
S. J.
, and
Peake
,
N.
,
2007
, “
The Absolute Instability of the Boundary Layer on a Rotating Cone
,”
Eur. J. Mech. B-Fluid
,
26
(
3
), pp.
344
353
.10.1016/j.euromechflu.2006.08.002
97.
Garrett
,
S. J.
,
Hussain
,
Z.
, and
Stephen
,
S. O.
,
2009
, “
The Crossflow Instability of the Boundary Layer on a Rotating Cone
,”
J. Fluid Mech.
,
622
, pp.
209
232
.10.1017/S0022112008005181
98.
Garrett
,
S. J.
,
Hussain
,
Z.
, and
Stephen
,
S. O.
,
2010
, “
Boundary-Layer Transition on Broad Cones Rotating in an Imposed Axial Flow
,”
AIAA J.
,
48
(6), pp.
1184
1194
.10.2514/1.J050021
99.
Serre
,
E.
,
Crespo del Arco
,
E.
, and
Bontoux
,
P.
,
2001
, “
Annular and Spiral Patterns in Flows Between Rotating and Stationary Discs
,”
J. Fluid Mech.
,
434
, pp.
65
100
.10.1017/S0022112001003494
100.
Crespo del Arco
,
E.
,
Serre
,
E.
, and
Bontoux
,
P.
,
2005
, “
Stability, Transition and Turbulence in Rotating Cavities
,”
Advances in Fluid Mechanics
,
M.
Rahman
, ed., Vol.
41
,
WIT Press
,
Southampton
, pp.
141
196
.
101.
Hewitt
,
R. E.
, and
Hazel
,
A. L.
,
2007
, “
Midplane-Symmetry Breaking in the Flow Between Two Counter-Rotating Disks
,”
J. Eng. Math.
,
57
(3), pp.
273
288
.10.1007/s10665-006-9098-2
102.
Le Gal
,
P.
,
Tasaka
,
Y.
, and
Nagao
,
J.
,
2007
, “
A Statistical Study of Spots in Torsional Couette Flow
,”
J. Eng. Math.
,
57
(3), pp.
289
302
.10.1007/s10665-006-9100-z
You do not currently have access to this content.