Laminar and turbulent Poiseuille–Ekman flows at different rotation rates have been investigated by means of analytical and numerical approaches. A series of direct numerical simulations (DNSs) with various rotation rates (Ro2=01.82) for Reynolds number Reτ0=180 based on the friction velocity in the nonrotating case has been conducted. Both (laminar and turbulent) flow states are highly sensitive to the rotation. Even a small rotation rate can reduce the mean streamwise velocity and induce a very strong flow in the spanwise direction, which, after attaining a maximum, decreases by further increasing the rotation rate. It has been further observed that turbulence is damped by increasing the rotation rate and at about Ro2=0.145 a transition from the fully turbulent to a quasilaminar state occurs. In this region Reynolds number is only large enough to sustain some perturbations and the mean velocity profiles have inflection points. The instability of the turbulent shear stress is probably the main reason for the formation of the elongated coherent structures (roll-like vortices) in this region. In the fully turbulent parameter domain all six components of Reynolds stress tensor are nonzero due to the existence of the spanwise mean velocity. The Poiseuille–Ekman flow in this region can be regarded as a turbulent two-dimensional channel flow with a mean flow direction inclining toward the spanwise direction. Finally, due to the further increase in the rotation rate, at about Ro2=0.546 turbulence is completely damped and the flow reaches a fully laminar steady state, for which an analytical solution of the Navier–Stokes equations exists. The DNS results reproduce this analytical solution for the laminar state.

1.
J. P.
Johnston
,
R. M.
Halleent
, and
D. K.
Lezius
, “
Effects of spanwise rotation on the structure of two-dimensional fully developed turbulent channel flow
,”
J. Fluid Mech.
56
,
533
(
1972
).
2.
K.
Nakabayashi
and
O.
Kitoh
, “
Low Reynolds number fully developed two- dimensional turbulent channel flow with system rotation
,”
J. Fluid Mech.
315
,
1
(
1996
).
3.
J.
Kim
, “
The effect of rotation on turbulence structure
,”
Proceedings of the Fourth Symposium on Turbulent Shear Flows
, Karlsruhe, West Germany, 12–14 September
1983
(
Pennsylvania State University
,
University Park, PA
,
1984
), Proceedings No. A85-1426 04-34, pp.
6
14
6
19
.
4.
R.
Kristofferson
and
H. I.
Anderson
, “
Direct simulations of low Reynolds- number turbulent flow in a rotating channel
,”
J. Fluid Mech.
256
,
163
(
1993
).
5.
E.
Lamballais
,
O.
Me’tais
, and
M.
Lesieur
, “
Spectral-dynamic model for large-eddy simulations of turbulent rotating channel flow
,”
Theor. Comput. Fluid Dyn.
12
,
146
(
1998
).
6.
O.
Grundestam
,
S.
Wallin Halleen
, and
V.
Johanson
, “
Direct simulations of rotating turbulent channel flow
,”
J. Fluid Mech.
598
,
177
(
2008
).
7.
M.
Oberlack
,
W.
Cabot
, and
M. M.
Rogers
,
Group Analysis, DNS and Modelling of a Turbulent Channel Flow with Streamwise Rotation
,
Studying Turbulence Using Numerical Database
Vol.
7
(
Center for Turbulence Research, Stanford University/NASA
,
Ames
,
1998
), pp.
221
242
.
8.
M.
Oberlack
,
W.
Cabot
,
B. A.
Pettersson Reif
, and
T.
Weller
, “
Group analysis, DNS and modelling of a turbulent channel flow with streamwise rotation
,”
J. Fluid Mech.
562
,
383
(
2006
).
9.
I.
Recktenwald
,
T.
Weller
,
W.
Schroeder
, and
M.
Oberlack
, “
Comparison of direct numerical simulation and particle-image velocimetry data of turbulent channel flow rotating about the streamwise axis
,”
Phys. Fluids
19
,
085114
(
2007
).
10.
H.
Wu
and
N.
Kasagi
, “
Effects of arbitrary directional system rotation on turbulent channel flow
,”
Phys. Fluids
16
,
979
(
2004
).
11.
B. -Y.
Li
,
N. -S.
Liu
, and
X. -Y.
Lu
, “
Direct numerical simulation of wall-normal rotating channel flow with heat transfer
,”
Int. J. Heat Mass Transfer
49
,
1162
(
2006
).
12.
V. W.
Ekman
, “
On the influence of the Earth’s rotation on ocean-currents
,”
Ark. Mat., Astron. Fys.
52
,
32
(
1905
).
13.
H. P.
Greenspan
,
The Theory of Rotating Fluids
(
Breuklin
,
Brooklin
,
1990
).
14.
A.
Lundbladh
,
D.
Henningson
, and
A.
Johanson
,
An Efficient Spectral Integration Method for the Solution of the Navier-Stokes Equations
, (
Aeronautical Research Institute of Sweden
,
Bromma
,
1992
).
15.
P.
Moin
and
J.
Kim
, “
Numerical investigation of turbulent channel flow
,”
J. Fluid Mech.
118
,
341
(
1982
).
16.
O.
El-Samni
, “
Heat and momentum transfer in turbulent rotating channel flow
,” Ph.D. thesis,
The University of Tokyo
, Tokyo, Japan,
2001
.
17.
G. N.
Coleman
,
J. H.
Ferziger
, and
P. R.
Spalart
, “
A numerical study of the turbulent Ekman layer
,”
J. Fluid Mech.
213
,
313
(
1990
).
18.
P. R.
Spalart
,
G. N.
Coleman
, and
R.
Johnstone
, “
Direct numerical simulation of the Ekman layer: A step in Reynolds number, and cautious support for a log law with a shifted origin
,”
Phys. Fluids
20
,
101507
(
2008
).
19.
K.
Shingai
and
H.
Kawamura
, “
A study of turbulence structure and large-scale motion in the Ekman layer through direct numerical simulations
,”
J. Turbul.
5
,
13
(
2004
).
20.
H. L.
Grant
, “
The large eddies of turbulent motion
,”
J. Fluid Mech.
4
,
149
(
1958
).
21.
A. A.
Townsend
,
The Structure of Turbulent Shear Flow
(
Cambridge University Press
,
New York
,
1956
).
22.
A. J.
Faller
, “
Large eddies in the atmospheric boundary layer and their possible role in the formation of cloud rows
,”
J. Atmos. Sci.
22
,
176
(
1965
).
23.
M. A.
LeMone
, “
The structure and dynamics of horizontal rolls notices in the planetary boundary layer
,”
J. Atmos. Sci.
30
,
1077
(
1973
).
24.
J. W.
Deardorff
, “
Numerical investigation of neutral and unstable planetary boundary layers
,”
J. Atmos. Sci.
29
,
91
(
1972
).
25.
R. A.
Brown
,
Analytical Methods in Planetary Boundary-Layer Modeling
(
Wiley
,
New York
,
1974
).
26.
D.
Etling
and
R. A.
Brown
, “
Roll vortices in the planetary boundary layer: A review
,”
Boundary-Layer Meteorol.
65
,
215
(
1993
).
27.
A. J.
Faller
, “
An experimental study of the instability of the laminar Ekman boundary layer
,”
J. Atmos. Sci.
15
,
560
(
1963
).
28.
D. R.
Caldwell
and
C. W.
Van Atta
, “
Characteristics of Ekman boundary layer instabilities
,”
J. Fluid Mech.
44
,
79
(
1970
).
You do not currently have access to this content.