We describe the first DNS-based measurement of the complete mean response of a turbulent channel flow to small external disturbances. Space-time impulsive perturbations are applied at one channel wall, and the linear response describes their mean effect on the flow field as a function of spatial and temporal separations. The turbulent response is shown to differ from the response of a laminar flow with the turbulent mean velocity profile as the base flow.

1.
J.
Kim
and
J.
Lim
, “
A linear process in wall-bounded turbulent flows
,”
Phys. Fluids
12
,
1885
(
2000
).
2.
J.
Kim
, “
Control of turbulent boundary layers
,”
Phys. Fluids
15
,
1093
(
2003
).
3.
T.
Bewley
, “
Flow control, new challenges for a new renaissance
,”
Prog. Aerosp. Sci.
37
,
21
(
2001
).
4.
M.
Högberg
,
T. R.
Bewley
, and
D.
Henningson
, “
Relaminarization of Reτ=100 turbulence using gain scheduling and linear state-feedback control
,”
Phys. Fluids
15
,
3572
(
2003
).
5.
M.
Högberg
and
D.
Henningson
, “
Linear optimal control applied to instabilities in spatially developing boundary layers
,”
J. Fluid Mech.
470
,
151
(
2002
).
6.
M. R.
Jovanović
and
B.
Bamieh
, “
Componentwise energy amplification in channel flows
,”
J. Fluid Mech.
534
,
145
(
2005
).
7.
A. K. M. F.
Hussain
and
W. C.
Reynolds
, “
The mechanics of an organized wave in turbulent shear flow
,”
J. Fluid Mech.
41
,
241
(
1970
).
8.
M.
Quadrio
and
P.
Luchini
, “
The linear response of a turbulent channel flow
,” in
Proceedings of the IX European Turbulence Conference, Southampton, UK
, July 2–5,
2002
, pp.
715
718
.
9.
P.
Luchini
,
M.
Quadrio
, and
T.
Bewley
, “
An optimal feedback controller for the reduction of turbulent energy in 3D plane-duct flow
,”
APS Meeting, Chicago, IL
, November 20–22,
2005
.
10.
P.
Luchini
and
M.
Quadrio
, “
A low-cost parallel implementation of direct numerical simulation of wall turbulence
,”
J. Comput. Phys.
211
,
551
(
2006
).
11.
R.
Moser
,
J.
Kim
, and
N. N.
Mansour
, “
Direct numerical simulation of turbulent channel flow up to Reθ=590
,”
Phys. Fluids
11
,
943
(
1999
).
12.
Being limited to small control amplitudes is a reasonable hypothesis, as long as control is aimed at turbulent drag reduction.
You do not currently have access to this content.