In the following, the present authors comment on a paper by Zhou and Sirovich (ZS) [Phys. Fluids A 4, 2855 (1992)] which contained a critical appraisal of the models developed by Aubry et al. (AHLS) [J. Fluid Mech. 192, 115 (1988)]. It is found that ZS’s suggestion to use ‘‘a full channel interpretation of wall eigenfunctions,’’ thereby avoiding boundary terms, while attractive mathematically, is questionable in fluid mechanical terms. A major point of AHLS’s study was precisely to isolate the wall region and use the boundary terms to investigate the interaction with the outer flow. Also, it is demonstrated that certain instances of ‘‘irregular’’ bursting, as reported by ZS, are probably numerical effects.
REFERENCES
1.
X.
Zhou
and L.
Sirovich
, “Coherence and chaos in a model of turbulent boundary layer
,” Phys. Fluids A
4
, 2855
(1992
).2.
N. Aubry and S. Sanghi, “Streamwise and cross-stream dynamics of the turbulent wall layer,” in Chaotic Dynamics and in Fluid Mechanics, Proceedings of the 3rd Joint ASCE-ASME Mechanics, UCSD, La Jolla, 9–12 July 1989, edited by K. N. Ghia and U. Ghia (ASME, New York, 1990), pp. 110–118.
3.
N. Aubry and S. Sanghi, “Bifurcations and bursting of streaks in the turbulent wall layer,” in Turbulence and Coherent Structures, Proceedings of the Grenoble Conference on Organized Structures and Turbulence, 18–21 September 1991, edited by O. Metais and M. Lesieur (Kluwer Academic, Dordrecht, The Netherlands, 1991), pp. 227–251.
4.
S.
Sanghi
and N.
Aubry
, “Mode interaction models for near wall turbulence
,” J. Fluid Mech.
247
, 455
(1993
).5.
D.
Armbruster
, J.
Guckenheimer
, and P.
Holmes
, “Heteroclinic cycles and modulated travelling waves in systems with O(2) symmetry
,” Physica D
29
, 257
(1988
).6.
S. A.
Campbell
and P.
Holmes
, “Bifurcation from O(2) symmetric heteroclinic cycles in systems with O(2) symmetry
,” Nonlinearity
4
, 697
(1991
).7.
N.
Aubry
, P.
Holmes
, J. L.
Lumley
, and E.
Stone
, “The dynamics of coherent structures in a turbulent boundary layer
,” J. Fluid Mech.
192
, 115
(1988
).8.
E.
Stone
and P.
Holmes
, “Noise-induced intermittency in a model of a turbulent boundary layer
,” Physica D
37
, 20
(1989
).9.
E.
Stone
and P.
Holmes
, “Random perturbations of heteroclinic attractors
,” SIAM J. Appl. Math.
50
, 726
(1990
).10.
E.
Stone
and P.
Holmes
, “Unstable fixed points, homoclinic orbits and exponential tails in turbulence production
,” Phys. Lett. A
155
, 29
(1991
).11.
G.
Berkooz
, P.
Holmes
, and J. L.
Lumley
, “Intermittent dynamics in simple models of the wall layer
,” J. Fluid. Mech.
230
, 75
(1992
).12.
C.
Foias
, O.
Manley
, and L.
Sirovich
, “Empirical and Stokes eigenfunctions in the far dissipative turbulent spectrum
,” Phys. Fluids A
2
, 464
(1990
).13.
Z. Herzog, “The large scale structure in the near-wall region of turbulent pipe flow,” Report No. FDA-86–07 Cornell University, Ithaca, NY, 1986.
14.
I.
Melbourne
, P.
Chossat
, and M.
Golubitsky
, “Heteroclinic cycles involving periodic solutions in mode interactions with O(2) symmetry
,” Proc. R. Soc. Edinburgh A
113
, 357
(1989
).15.
P. Holmes and E. Stone, “Heteroclinic cycles, exponential tails and intermittency in turbulence production, in Studies in Turbulence. In Recognition of Contributions by John Lumley, edited by T. Gatski, S. Sarkar, and C. Speziale (Springer-Verlag, Berlin, 1992), pp. 179–189.
16.
L.
Sirovich
, K. S.
Ball
, and L. R.
Keefe
, “Plane waves and structure in turbulent channel flow
,” Phys. Fluids A
2
, 2217
(1990
).17.
L.
Sirovich
, K. S.
Ball
, and R. A.
Handler
, “Propagating structures in wall-bounded turbulent flows
,” Theoret. Comput. Fluid Dyn.
2
, 307
(1991
).18.
J. O. Hinze, Turbulence (McGraw-Hill, New York, 1959).
This content is only available via PDF.
© 1994 American Institute of Physics.
1994
American Institute of Physics
You do not currently have access to this content.
