Fluid flows have been studied systematically for more than a century and their equations of motion are well known, yet the transition from laminar flow to turbulent flow remains an enigma. The difficulty lies in the intractability of the nonlinear hydrodynamic equations that express the conservation of mass, momentum and energy for a fluid continuum. Although these equations can be linearized and readily solved for a system near thermodynamic equilibrium, the solutions of the nonlinear equations—required to describe fluids far from equilibrium—are generally neither unique nor obtainable.

1.
S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Oxford U.P., London (1961);
D. D. Joseph, Stability of Fluid Motions I and II, Springer, New York (1976);
D. J. Tritton, Physical Fluid Dynamics, Van Nostrand Reinhold, New York (1977);
J. Whitehead, in Fluctuations, Instabilities and Phase Transitions (T. Riste, ed.).
Plenum, N.Y., (1975).
2.
R. M.
May
,
Nature
261
,
459
(
1976
);
Synergetics (H. Haken, ed.) Springer, New York (1977);
G. Nicolis, I. Prigogine, Self‐Organization in Nonequilibrium Systems, Wiley, New York (1977).
3.
G. I.
Taylor
,
Phil. Trans. Roy. Soc. (London) A
223
,
289
(
1923
).
4.
Lord
Rayleigh
,
Phil. Mag.
32
,
529
(
1916
).
5.
T. S. Durrani, C. A. Greated, Laser Systems in Flow Measurement, Plenum, New York (1977).
6.
G.
Ahlers
,
Phys. Rev. Lett.
33
,
1185
(
1974
);
G.
Ahlers
,
R.
Behringer
,
Phys. Rev. Lett.
40
,
712
(
1978
);
P.
Bergé
,
M.
Dubois
,
Opt. Comm.
19
,
129
(
1976
);
J. P.
Gollub
,
M. H.
Freilich
,
Phys. Fluids
19
,
618
(
1976
);
R. W.
Walden
,
R. J.
Donnelly
,
Bull. Am. Phys. Soc.
23
,
524
(
1978
).
7.
J. P.
Gollub
,
H. L.
Swinney
,
Phys. Rev. Lett.
35
,
927
(
1975
);
H. L. Swinney, P. R. Fenstermacher, J. P. Gollub, in Synergetics (H. Haken, ed.), Springer, New York (1977) page 60.
8.
E. N.
Lorenz
,
J. Atm. Sci.
20
,
448
(
1963
).
9.
A.
Davey
,
R. C.
DiPrima
,
J. T.
Stuart
,
J. Fluid Mech.
31
,
17
(
1968
);
R. M.
Clever
,
F. H.
Busse
,
J. Fluid Mech.
65
,
625
(
1974
).
10.
L.
Landau
,
C. R. (Dokl.) Acad. Sci. USSR
44
,
311
(
1944
);
L. D. Landau, E. M. Lifshitz, Fluid Mechanics, Pergamon, London (1959).
11.
T.
Li
,
J. A.
Yorke
,
Am. Math. Monthly
82
,
985
(
1975
).
12.
Ya
Sinai
,
Sov. Math.‐Dokl.
4
,
1818
(
1963
).
13.
D.
Ruelle
,
F.
Takens
,
Commun. Math. Phys.
20
,
167
(
1971
).
14.
J. B.
McLaughlin
,
P. C.
Martin
,
Phys. Rev. A
12
,
186
(
1975
).
15.
J. Kaplan, J. Yorke, E. Yorke, in Bifurcation Theory and Its Applications in Scientific Disciplines (O. Gurel, O. E. Rössler, eds.) N.Y. Acad. Sci., New York (1978).
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