A new theory of turbulence is initiated, based on the analogy between electromagnetism and turbulent hydrodynamics, for the purpose of describing the dynamical behavior of averaged flow quantities in incompressible fluid flows of high Reynolds numbers. The starting point is the recognition that the vorticity (w=∇×u) and the Lamb vector (l=w×u) should be taken as the kernel of a dynamical theory of turbulence. The governing equations for these fields can be obtained by the Navier–Stokes equations, which underlie the whole evolution. Then whatever parts are not explicitly expressed as a function of w or l only are gathered and treated as source terms. This is done by introducing the concepts of turbulent charge and turbulent current. Thus we are led to a closed set of linear equations for the averaged field quantities. The premise is that the earlier introduced sources will be apt for modeling, in the sense that their distribution will depend only on the geometry and the total energetics of the flow. The dynamics described in the preceding manner is what we call the metafluid dynamics.

1.
M. J.
Lighthill
, “
On sound generated aerodynamically. I. General theory
,”
Proc. R. Soc. London, Ser. A
211
,
564
(
1952
).
2.
C. Truesdell, The Kinematics of Vorticity (Indiana U. P., Bloomington, 1952).
3.
M. J. Lighthill, “Introduction: Boundary layer theory,” in Laminar Boundary Layer, edited by L. Rosenhead, (Oxford U.P., Oxford, 1963), pp. 46–113.
4.
J. Z.
Wu
and
J. M.
Wu
, “
Vorticity dynamics on boundaries
,”
Adv. Appl. Mech.
32
,
119
(
1996
).
5.
D.
Küchemann
, “
Report on the IUTAM Symposium on concentrated vortex motions in fluids
,”
J. Fluid Mech.
21
,
1
(
1965
).
6.
R. H.
Kraichnan
and
R.
Panda
, “
0epression of nonlinearity in decaying isotropic turbulence
,”
Phys. Fluids
31
,
2395
(
1988
).
7.
J. Z. Wu, Y. Zhou, and J. M. Wu, Reduced stress tensor and dissipation and the transport of Lamb vector, ICASE Rept. 96-21, (1996).
8.
P. M. Morse and H. Feshbach, Methods of theoretical physics (McGraw–Hill, New York, 1953).
9.
O. V.
Troshkin
, “
Perturbation waves in turbulent media
,”
Zh. Vychisl. Mat. Mat. Fiz.
33
,
1844
(
1993
).
10.
J. D. Jackson, Classical Electrodynamics (J. Wiley, New York, 1975).
11.
G.
Russakoff
, “
A derivation of the macroscopic Maxwell equations
,”
Am. J. Phys.
38
,
1188
(
1970
).
12.
H. Schlichting, Boundary Layer Theory, 7th ed. (McGraw–Hill, New York, 1979).
13.
C. Crawford and G. Em. Karniadakis, Shear stress modification and vorticity dynamics in near-wall turbulence, Tech. Rept.CFM 96-2 (Center for Fluid Mechanics, Brown Univ., Providence, 1996).
14.
E. L. Mollo-Christensen, “Jet noise and shear-flow instability seen from an experimenter’s viewpoint,” ASME J. Appl. Mech. Ser. E, 89, (1967).
15.
A. K. M. F.
Hussain
and
W. C.
Reynolds
, “
The mechanics of an organized wave in turbulent shear flow
,”
J. Fluid Mech.
41
(
2
),
241
(
1970
).
16.
P. E.
Dimotakis
and
G. L.
Brown
, “
The mixing layer at high Reynolds number: large-structure dynamics and entrainment
,”
J. Fluid Mech.
78
,
535
(
1976
).
17.
T. R.
Heidrick
,
S.
Banerjee
, and
R. S.
Azad
, “
Experiments on the structure of turbulence in fully developed pipe flow: interpretation of the measurements by a wave model
,”
J. Fluid Mech.
81
,
137
(
1977
).
18.
J.
Jimenez
,
P.
Moin
,
R.
Moser
, and
L.
Keefe
, “
Ejection mechanisms in the sublayer of a turbulent channel
,”
Phys. Fluids
31
,
1311
(
1988
).
19.
W.
Thomson
, “
On the propagation of laminar motion through a turbulently moving inviscid liquid
,”
Philos. Mag.
4
(
47
),
342
(
1887
).
20.
M. T.
Landahl
,“
A wave-guide model for turbulent shear flow
,”
J. Fluid Mech.
29
,
441
(
1967
).
21.
O. V. Troshkin, The Wave Theory of Turbulence (VTs Akad. Nauk S.S.S.R., Moscow, 1989).
22.
J. T. C.
Liu
, “
Contributions to the understanding of large-scale coherent structures in Developing Free Turbulent Shear Flows
,”
Adv. Appl. Mech.
26
,
183
(
1988
).
23.
J. T.
Stuart
, “
On the nonlinear mechanics of hydrodynamic stability
,”
J. Fluid Mech.
4
,
1
(
1958
).
24.
A. C.
Poje
and
J. L.
Lumley
, “
A model for large-scale structures in turbulent shear flows
,”
J. Fluid Mech.
285
,
349
(
1995
).
25.
V. E.
Zakharov
,
S. L.
Musher
, and
A. M.
Rubenchik
, “
Hamiltonian approach to the description of non-linear plasma phenomena
,”
Phys. Rep.
129
(
5
),
285
(
1985
).
26.
V. E. Zakharov, V. S. L’vov, and G. Falkovich, Kolmogorov Spectra of Turbulence I. Wave Turbulence (Springer-Verlag, New York, 1992).
27.
A. A.
Townsend
, “
Equilibrium layers and wall turbulence
,”
J. Fluid Mech.
11
,
97
(
1961
).
28.
A. A. Townsend, The Structure of Turbulent Shear Flow, 2nd ed. (Cambridge U.P., Cambridge, 1976).
29.
M. J. Lighthill, “The outlook for a wave theory of turbulent shear flow,” in Proc. Comp. Turbulent Boundary Layers, edited by S. J. Kline, M. V. Morkovin, G. Sovran, and D. J. Cockrell (Stanford U.P., Stanford, 1969), Vol. 1, pp. 511–520.
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