Analogy between the Navier–Stokes equations and Maxwell’s equations: Application to turbulence

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 dy...

[1]  Erik Mollo-Christensen,et al.  Jet Noise and Shear Flow Instability Seen From an Experimenter’s Viewpoint , 1967 .

[2]  A. Townsend,et al.  Equilibrium layers and wall turbulence , 1961, Journal of Fluid Mechanics.

[3]  P. Moin,et al.  Ejection mechanisms in the sublayer of a turbulent channel , 1987 .

[4]  Alexander M. Rubenchik,et al.  Hamiltonian approach to the description of non-linear plasma phenomena , 1985 .

[5]  G. Russakoff,et al.  A Derivation of the Macroscopic Maxwell Equations , 1970 .

[6]  C. Truesdell The Kinematics Of Vorticity , 1954 .

[7]  R. Kraichnan,et al.  Depression of nonlinearity in decaying isotropic turbulence , 1988 .

[8]  J. Liu Contributions to the understanding of large-scale coherent structures in developing free turbulent shear flows , 1988 .

[9]  J. Lumley,et al.  A model for large-scale structures in turbulent shear flows , 1995, Journal of Fluid Mechanics.

[10]  J. Wu,et al.  Vorticity Dynamics on Boundaries , 1996 .

[11]  M. Landahl,et al.  A wave-guide model for turbulent shear flow , 1967, Journal of Fluid Mechanics.

[12]  Gregory Falkovich,et al.  Kolmogorov Spectra of Turbulence I: Wave Turbulence , 1992 .

[13]  A. Hussain,et al.  The mechanics of an organized wave in turbulent shear flow , 1970, Journal of Fluid Mechanics.

[14]  D. Küchemann,et al.  Report on the I.U.T.A.M. symposium on concentrated vortex motions in fluids , 1965, Journal of Fluid Mechanics.

[15]  A. Townsend The Structure of Turbulent Shear Flow , 1975 .

[16]  J. T. Stuart On the non-linear mechanics of hydrodynamic stability , 1958, Journal of Fluid Mechanics.

[17]  Jiezhi Wu,et al.  Reduced Stress Tensor and Dissipation and the Transport of Lamb Vector , 1996 .

[18]  P. Dimotakis,et al.  The mixing layer at high Reynolds number: large-structure dynamics and entrainment , 1976, Journal of Fluid Mechanics.

[19]  O. V. Troshkin Perturbation waves in turbulent media , 1993 .

[20]  H. Schlichting Boundary Layer Theory , 1955 .

[21]  Sir William Thomson F.R.S. XLV. On the propagation of laminar motion through a turbulently moving inviscid liquid , 1887 .

[22]  Sanjoy Banerjee,et al.  Experiments on the structure of turbulence in fully developed pipe flow: interpretation of the measurements by a wave model , 1977, Journal of Fluid Mechanics.

[23]  M. Lighthill On sound generated aerodynamically I. General theory , 1952, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.