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 $({w}={\nabla \times u})$ and the Lamb vector $({l}={w\times u})$ 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.