On the analogy between electromagnetism and turbulent hydrodynamics

In this note, we propose an exegesis of the Maxwell equations for electromagnetism. We begin with an analogy between the homogeneous Maxwell equations and the equations needed to describe the vorticity field of an incompressible inviscid fluid. We suggest that the inhomogeneous equations are analogous to two equations valid in turbulent hydrodynamics. Once the analogy is completed we give the mechanical analogue of the Poynting vector and we explain the influence of a long solenoid on the motion of a charged particle.