Analogy between vortex waves and EM waves

Abstract

Listen

Translate article

Various analogies between fluid dynamics and electromagnetism can be found in the literature. It follows that the conservation equations of mass and momentum can be put in the form of Maxwell’s equations, with the convective acceleration corresponding to the electric field and the vorticity to the magnetic field. These equations are non linear because of the convective acceleration term. To obtain linear equations we decompose the variables in a stationary part representing equilibrium, and an unsteady part representing a deviation from equilibrium. Writing the conservation equations of mass and momentum with a first order approximation in the form of Maxwell’s equations allows us to put in relation the perturbation of pressure and velocity with the perturbation of vorticity and centripetal acceleration. These equations describe the oscillation of a vortex flow. An oscillating vortex is characterised by the oscillations of the centripetal acceleration and the vorticity fields which are comparable to the oscillations of the electric and magnetic fields. This analogy suggests that atmospheric phenomena such as tornadoes have a wavelike behaviour that is comparable to EM waves.