On a formal equivalence between electro-magnetic waves in cold plasma and shallow water inertio-gravity waves

TL;DR

This paper demonstrates a formal mathematical equivalence between electromagnetic waves in cold plasma and inertio-gravity waves in shallow water, revealing deep connections between these physical systems.

Contribution

It establishes a formal equivalence in the governing linearized equations, linking plasma physics and geophysical fluid dynamics.

Findings

Dispersion relations are formally equivalent

Coriolis frequency corresponds to plasma frequency

Shallow water wave speed relates to light speed

Abstract

The fundamental dispersion relation of transverse electro-magnetic waves in a cold collisionless plasma is formally equivalent to the two dimensional dispersion relation of inertio-gravity waves in a rotating shallow water system, where the Coriolis frequency can be identified with the plasma frequency, and the shallow water gravity wave phase speed plays the role of the speed of light. Here we examine this formal equivalence in the governing linearised equations, and compare between the propagation wave mechanisms in these seemingly unrelated physical systems.