Electrodynamics in a rotating frame of reference with application to global ocean circulation

The electrodynamic equations in a rotating reference frame (with velocities of rotation much less than the speed of light) are derived for the cases of a medium stationary in the rotating frame, and a medium with a general velocity relative to the rotating frame. The second case is considered as a necessary formalism for use in the modelling of large-scale electromagnetic fields induced by a prescribed ocean circulation. The terms that include rotational effects depend not only on the relative velocities but also on the electric properties of the material media. Hence, the assumption that rotational terms can be neglected simply because the velocities involved are much less than that of light in a vacuum is not supported. For typical values of the parameters describing the electric properties of the ocean, three of the four Maxwell equations (in Minkowskian form) are similar in form to those in an inertial frame. A governing induction equation in one vector variable (the magnetic field, b) is derived and written out explicitly in various coordinate systems.