Three-dimensional modelling of ocean electrodynamics using gauged potentials

Abstract

It is appreciated that one of the ‘bottlenecks’ in understanding low-frequency electrodynamical processes in the solid earth, oceans, and lower atmosphere is the limitations of current numerical models capable of simulating realistic 3-D aspects of these phenomena. The limitations have primarily been set by the computational demands of such calculations, as well as by the fact that the numerical implementation of the Maxwell equations can be at times cumbersome when compared with formulations such as the heat equation, which afford simple intuitive numerical implementation based on simple flux conservations. Here we discuss the advantages of formulations based on the electromagnetic gauge potentials. This formulation appears to offer several advantages. Some, for instance the continuity of these potentials (as opposed to the discontinuous electric field, for example), are well known. Others, however, do not appear—at least explicitly—to have been previously examined. For frequency-domain studies, we note that the gauge formulation can be written as a generic set of coupled elliptic equations, allowing a simple modular numerical approach using simple conservation principles. More importantly, by writing the governing equations using gauge potentials, an extra degree of freedom is introduced into the system. We show that this extra degree of freedom can be exploited to increase performance, accuracy, and simplicity. We have implemented the gauge approach in a 3-D numerical model which we call MOED (Model for Ocean ElectroDynamics). We validate the formulation as well as the software by comparing MOED results with several analytical and numerical results taken from oceanographic and geophysical applications.