The adjustment to Taylor's constraint in the presence of an ambient field

Abstract

The need to satisfy Taylor's constraint is probably the single most important constraint on the dynamics of planetary magnetic fields. We point out that the adjustment to Taylor's constraint is considerably more difficult in the Galilean moons of Jupiter than in the Earth, e.g., simply due to the presence of the ambient Jovian field. In particular, if the ambient field is of sufficient strength, weak field solutions are disallowed. The `default option' of falling back to an Ekman state, if Taylor's constraint cannot be satisfied in any other way, is therefore no longer available. The magnetic field must therefore be in a Taylor state, a model-Z state, or something else entirely, but it cannot be in an Ekman state. In this work, we present a simple model of magnetoconvection specifically designed to explore this adjustment to Taylor's constraint in the limit of vanishing viscosity, in the presence of an ambient field. We find that for a weak imposed thermal wind, the system approaches a Taylor state as the strength of the ambient field is increased. Strong thermal wind solutions behave in a very different manner. Initially, as the ambient field strength is increased, the system exhibits many features, indicating that a Taylor state is being approached. However, it never reaches a Taylor state, evolving instead to a model-Z state as the ambient field strength is increased yet further.