A Rossby-wave dynamo for the sun, I

There is increasing interest in the possible existence of large horizontally flowing eddies or 'Rossby waves' in the sun's convection zone and photosphere. We present here and in Part II a mathematical model which shows that flows of this type, driven by an assumed latitudinal temperature gradient, can act as hydromagnetic dynamos to induce magnetic fields that periodically reverse. In this part, we discuss the assumptions for the model, review earlier linear analyses that demonstrate the ability of Rossby waves to induce solar-like magnetic fields, and finally derive the non-linear equations that govern the model. The analysis is simplified by confining the fluid and magnetic fields to a thin rotating annulus. The flow is taken to be nearly incompressible, heliostrophic and hydrostatic. Induced magnetic fields are allowed to react upon the inducing motions. Transports of momentum and magnetic flux by smaller scale convective motions, and the transport of heat by these motions and radiation, are parameterized by diffusion coefficients. The solar convection is also assumed to be responsible for the latitudinal temperature gradient.