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In this first part, a reduced model of the tachocline is derived in which the effects of compressibility and energy transport on the system are neglected; the meridional motions are driven instead by Ekman—Hartmann pumping. Through this simplification, the interaction of the fluid flow and the magnetic field can be isolated and is studied through non-linear numerical analysis for various field strengths and diffusivities.

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We find that after the inclusion of the meridional circulation, a tachocline can be formed even when the poloidal field lines are crossing the boundary between the radiative zone and the convection zone. We also discuss the effects of the magnetic Prandtl number as well as of the magnetic Reynolds number on the properties of the tachocline. However, the model requires the initial magnetic field to be in a narrow range to satisfy tachocline solutions.

The simulations including a stable temperature gradient produce a shallower as well as slower meridional circulation than the ones without it, as required from the lithium abundance at the solar surface. Data correspond to usage on the plateform after The current usage metrics is available hours after online publication and is updated daily on week days.

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