6.8 Where do we go from here?

Recent years have witnessed a number of significant advances in solar cycle modelling. Local magnetohydrodynamical simulations of thermally-driven convection have now allowed measurements of the α-tensor, and of its variation with depth and latitude in the solar interior, and with rotation rate; and global magnetohydrodynamical simulation of solar convection are now producing large-scale magnetic fields, in some cases even undergoing polarity reversals on decadal timescales. Such simulations are ideally suited for investigating a number of important issues, such as the mechanism(s) responsible for regulating the amplitude of the solar cycle, the magnetically-driven temporal variations of the large-scale flows important for the solar cycle, and the possible impact of a cycling large-scale magnetic field on convective energy transport, to mention but a few.

Despites continuing advances in computing power, global MHD simulations remain extremely demanding, and proper capture of important solar cycle elements —most notably the formation, emergence and surface decay sunspots and active regions— are certainly not forthcoming. Nonetheless, comparison between cyclic solutions arising in full numerical simulations and those characterizing simpler mean-field-like models should also allow to test the validity limit of the kinematic approximation and of the simple algebraic amplitude-limiting nonlinearities still so prevalent in the latter class of solar cycle models. It appears likely that in the foreseeable future, the simpler, mean-field and mean-field-like solar cycle models reviewed here will remain the workhorses of research on long timescale phenomena such as grand activity minima and maxima, on the evolution of surface magnetic flux, on dynamo-model-based solar cycle prediction, and on the modelling and interpretation of stellar activity cycles.

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