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Reversals of a large-scale field generated over a turbulent background

We present a study of several systems in which a large-scale field is generated over a turbulent background. These large-scale fields break a symmetry of the forcing by selecting a direction. Under certain conditions, the large-scale field displays reversals so that the symmetry of the forcing is recovered statistically. We present examples of such dynamics in the context of the dynamo instability, of two-dimensional turbulent Kolmogorov flows and of turbulent Rayleigh–Bénard convection. In these systems reversals occur respectively for the dynamo magnetic field, for the large-scale circulation generated by a periodic forcing in space and for the large-scale roll generated by turbulent thermal convection. We compare the mechanisms involved and show that their properties depend on some symmetries of the system and on the way they are broken.