Some travels in the land of nonlinear convection and magnetism

Rotating stars with convection zones are the great builders of magnetism in our universe. Seeking to understand how turbulent convection actually operates, and so too the dynamo action that it can achieve, has advanced through distinctive stages in which Jean-Paul Zahn was often a central player, or joined by his former students. Some of the opening steps in dealing with the basic nonlinearity in such dynamics involved modal equations (with specified horizontal structure) to study convective amplitudes and heat transports achieved as solutions equilibrated by feeding back on the mean stratification. These dealt in turn with laboratory convection, with penetrative convection in Boussinesq settings, then with compressible penetration via anelastic equations in simple geometries, and finally with stellar penetrative convection in A-type stars that coupled two convection zones. Advances in computation power allowed 2-D fully compressible simulations, and then 3-D modeling including rotation, to revisit some of these convection and penetration settings within planar layers. With externally imposed magnetic fields threading the 2-D layers, magnetoconvection could then be studied to see how the flows concentrated the fields into complex sheets, or how new classes of traveling waves could result. The era of considering turbulent convection in rotating spherical shells had also arrived, using 3-D MHD codes such as ASH to evaluate how the solar differential rotation is achieved and maintained. Similarly the manner in which global magnetic fields could be built by dynamo action within the solar convection zone took center stage, finding that coherent wreaths of strong magnetism could be built, and also cycling solutions with field reversals. The coupling of convection and magnetism continues as a vibrant research subject. It is also clear that stars like the Sun do not give up their dynamical mysteries readily when highly turbulent systems are at play