Lagrangian dynamics of a magnetoconvective flow

This study analyzes the transitions in Lagrangian orbits of a magnetoconvective flow resulting from variations in the Rayleigh and Hartmann numbers. The system is a cubic cell filled with an incompressible Newtonian fluid. The governing equations have been solved using the second-order time-splitting method combined with a pseudospectral method for spatial discretization, using the Chebyshev polynomials. One of the main findings is that, analogous to Hamiltonian systems, the KAM tori structure can be sequenced as a function of the orbit's frequency. The topological characterization of the flow is done using the rotation number Ω, which is a measure of the topological complexity of the flow. This organization facilitates understanding of how orbits are spatially arranged, making it easier to identify which orbits exhibit greater stability and which are more chaotic. The observed changes link symmetry-breaking phenomena to modifications in the topological structure of the Lagrangian flow, providing valuable insights into transport mechanisms. These findings have potential applications in fluid mixing, magnetically influenced convection, and the optimization of flow processes in engineering systems.