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Our understanding of the material organization of complex fluid flows hasrecently benefited from mathematical developments in the theory of objectivecoherent structures. These methods have provided a wealth of approaches thatidentify transport barriers in three-dimensional (3D) turbulent flows.Specifically, theoretical advances have been incorporated into numericalalgorithms that extract the most influential advective, diffusive and activebarriers to transport from data sets in a frame-indifferent fashion. To date,however, there has been very limited investigation into theseobjectively-defined transport barriers in 3D unsteady flows with complicatedspatiotemporal dynamics. Similarly, no systematic comparison of advective,diffusive and active barriers has been carried out in a 3D flow with boththermal and shear-driven features. In our study, we utilize simulations ofturbulent rotating Rayleigh-B\'enard convection to uncover the interplaybetween advective transport barriers (Lagrangian coherent structures), materialbarriers to diffusive heat transport and objective Eulerian barriers tomomentum transport. For a range of (inverse) Rossby numbers, we visualize eachtype of barrier and quantify their role as barriers to momentum and heattransport under changes in the relative influence of mechanical and thermalforces.

Interplay between advective, diffusive, and active barriers in Rayleigh-B\'enard flow