Pattern formation, boundary layer dynamics and turbulent heat transfer in Rayleigh-Bénard convection flows

Rayleigh-Bénard convection (RBC) in a fluid layer between two parallel walls, uniformly heated from below and cooled from above, is one of the fundamental flows with numerous applications in nature and technology. The three-dimensional Boussinesq equations which couple the velocity and temperature fields are studied by direct numerical simulations applying a spectral element method. We investigate two configurations of convection: (i) RBC in closed cylindrical cells at high Rayleigh numbers, the typical laboratory experiment configuration; (ii) RBC in horizontally extended domains at moderate Rayleigh numbers. We will discuss the global transport of heat and momentum and its close connection to the dynamics in the boundary layers of temperature and velocity fields at the walls for the first case. We will also present recent analysis results on the structure formation at large-scales for the second case. This includes the detection of defects in the time-averaged temperature and velocity patterns as well as Lagrangian trajectory-based methods that reveal how the heat is carried across the fluid layer.