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Thermal convection in a gravitational field is the source of most large-scale flows on Earth, planets and stars. It is also used to heat houses or to cool passively with metal vanes, as for example in most electronic equipment. The driving force for thermal convection is buoyancy. When a fluid is heated it expands, i.e., it changes its mass density. If the fluid in a gravitational field and heating is applied in such a way that cold, dense fluid is on top of that which is warmer and lighter, the warm fluid will rise when the driving forces of buoyancy overcome viscous drag and thermal diffusion.
The experimentally best defined and most studied example is Rayleigh–Bénard convection (RBC), where a horizontal fluid layer is heated from below and cooled from above. For an incompressible fluid and Boussinesq conditions, where due to modest temperature gradients only the linear temperature dependence of density governs the physics, two dimensionless parameters describe the physics. One is the Rayleigh number, Ra, which is proportional to the temperature difference across the fluid layer of thickness, d, and to d3, implying that high Ra can be achieved experimentally at modest temperature differences only with a large d. The other parameter is the Prandtl number, Pr, which describes the relative importance of the convective nonlinearities in the momentum and heat equations. The geometry and thermal boundary conditions of the experimental apparatus are other important factors. Experiments usually strive to realize the theoretically most easily studied boundary conditions, i.e. perfectly conducting top and bottom plates and insulating sidewalls. As mentioned above, situations with large Ra require large cell heights. In experiments, typical geometries chosen are mostly cylindrical, with aspect ratios Γ = diameter/height between 1/4 and 2.
For RBC, the onset of convection in an infinitely extended layer between no-slip walls is independent of the Prandtl number and occurs at Ra = 1708 in the form of convection rolls, whose periodicity is given by the layer height. When the temperature difference, and thus the Rayleigh number, increases, i.e., to the order of Ra ~ 107 and larger, the fluid flow becomes turbulent in the bulk and the flow is controlled by instabilities at the boundary layer. The turbulent fluctuations in turn conspire to create large-scale sweeping flows, the so-called 'mean winds' that couple back to the boundary layer dynamics.
In addition to the idealized situation of RBC in a Boussinesq fluid, situations closer to the convective flows occuring in nature are of increasingly central interest. One such is the influence of rotation around a vertical axis, with its application to planetary flows, and another is convection with phase changes, with its application to convection and cloud formation in the atmosphere.
The global transport of heat and momentum is the persistent riddle in high-Rayleigh number turbulent convection. Detailed knowledge of the physics is required to better understand the energy budgets in the atmospheric flows of stars and planets. The fundamental challenge lies in basic physics, namely the understanding of the complex interaction of boundary layer instabilities, bulk turbulence, coupling to the large-scale sweeping flows, and the trends of the dynamics with increasing Rayleigh number.
In this focus issue, the cutting-edge questions of the field are addressed. How important are the boundary layers of the temperature and velocity fields for the global transport? Which flow structures are connected with the local transport processes of heat and momentum? Is there an 'ultimate' regime for heat transport for very high Rayleigh number? How are the transport properties affected when thermodynamic phase changes of the working fluid or rotation are present?
These are some of the topics discussed in the contributions to this issue, invited papers from around the world, comprising numerical, theoretical and experimental state-of-the-art works from this research field. We would like to thank all of the contributors for their efforts, and also the referees, whose careful revision added much value to each of the contributions. This focus issue gives a comprehensive overview of recent progress in this exciting and rapidly developing field.
