What problem is addressed?
Rayleigh-Bénard (RB) convection, which involves fluid flow in a box heated from below and cooled from above, serves as a fundamental model in fluid dynamics. It is used to test concepts such as non-linear dynamics, pattern formation, and turbulence. RB convection is particularly ideal for examining the interactions between boundary layers and bulk fluid dynamics. Additionally, turbulent thermal convection is crucial in a wide range of natural and industrial settings, from astrophysical and geophysical flows to process engineering. The paradigmatic representation of thermal convection is RB flow. A major challenge is to determine the scaling relation of the Nusselt number (Nu), i.e. the dimensionless heat transport, with the Rayleigh number (Ra), which is the dimensionless temperature difference between the two plates, expressed as Nu~Ra^gamma. Theory predicts that the scaling exponent gamma increases for extremely strong driving when the boundary layers transition from laminar to turbulent. Understanding the transition to this so-called ‘ultimate’ regime is crucial since an extrapolation of results from lab-scale experiments and simulations to astro- and geophysical phenomena becomes meaningless when the transition to this ‘ultimate’ state is not understood. So far, there is no consensus among experimental efforts for obtaining the ‘ultimate’ regime. We propose using direct numerical simulations (DNS) to gain a better understanding of the transition towards the ‘ultimate’ regime. While obtaining ‘ultimate’ thermal convection in simulations has been elusive, new developments make this feasible now. The benefit of simulations is that they allow full access to the flow and temperature fields, while all boundary conditions are set exactly and independently. This allows us to test various physical effects at full dynamic similarity. To trigger the excitation of the ‘ultimate’ regime at lower Ra than in standard small aspect ratio cells, we want to study the effect of roughness, additional shear, and large domains in which a stronger flow can develop than in confined small aspect ratio cells that are traditionally considered. The addition of rotation will be studied to disentangle the complicated effect of rotation on high Ra number thermal convection.
Why is it important for society?
Fluid dynamics and turbulence are key areas in physics, applied mathematics, and engineering with applications in industries like process technology, automotive, and transportation. They are essential in diverse environments, including the atmosphere and oceans, as well as in geophysical and astrophysical studies. The simulation tool AFiD, which is publicly available, to explore turbulent flows with great precision. AFiD supports simulations of canonical flows. Given its capacity to handle the exact balance of driving forces and dissipation rates, the RB system is highly effective for developing new criteria for simulating highly turbulent flows. The methodologies and insights from this project will significantly impact the broader field of fluid dynamics.
What are the overall objectives?
Developing groundbreaking DNS to enhance our understanding of very high Ra number convection; project objectives include
* Developing a code to perform DNS of 'ultimate' RB convection
* Study impact of superstructures on the fundamental properties of thermal convection
* Model heat transfer in rotating high Ra number convection
Conclusions
The methodologies, simulation methods, and scientific discoveries related to the physical phenomena have been thoroughly documented and are accessible to the scientific communities. The developed software is publicly available at:
* AFiD software: github.com/PhysicsofFluids/AFiD
* GPU-version: github.com/PhysicsofFluids/AFiD_GPU_opensource
* AFiD-MuRPhFi: github.com/chowland/AFiD-MuRPhFi
