Turbulent rotating Rayleigh-Bénard convection: the geostropic regime

Most geo- and astrophysical flows are driven by strong thermal forcing and affected by high rotation rates. In these systems, direct measurements of the physical quantities are not possible due to their large scales, remoteness and complexity. Turbulent rotating Rayleigh-Bénard convection (RRBC) represents a model that contains the main physical constituents: it consists of a rotating fluid layer heated from below and cooled from above. Two approaches are generally popular to investigate flow and transport properties of RRBC under these extreme conditions: 1) laboratory experiments in (slender) cylindrical convection cells and 2) numerical simulations of thermally-driven turbulence in horizontally-periodic domains between parallel (heated and cooled) plates.

Background rotation causes different flow structures and heat transfer efficiencies in turbulent RRBC. Three main regimes are known: rotation-unaffected (regime I), rotation-affected (regime II) and rotation-dominated (regime III). Regimes I and II are easily accessible with experiments and numerical simulations, thus they have been extensively studied during the last two decades, see for a recent review [1]. On the other hand, access to regime III is more challenging [2-4]. In this talk I will first introduce briefly the role of rotation on fluid flows and turbulence. Subsequently, I will focus in this talk on regime III, including the geostrophic turbulence regime. With the experimental setup TROCONVEX, proposed by Rudie Kunnen [5], an investigation of parameters closer than ever before to the ones of geo- and astrophysical flows has become possible. Results from flow measurements based on this unique experimental setup, using stereoscopic particle image velocimetry, will be presented. We will in particular discuss the large-scale organization of the flow [3] and compare this with available numerical results. A significant discrepancy in total heat transport is observed between experimental data obtained from the confined cylindrical domain (like TROCONVEX) and numerical data obtained from simulations on a horizontally-periodic domain. This discrepancy is further explored with direct numerical simulations on a cylindrical domain [6]. An analysis of the flow field reveals a region of enhanced convection near the wall, the sidewall circulation. We will discuss that bulk heat transfer in cylindrical convection cells are nevertheless representative for heat transfer in laterally unbounded (or horizontally-periodic) domains, at least for the parameter regime under consideration. This makes this kind of laboratory setups suitable for exploring the geostrophic turbulent regime in the lab.  

[1] R. Stevens, H. Clercx & D. Lohse, EJMB/F 40, 41-49 (2013).

[2] H. Rajaei, R. Kunnen & H. Clercx, PoF 29, 045105 (2017).

[3] M. Madonia, A. Aguirre Guzmán, H. Clercx & R. Kunnen, EPL 135, 54002 (2021).

[4] R. Kunnen, JoT 22, 267-296 (2021).        

[5] R. Kunnen, European Research Council (ERC), grant number 678634.         

[6] X. de Wit, A. Aguirre Guzman, M. Madonia, J. Cheng, H. Clercx & R. Kunnen, PRF 5, 023502 (2020).