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Rotating turbulent thermal convection at large Rayleigh numbers

Subject Area Fluid Mechanics
Term from 2017 to 2022
Project identifier Deutsche Forschungsgemeinschaft (DFG) - Project number 324106305
 
Final Report Year 2022

Final Report Abstract

In this project we wanted to investigate the influence of rotation on the heat transport and the flow structure in Rayleigh–B´nard convection. The goal was to reach very high Ra up to 1015 by using pressurised sulfur-hexafluoride in a 2.20 m tall cylindrical cell. With this we wanted to enter the regime of geostrophic turbulence and which is relevant for many geo- and astrophysical systems such as the Earths’ atmosphere. While experimental measurements at such large Ra allow for very good temporal statistics, temperature measurements could only be done at very few locations and hence we utilised direct numerical simulations in order to gain a highly resolved and detailed view of the entire velocity and temperature field, albeit at significantly smaller Ra. We have conducted comprehensive heat flux measurements for Ra over 5 decades up to Ra = 8 × 10^14 for Pr ≈ 0.8 and have investigated the transition between the buoyancy dominated to the rotation dominated regime with increasing rotation rates. Furthermore, we have measured and analysed the temperature close to the sidewall. The most important finding was the boundary zonal flow (BZF), a new unexpected flow structure close to the sidewall of our cylindrical convection cell. In a cell of aspect ratio between its diameter and height of Γ = D/H = 0.5 the BZF occurs in a thin area of width δ0 where warm fluid is transported along one side from the bottom to the top whereas cold fluid is transported on the opposite side from the top to the bottom. Hence, both the vertical velocity as well as the temperature are periodic as a function of the azimuthal angle, with wave number of k = 1. Inside this region, the azimuthal velocity is positive (cyclonic), whereas the structure itself moves against the rotation of the cylinder (anticyclonic). We have also measured experimentally and numerically the drift rates and the width of the BZF, as well as the maximal time-averaged azimuthal velocity of the BZF and its radial location as function of the control parameters Ra, Pr, and Ek, both in the experiment and DNS. Direct numerical simulations for 0.1 ≤ Pr ≤ 12.3, 10^7 ≤ Ra ≤ 5 × 10^9 , 105 ≤ 1/Ek ≤ 10^7 and Γ = 1/3, 1/2, 3/4, 1 and 2 show that the BZF width δ0 scales with the Rayleigh number Ra and Ekman number Ek as δ0 /H ∼ Γ^0 Pr^{−1/4,0} Ra1/4 Ek2/3 ({Pr < 1, Pr > 1}) and the drift frequency as ω/Ω ∼ Γ^0 Pr^−4/3 RaEk^5/3 , where H is the cell height and Ω the angular rotation rate. The mode number of the BZF is 1 for Γ 1 and 2Γ for Γ = {1,2} independent of Ra and Pr. The BZF is quite reminiscent of wall mode states in rotating convection. In summary, this project was very successful. It has led to 10 peer-reviewed publication in high-ranked journals such as Physical Review Letters or the Journal of Fluid Mechanics. Our first paper on the discovery of the boundary zonal flow by Zhang et al. (2020) has by now been cited already 33 times according to Google Scholar, showing a significant impact on the community.

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