Sharp transitions in rotating turbulent convection: Lagrangian acceleration statistics reveal a second critical Rossby number

Kim M. J. Alards; Rudie P. J. Kunnen; Richard J. A. M. Stevens; Detlef Lohse; Federico Toschi.; Herman J. H. Clercx

doi:10.1103/PhysRevFluids.4.074601

paper

Sharp transitions in rotating turbulent convection: Lagrangian acceleration statistics reveal a second critical Rossby number

arXiv:1907.02451 · doi:10.1103/PhysRevFluids.4.074601

Abstract

In RB convection for fluids with Prandtl number $P r ≳ 1$ , rotation beyond a critical (small) rotation rate is known to cause a sudden enhancement of heat transfer which can be explained by a change in the character of the BL dynamics near the top and bottom plates of the convection cell. Namely, with increasing rotation rate, the BL signature suddenly changes from Prandtl--Blasius type to Ekman type. The transition from a constant heat transfer to an almost linearly increasing heat transfer with increasing rotation rate is known to be sharp and the critical Rossby number $R o_{c}$ occurs typically in the range $2.3 ≲ R o_{c} ≲ 2.9$ (for Rayleigh number $R a = 1.3 \times 1 0^{9}$ , $P r = 6.7$ , and a convection cell with aspect ratio $Γ = \frac{D}{H} = 1$ , with $D$ the diameter and $H$ the height of the cell). The explanation of the sharp transition in the heat transfer points to the change in the dominant flow structure. At $1/ R o ≲ 1/ R o_{c}$ (slow rotation), the well-known LSC is found: a single domain-filling convection roll made up of many individual thermal plumes. At $1/ R o ≳ 1/ R o_{c}$ (rapid rotation), the LSC vanishes and is replaced with a collection of swirling plumes that align with the rotation axis. In this paper, by numerically studying Lagrangian acceleration statistics, related to the small-scale properties of the flow structures, we reveal that this transition between these different dominant flow structures happens at a second critical Rossby number, $R o_{c_{2}} \approx 2.25$ (different from $R o_{c_{1}} \approx 2.7$ for the sharp transition in the Nusselt number $N u$ ; both values for the parameter settings of our present numerical study). When statistical data of Lagrangian tracers near the top plate are collected, it is found that the root-mean-square (rms) values and the kurtosis of the horizontal acceleration of these tracers show a sudden increase at $R o_{c_{2}}$ .

arXiv comment16 pages, 9 Figures

Sharp transitions in rotating turbulent convection: Lagrangian acceleration statistics reveal a second critical Rossby number

Abstract

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