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

Kim Alards, Rudie Kunnen, R.J.A.M. Stevens, Detlef Lohse, Federico Toschi, Herman Clercx (Corresponding author)

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Abstract

In Rayleigh–Bénard convection (RBC) for fluids with Prandtl number Pr≳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 boundary layer (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 Roc occurs typically in the range 2.3≲Roc≲2.9 (for Rayleigh number Ra=1.3×109, Pr=6.7, and a convection cell with aspect ratio Γ=DH=1, with D the diameter and Hthe 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/Ro≲1/Roc (slow rotation), the well-known large-scale circulation (LSC) is found: a single domain-filling convection roll made up of many individual thermal plumes. At 1/Ro≳1/Roc (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, Roc2≈2.25(different from Roc1≈2.7 for the sharp transition in the Nusselt number Nu; 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 values and the kurtosis of the horizontal acceleration of these tracers show a sudden increase at Roc2. To better understand the nature of this transition we compute joint statistics of the Lagrangian velocity and acceleration of fluid particles and vertical vorticity near the top plate. It is found that for Ro≳2.25 there is hardly any correlation between the vertical vorticity and extreme acceleration events of fluid particles. For Ro≲2.25, however, vortical regions are much more prominent and extreme horizontal acceleration events are now correlated to large values of positive (cyclonic) vorticity. This suggests that the observed sudden transition in the acceleration statistics is related to thermal plumes with cyclonic vorticity developing in the Ekman BL and subsequently becoming mature and entering the bulk of the flow for Ro≲2.25.
Original languageEnglish
Article number074601
Pages (from-to)1-19
Number of pages19
JournalPhysical Review Fluids
Volume4
Issue number7
DOIs
Publication statusPublished - 3 Jul 2019

Bibliographical note

16 pages, 9 Figures

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