Sharp transitions in rotating turbulent convection: Lagrangian acceleration statistics reveal a second critical Rossby number
Abstract
In RB convection 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 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 =DH=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/Ro 1/Roc (slow rotation), the well-known 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 (rms) values and the kurtosis of the horizontal acceleration of these tracers show a sudden increase at Roc2.