Multiple Transitions in Rotating Turbulent Rayleigh-Bénard Convection

Abstract

Sharp transitions between potentially different turbulent states are unexpected because one might think that they should be washed out by the prevailing intense fluctuations and short coherence lengths and times. Contrary to this expectation, we found a sequence of such transitions in turbulent rotating Rayleigh-Bénard convection as the rotation rate was increased. This phenomenon became most prominent at very large Rayleigh numbers up to 2 × 10 12 where the fluctuations are extremely vigorous. It was found in the heat transport as well as in the temperature gradient near the sample center. We conjecture that the transitions are between different large-scale structures which involve changes of symmetry and thus can not be gradual [5,6,7].It has been argued that Kolmogorov's theory of turbulence [4] implies that turbulent flows become featureless when the Reynolds number is large enough (for a discussion of this issue see for instance [2]). Apparently in contradiction to this expectation several experiments recently showed a sharp transition between two different turbulent states [9,8,10,1,2]. However, all of these investigations were carried out on systems with geometrical constraints in all physical directions, and it is not clear whether the sharp transitions are caused by boundary conditions or whether they would survive in an unconstrained system. Indeed for one of these systems, turbulent rotating Rayleigh-Bénard convection, measurements were made as a function of the lateral extent (aspect ratio) of the system, and it was found that the observed transition moves toward zero rotation rate as the lateral system size approaches infinity [12,11]. Here we report measurements of the heat transport, expressed in terms of the Nusselt number N u, and of the temperature gradient near the center of a cylindrical sample of fluid heated from below and rotated about its vertical axis at a rate Ω. The Prandtl number was 12.3, and the aspect ratio Γ (diameter over height) was 1.00. The rotation rate is expressed in terms of the inverse Rossby number which is proportional to Ω. Results are shown in Fig. 1. They reveal three sharp continuous transitions. The first, identified as 1/Ro c , was found previously for P r ≃ 4 and is associated with the onset of the formation of Ekman vortices which enhance the heat transport by extracting fluid from thermal boundary layers near the plates. It was shown to approach zero as Γ → ∞ and thus it is not a feature of the laterally unbounded system. The second and third transitions are found at 1/Ro c,2 ≃ 0.492 and 1/Ro c,3 ≃ 1.55 for Ra = 2.07 × 10 11 . While 1/Ro c,2 seems independent of Ra, 1/Ro c,3 is smaller for smaller Ra.

Thermal convection in inclined cylindrical containers

“…When the parameter β also varies, the situation becomes even more complicated, as with increasing β the onset of turbulence moves to larger Ra. Moreover, with changing β, the symmetries of the flow change, influencing the Nu(Ra, Pr, β) and Re(Ra, Pr, β) dependences (see also Wei, Weiss & Ahlers (2015) on sharp transitions in RBC, caused by changes of flow symmetries).…”

Geometry of tracer trajectories in rotating turbulent flows

“…The boundary layer is a special region of the flow, where the typical statistical characteristics of bulk turbulence are not applicable anymore [26,27]. In RBC, the boundary layer dynamics is significantly influenced by rotation [13,14] and moreover plays an important role in the transition to the enhanced heat flux state, mentioned before [8,15]. More precisely, a transition is observed from a Prandtl-Blasius boundary layer for lower rotation rates, to an Ekman boundary layer for higher rotation rates [13].…”

“…In RBC the flow is buoyancy driven: a fluid is heated from below and cooled from above. Rotating a RBC system around its vertical axis induces sharp transitions in the heat flux and boundary layer dynamics and a significant change of the dominant coherent flow structures [8,[13][14][15].…”

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

“…In RBC, however, sudden transitions between different turbulent states do occur when the set-up is rotated about its vertical axis (see, e.g, [9][10][11][12][13][14][15][16][17][18][19]). These turbulent states are typically characterized by different large-scale coherent flow structures and different Table I: Several values for the critical Rossby number Ro c as found in numerical simulations [10,11,16] and experiments [11,12,[14][15][16][17]. Note that the estimated value for Ro c reported by Wei et al [17] is based on the same dataset as the one reported by Zhong and Ahlers for the case with P r = 4.38 [12,15].…”

“…These turbulent states are typically characterized by different large-scale coherent flow structures and different Table I: Several values for the critical Rossby number Ro c as found in numerical simulations [10,11,16] and experiments [11,12,[14][15][16][17]. Note that the estimated value for Ro c reported by Wei et al [17] is based on the same dataset as the one reported by Zhong and Ahlers for the case with P r = 4.38 [12,15]. For all these cases convection cells with Γ = 1 are considered.…”