SignificanceThe large-scale circulation (LSC) is the key dynamical feature of turbulent thermal convection. It is the underlying structure that shapes the appearance of geo- and astrophysical systems, such as the solar granulation or cloud streets, and the cornerstone of theoretical models. Our laboratory-numerical experiments reveal that the LSC can perform a fully 3D motion resembling a twirling jump rope. The discovery of this LSC mode implies that the currently accepted paradigm of a quasi-planar oscillating LSC needs to be augmented. Moreover, it provides an important link between studies in confined geometries used in experiments and simulations and the effectively unconfined fluid layers in natural settings where an agglomeration of LSCs forms larger patterns.

We report a new thermal boundary layer equation for turbulent Rayleigh-Bénard convection for Prandtl number Pr > 1 that takes into account the effect of turbulent fluctuations. These fluctuations are neglected in existing equations, which are based on steady-state and laminar assumptions. Using this new equation, we derive analytically the mean temperature profiles in two limits: (a) Pr 1 and (b) Pr ≫ 1. These two theoretical predictions are in excellent agreement with the results of our direct numerical simulations for Pr = 4.38 (water) and Pr = 2547.9 (glycerol) respectively.PACS numbers: 44.20.+b, 44.25.+f, 47.27.ek, 47.27.te Turbulent Rayleigh-Bénard convection (RBC) [1][2][3][4][5], consisting of a fluid confined between two horizontal plates, heated from below and cooled from above, is a system of great research interest. It is a paradigm system for studying turbulent thermal convection, which is ubiquitous in nature, occurring in the atmosphere and the mantle of the Earth as well as in stars like our Sun. Convective heat transfer is also an important problem in engineering and technological applications. The state of fluid motion in RBC is determined by the Rayleigh number Ra = αg∆H 3 /(κν) and Prandtl number Pr = ν/κ. Here α denotes the isobaric thermal expansion coefficient, ν the kinematic viscosity and κ the thermal diffusivity of the fluid, g the acceleration due to gravity, ∆ the temperature difference between the bottom and top plates, and H the distance between the plates.In turbulent RBC, there are viscous boundary layers (BLs) near all rigid walls and two thermal BLs, one above the bottom plate and one below the top plate. We denote the thicknesses of the viscous and thermal BLs by l and λ respectively. Both viscous and thermal BLs play a critical role in the turbulent heat transfer of the system and in particular λ is inversely proportional to the heat transport. Grossmann and Lohse (GL) [6], [7] developed a scaling theory of how the Reynolds number Re, determined by the mean large-scale circulation velocity U 0 above the viscous BL, and the dimensionless Nusselt number Nu, measuring the heat transport, depend on Ra and Pr for moderate Ra. The theory makes explicit use of the result l/H ∝ Re −1/2 with the proportionality constant depending only on Pr. This result follows from the assumptions that the BLs are laminar and their mean profiles, averaged over time, are described by the Prandtl-Blasius-Pohlhausen (PBP) theory [8-10] for steady-state forced convection above an infinite weakly-heated plate. Although the GL theory gives perfect agreement with the heat transport measurements, the assumption that the BLs are described by PBP theory is not fulfilled. Systematic deviations of the mean velocity and temperature profiles from the PBP predictions have been reported both in experiments and in direct numerical simulations (DNS) [11][12][13][14][15]. These deviations remain even after a dynamical rescaling procedure [16] that takes into account of the time variations of λ is used, and increase ...

For rapidly rotating turbulent Rayleigh-Bénard convection in a slender cylindrical cell, experiments and direct numerical simulations reveal a boundary zonal flow (BZF) that replaces the classical large-scale circulation. The BZF is located near the vertical side wall and enables enhanced heat transport there. Although the azimuthal velocity of the BZF is cyclonic (in the rotating frame), the temperature is an anticyclonic traveling wave of mode one whose signature is a bimodal temperature distribution near the radial boundary. The BZF width is found to scale like Ra 1/4 Ek 2/3 where the Ekman number Ek decreases with increasing rotation rate.Turbulent fluid motion driven by buoyancy and influenced by rotation is a common phenomenon in nature and is important in many industrial applications. In the widely studied laboratory realization of turbulent convection, Rayleigh-Bénard convection (RBC) [1, 2], a fluid is confined in a convection cell with a heated bottom, cooled top, and adiabatic vertical walls. For these conditions, a large scale circulation (LSC) arises from cooperative plume motion and is an important feature of turbulent RBC [1]. The addition of rotation about a vertical axis produces a different type of convection as thermal plumes are transformed into thermal vortices, over some regions of parameter space heat transport is enhanced by Ekman pumping [3][4][5][6][7][8][9][10], and statistical measures of vorticity and temperature fluctuations in the bulk are strongly influenced [11][12][13][14][15][16][17]. A crucial aspect of rotation is to suppress, for sufficiently rapid rotation rates, the LSC of non-rotating convection [12,13,18,19], although the diameter-to-height aspect ratio Γ = D/H appears to play some role in the nature of the suppression [20].In RBC geometries with 1/2 ≤ Γ ≤ 2, the LSC usually spans the cell in a roll-like circulation of size H. For rotating convection, the intrinsic linear scale of separation of vortices is reduced with increasing rotation rate [21,22], suggesting that one might reduce the geometric aspect ratio, i.e., Γ < 1 while maintaining a large ratio of lateral cell size to linear scale [5]; such convection cells are being implemented in numerous new experiments [23]. Thus, an important question about rotating convection in slender cylindrical cells is whether there is a global circulation that substantially influences the internal state of the system and carries appreciable global heat transport. Direct numerical simulations (DNS) of rotat-ing convection [24] in cylindrical geometry with Γ = 1, inverse Rossby number 1/Ro = 2.78, Rayleigh number Ra = 10 9 and Prandtl number Pr = 6.4 (Ro, Ra and Pr defined below) revealed a cyclonic azimuthal velocity boundary-layer flow surrounding a core region of anticyclonic circulation and localized near the cylinder sidewall. The results were interpreted in the context of sidewall Stewartson layers driven by active Ekman layers at the top and bottom of the cell [25,26].Here we show through DNS and experimental measurements for a...