Boundary Zonal Flow in Rotating Turbulent Rayleigh-Bénard Convection

Abstract

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...

Subcritical turbulent condensate in rapidly rotating Rayleigh–Bénard convection

“…For yet larger Rayleigh numbers we observed a secondary transition associated with a shear instability of the mean zonal flow driven nonlinearly by the traveling wall state. The resulting complex chaotic structure is confined to the vicinity of the wall and survives the onset of the bulk mode at higher Rayleigh numbers and even bulk turbulence that is present at yet higher Rayleigh numbers (de Wit et al 2020;Zhang et al 2020).…”

“…Despite this, we show here that these modes bear all the hallmarks of topologically protected states. We first show -in a cylindrical geometry -that these modes are robust with respect to secondary instabilities and to a turbulent bulk state as in the experiments (de Wit et al 2020;Zhang et al 2020) by gradually increasing the Rayleigh number until the bulk becomes turbulent. Second, we show that these states persist in the presence of different types of barriers, and show that the wall modes happily follow whatever boundary geometry is provided.…”

“…Our work is motivated in part by the zonal currents found independently by two groups in high Rayleigh number experiments and simulations on rapidly rotating convection in a right circular cylinder rotating with constant angular velocity about its vertical axis (de Wit et al 2020;Zhang et al 2020). While the results differ in detail both groups observe an intense zonal flow that precesses with respect to the rotating frame and is nearly indifferent to the bulk turbulent state.…”

“…where u ≡ (u, v, w) is the velocity, p is the pressure and θ is the temperature fluctuation relative to the conduction profile that varies linearly with respect to the vertical Figure 1. Summary of the runs performed for this study (full symbols ), along with past studies (Ecke et al 1992;Scheel et al 2003;de Wit et al 2020;Zhang et al 2020). The blue line corresponds to the onset of the wall mode while the red line corresponds to the onset of the bulk mode.…”

“…Recent experiments and simulations have shown the emergence of a boundary zonal flow in confined rotating Rayleigh-Bénard convection (Kunnen et al 2011;de Wit et al 2020;Zhang et al 2020). However, a link between this flow and the wall modes was not explicitly made.…”