Strength Of Large-scale Circulation Research Articles

Dynamics of large-scale circulation and energy transfer mechanism in turbulent Rayleigh–Bénard convection in a cubic cell

We present the characteristics and dynamics of large-scale circulation (LSC) in turbulent Rayleigh–Bénard convection (RBC) inside a cubic cell. The simulations are carried out for a Rayleigh number range of 2 × 106 ≤ Ra ≤ 109 and using air (at Prandtl number Pr = 0.7) as the working fluid. Using the Fourier mode analysis, the strength, orientation, and associated dynamics of LSC are characterized. Following previous two-dimensional studies in RBC, we propose a mechanism of flow reversals based on the dynamics of corner vortices, which is less attempted in three-dimensional counterparts. We observe that the plane containing LSC is generally aligned along one of the diagonals of the box accompanied by a four-roll structure in the other. In addition to the primary roll, two secondary corner-roll structures are also observed in the LSC plane, which grow in size and destabilize the LSC, resulting in partial (ΔΦ1 ≈ π/2) and complete (ΔΦ1 ≈ π) reversals. In addition to previously reported rotation-led reorientations, we also observe cessation events that are rare in cubic cells. We observe that as the Rayleigh number is increased from Ra = 2 × 106 to 107, the number of reorientations reduces by one third. With an increase in Ra, the strength of LSC (SLSC) increases and the corner rolls reduce in size, which leads to the reduction in the occurrence of reorientations. At higher Rayleigh numbers (Ra > 108), the strength saturates around SLSC ≈ 0.75. To connect the dynamics between different coherent structures, we evaluate the turbulent kinetic energy (TKE) budget. Notably, our novel approach to study the variation of TKE along the azimuthal direction helps in identifying the dynamical coupling between the LSC and non-LSC planes. The analysis suggests that TKE is generally produced in localized regions in both the planes, while its dissipation mainly happens in the vicinity of the plane that contains LSC. The transport mechanism redistributes the energy between these planes and thus sustains the LSC and other coherent structures.

Dynamics and statistics of reorientations of large-scale circulation in turbulent rotating Rayleigh-Bénard convection

We present a direct numerical simulation to investigate the dynamics and statistics of reorientations of large-scale circulation (LSC) in turbulent rotating Rayleigh-Bénard convection for air (Pr = 0.7) contained in a cylindrical cell with unit aspect ratio. A wide range of rotation rates (0 ≤ Ro−1 ≤ 30) is considered for two different Rayleigh numbers Ra = 2 × 106 and 2 × 107. Using the Fourier mode analysis of time series data obtained from the different probes placed in the azimuthal direction of the container at the midplane, the orientation and associated dynamics of LSC are characterized. The amplitude of the first Fourier mode quantifies the strength of LSC, and its phase Φ1 gives the information on the azimuthal orientation of LSC. Based on the energy contained in the Fourier modes, different flow regimes are identified as the rotation rate is varied for a given Rayleigh number. The LSC structure is observed in the low rotation regime (Ro−1 ≲ 1), while the presence of other flow structures, namely, quadrupolar and sextupolar, is obtained at high rotation rates. In the LSC regime, a strong correlation between the orientation of LSC structure and the heat transfer and boundary layer dynamics is observed. At low rotation rates, the dissipation rates follow the log-normal behavior, while at higher rotation rates, a clear departure from log-normality is noted. Different types of reorientations, namely, rotation-led, cessation-led, partial, and complete reversal, are identified. The distribution of change in orientation of LSC follows a power law behavior as P(|ΔΦ1|) ∝|ΔΦ1|−m, with the exponent m ≈ 3.7. In addition, the statistics of time interval between successive reorientations follow a Poisson distribution. These observations are in good agreement with earlier experimental results.

Global-mean Vertical Tracer Mixing in Planetary Atmospheres. II. Tidally Locked Planets

Abstract In Zhang & Showman, we developed an analytical theory of 1D eddy diffusivity K zz for global-mean vertical tracer transport in a 3D atmosphere. We also presented 2D numerical simulations on fast-rotating planets to validate our theory. On a slowly rotating planet such as Venus or a tidally locked planet (not necessarily a slow-rotator) such as a hot Jupiter, the tracer distribution could exhibit significant longitudinal inhomogeneity and tracer transport is intrinsically 3D. Here we study the global-mean vertical tracer transport on tidally locked planets using 3D tracer-transport simulations. We find that our analytical K zz theory in Zhang & Showman is validated on tidally locked planets over a wide parameter space. K zz strongly depends on the large-scale circulation strength, horizontal mixing due to eddies, and waves, and local tracer sources and sinks due to chemistry and microphysics. As our analytical theory predicted, K zz on tidally locked planets also exhibit three regimes. In Regime I where the chemical and microphysical processes are uniformly distributed across the globe, different chemical species should be transported via different eddy diffusivity. In Regime II where the chemical and microphysical processes are nonuniform—for example, photochemistry or cloud formation that exhibits strong day–night contrast—the global-mean vertical tracer mixing does not always behave diffusively. In the third regime where the tracer is long-lived, non-diffusive effects are significant. Using species-dependent eddy diffusivity, we provide a new analytical theory of the dynamical quench points for disequilibrium tracers on tidally locked planets from first principles.

Breakdown of the large-scale circulation inΓ=1/2rotating Rayleigh-Bénard flow

Experiments and simulations of rotating Rayleigh-Bénard convection in cylindrical samples have revealed an increase in heat transport with increasing rotation rate. This heat transport enhancement is intimately related to a transition in the turbulent flow structure from a regime dominated by a large-scale circulation (LSC), consisting of a single convection roll, at no or weak rotation to a regime dominated by vertically aligned vortices at strong rotation. For a sample with an aspect ratio Γ=D/L=1 (D is the sample diameter and L is its height) the transition between the two regimes is indicated by a strong decrease in the LSC strength. In contrast, for Γ=1/2, Weiss and Ahlers [J. Fluid Mech. 688, 461 (2011)] revealed the presence of a LSC-like sidewall temperature signature beyond the critical rotation rate. They suggested that this might be due to the formation of a two-vortex state, in which one vortex extends vertically from the bottom into the sample interior and brings up warm fluid while another vortex brings down cold fluid from the top; this flow field would yield a sidewall temperature signature similar to that of the LSC. Here we show by direct numerical simulations for Γ=1/2 and parameters that allow direct comparison with experiment that the spatial organization of the vertically aligned vortical structures in the convection cell do indeed yield (for the time average) a sinusoidal variation of the temperature near the sidewall, as found in the experiment. This is also the essential and nontrivial difference with the Γ=1 sample, where the vertically aligned vortices are distributed randomly.

Effect of plumes on measuring the large scale circulation in turbulent Rayleigh-Bénard convection

We studied the properties of the large-scale circulation (LSC) in turbulent Rayleigh-Bénard (RB) convection by using results from direct numerical simulations in which we placed a large number of numerical probes close to the sidewall. The LSC orientation is determined by either a cosine or a polynomial fit to the azimuthal temperature or azimuthal vertical velocity profile measured with the probes. We study the LSC in Γ = D/L = 1/2 and Γ = 1 samples, where D is the diameter and L is the height. For Pr = 6.4 in an aspect ratio Γ = 1 sample at Ra = 1 × 108 and 5 × 108, the obtained LSC orientation is the same, irrespective of whether the data of only 8 or all 64 probes per horizontal plane are considered. In a Γ = 1/2 sample with Pr = 0.7 at Ra = 1 × 108, the influence of plumes on the azimuthal temperature and azimuthal vertical velocity profiles is stronger. Due to passing plumes and/or the corner flow, the apparent LSC orientation obtained using a cosine fit can result in a misinterpretation of the character of the large-scale flow. We introduce the relative LSC strength, which we define as the ratio between the energy in the first Fourier mode and the energy in all modes that can be determined from the azimuthal temperature and azimuthal vertical velocity profiles, to further quantify the large-scale flow. For Ra = 1 × 108, we find that this relative LSC strength is significantly lower in a Γ = 1/2 sample than in a Γ = 1 sample, reflecting that the LSC is much more pronounced in a Γ = 1 sample than in a Γ = 1/2 sample. The determination of the relative LSC strength can be applied directly to available experimental data to study high Rayleigh number thermal convection and rotating RB convection.

Azimuthal asymmetries of the large-scale circulation in turbulent Rayleigh–Bénard convection

Previously we published a dynamical model [E. Brown and G. Ahlers, Phys. Fluids 20, 075101 (2008)] for the large-scale-circulation (LSC) dynamics of Rayleigh–Bénard convection in cylindrical containers. The model consists of a pair of stochastic ordinary differential equations, motivated by the Navier–Stokes equations, one each for the strength δ and the orientation θ0 of the LSC. Here we extend it to cases where the rotational invariance of the system is broken by one of several physically relevant perturbations. As an example of this symmetry breaking we present experimental measurements of the LSC dynamics for a container tilted relative to gravity. In that case the model predicts that the buoyancy of the thermal boundary layers encourages fluid to travel along the steepest slope, that it locks the LSC in this direction, and that it strengthens the flow, as seen in experiments. The increase in LSC strength is shown to be responsible for the observed suppression of cessations and azimuthal fluctuations. We predict and observe that for large enough tilt angles, the restoring force that aligns the flow with the slope is strong enough to cause oscillations of the LSC around this orientation. This planar oscillation mode is different from coherent torsional oscillations that have been observed previously. The model was applied also to containers with elliptical cross sections and predicts that the pressure due to the side wall forces the flow into a preferred orientation in the direction of the longest diameter. When the ellipticity is large enough, then oscillations around this orientation are predicted. The model shows that various azimuthal asymmetries will lock the LSC orientation. However, only those that act on the δ-equation (such as tilting relative to gravity) will enhance the LSC strength and suppress cessations and other azimuthal dynamics. Those that affect only the θ0 equation, such as an interaction with Earth’s Coriolis force, will align the flow but will not influence its strength and the frequency of cessations.