Characterization of coherent structures in turbulent Rayleigh-Bénard convection using statistical measures is presented in the present work. Numerical simulations are carried out in a two-dimensional (2D) rectangular cell with aspect ratio 2 using air as the working fluid across four decades of Rayleigh number. The absence of one lateral dimension leads to entrapment of plumes which are consequently emitted in the form of thermal jets. Axial nonuniformity in thermal boundary layers is eliminated at high Rayleigh numbers. The so-called slope and 99% methods produce identical boundary layer thicknesses whose power law variation confirms theoretical inverse-Nu scaling. Turbulent kinetic energy budget unveils a transport-dissipation balance near the walls with buoyancy production nearly sustaining turbulent fluctuations in the bulk region. A higher threshold for the correlation between the vertical velocity and temperature results in faster convergence of plume and background share of dissipation, while decay in the volume fraction of the plume region continues. Exponential distribution of temperature fluctuations suggests the presence of hard turbulence at very large Rayleigh numbers with wider tails recording extreme fluctuating events. Changes in plume emission and its subsequent motion not only influence boundary layer instabilities but also cause departure from the −5/3 law in the frequency spectra.

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.

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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.

A direct numerical simulation of rotating Rayleigh–Bénard convection (RBC) for different fluids (Pr=0.015,0.7,1,7,20, and 100) in a cylindrical cell of aspect ratio Γ=0.5 is carried out in this work. The effect of rotation on the heat transfer rate, flow structures, their associated dynamics, and influence on the boundary layers are investigated. The Rayleigh number is fixed to Ra=106 and the rotation rates are varied for a wide range, starting from no rotation (Ro→∞) to high rotation rates (Ro≈0.01). For all the Prandtl numbers (Pr=0.015–100), a reduction in heat transfer with increase in rotation is observed. However, for Pr=7 and 20, a marginal increase of the Nusselt number for low rotation rates is obtained, which is attributed to the change in the flow structure from quadrupolar to dipolar state. The change in flow structure is associated with the statistical behavior of the boundary layers. As the flow makes a transition from quadrupolar to dipolar state, a reduction in the thermal boundary layer thickness is observed. At higher rotation rates, the thermal boundary layer thickness shows a power law variation with the rotation rate. The power law exponent is close to unity for moderate Pr, while it reduces for both lower and higher Pr. At extremely high rotation rates, the flow makes a transition to the conduction state. The critical rotation rate (1/Roc) for which transition to the conduction state is observed depends on the Prandtl number according to 1/Roc∝Pr0.5.