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

Abstract

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.