# Dynamics and Statistics of Reorientations of Large-Scale Circulation in Turbulent Rotating Rayleigh-B\'{e}nard Convection

## TL;DR

This study uses direct numerical simulations to analyze the dynamics, reorientations, and statistical behaviors of large-scale circulation in turbulent rotating Rayleigh-Bénard convection across various rotation rates and Rayleigh numbers.

## Contribution

It provides detailed numerical analysis of LSC reorientations, identifying different flow regimes and characterizing the statistical distribution of reorientation events in RRBC.

## Key findings

- LSC exists in low rotation regimes with strong correlation to heat transfer.
- Reorientation angles follow a power-law distribution with exponent ~3.7.
- Time intervals between reorientations follow a Poisson distribution.

## Abstract

We present a direct numerical simulation to investigate the dynamics and statistics of reorientations of large-scale circulation (LSC) in turbulent rotating Rayleigh-B\'{e}nard convection (RRBC) for air ($Pr=0.7$) contained in a cylindrical cell with unit aspect ratio. A wide range of rotation rates ($0\leq Ro^{-1}\leq 30$) is considered for two different Rayleigh numbers $Ra=2\times10^6$ and $2\times10^7$. Using the Fourier mode analysis of time series data obtained from the different probes placed in the azimuthal direction of the container at the mid-plane, the orientation and associated dynamics of LSC are characterized. The amplitude of the first Fourier mode quantifies the strength of LSC and its phase $\Phi_1$ gives the information of 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. LSC structure is observed in the low rotation regime ( $Ro^{-1} \lesssim 1$). A strong correlation between the orientation of LSC structure and the heat transfer and boundary layer dynamics is observed. In the LSC regime, the dissipation rates follow the log-normal behaviour, while at higher rotation rates, a clear departure from log-normality is noticed. 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 behaviour as $P(|\Delta \Phi_1|) \propto |\Delta \Phi_1|^{-m}$, with the exponent $m\approx 3.7$. In addition, the statistics of time interval between successive reorientations follow a Poisson distribution. These observations are in good agreement with earlier experimental results.