Statistics of coherent structures in two-dimensional turbulent Rayleigh-Bénard convection

Abstract

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.