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 report a numerical investigation of the effect of multiscale roughness on heat flux (Nu) and near-wall dynamics in turbulent Rayleigh–Bénard convection of air in a cell of aspect ratio 2 in the Rayleigh number (Ra) range 106≤Ra≤4.64×109. We observe that despite the same wetted area, taller roughness yields higher heat flux owing to a multiple roll state. Based on the number of roughness peaks penetrating the thermal boundary layer, three regimes are identified. In regime I, heat flux drops marginally as only 50% of the peaks emerge uncovered, followed by a nearly unaltered Nu in regime II. A sudden increase in Nu in regime III is noted with more than 65% penetrating peaks. In contrast to the previous observation, heat flux continues to increase even when all the peaks exceed the boundary layer. Transformation of two large-scale rolls into smaller multiple rolls favors better access to the trapped fluid in the roughness throat leading to greater mixing. A significant improvement in the mixing of fluid inside the cavities is found due to the cascade of secondary vortices, which is connected to the improved heat flux in the tallest roughness setup. A thin thermal boundary layer that envelopes the rough surface at higher Ra supports the enhanced inter-mixing of fluid inside the cavities. Greater perturbation of the thermal boundary layer for the smaller roughness setup shows consistent connection with the enhanced Nu(Ra) scaling.

We present a two-dimensional numerical study of turbulent Rayleigh–Bénard convection with air as the working fluid over a multi-scale randomly roughened surface in a rectangular box of aspect ratio 2 over three decades of Rayleigh number ( $10^8 \leq {\textit {Ra}} \leq 10^{11}$ ). With varied response of the roughness elements at different ${\textit {Ra}}$ , enhanced heat transfer scaling ( $\gamma =0.41$ ) is retained throughout the explored ${\textit {Ra}}$ range. The plume emission process is triggered from the taller roughness elements at a lower ${\textit {Ra}}$ , while smaller elements contribute significantly at higher ${\textit {Ra}}$ . Increased plume emission frequency compared to the smooth case is reflected from the enhanced volume fraction and thermal dissipation rate of plumes. The tip of the roughness elements exhibits the highest temperature and vertical velocity fluctuations, while washing out of the trapped fluid in the throat region holds the key to enhanced heat flux at higher ${\textit {Ra}}$ . Increased localized pockets of fluid at higher ${\textit {Ra}}$ indicate better inter-scale energy transfer, which is reflected in higher energy content at all scales in the computed temperature spectra. The decomposition of the flow field into orthogonal modes reveals that heat transfer enhancement at higher ${\textit {Ra}}$ is associated with multiple small-scale structures. Owing to better energy transfer and intense localized fluctuations, modal distribution of energy is less severe for higher ${\textit {Ra}}$ , and stable twin large-scale rolls do not favour an efficient heat transport process.

Using direct numerical simulations, two-dimensional tilted Rayleigh–Bénard convection (RBC) is studied in both smooth and roughness-facilitated convection cells of double aspect ratio ( $\varGamma =2$ ) for air as a working fluid. We investigate the effect of inclination angle ( $0^{\circ } \leq \phi \leq 90^{\circ }$ ) on heat flux ( $Nu$ ), Reynolds number ( $Re$ ) and flow structures. In a Rayleigh number range $10^{6}\leq Ra\leq 10^{9}$ , we address the $Ra$ dependence of $Nu(\phi )$ trend. In the smooth case, while greater tilt results in highest heat flux below $Ra=10^{8}$ , $Nu$ drops with $\phi$ monotonically above it (RBC transports heat most efficiently), which explains the different $Nu(\phi )$ trend observed in the previous studies due to $Ra$ dependence (Guo et al., J. Fluid Mech., vol. 762, 2015, pp. 273–287; Shishkina & Horn, J. Fluid Mech., vol. 790, 2016, R3; Khalilov et al., Phys. Rev. Fluids, vol. 3, 2018, 043503). For the smooth case, we identify the control parameters ( $\phi =75^{\circ }$ and $Ra=10^{7}$ ) that yield maximum heat flux (an increment of $18\,\%$ with respect to the level case). On the other hand, among the three roughness set-ups used in the present study, the tallest roughness configuration yields the maximum increment in heat flux ( $25\,\%$ ) in vertical convection ( $\phi =90^{\circ }$ ) at $Ra=10^{6}$ . With increase in $Ra$ , $Re$ changes with $\phi$ marginally in the smooth case, whereas it shows notable changes in its roughness counterpart. We find that the weakening of thermal stratification is related directly to the height of roughness peaks. While $Ra$ delays the onset of thermal stratification (in terms of inclination angle) in the smooth case, an increase in roughness height plays the same role in roughness-facilitated convection cells.

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