Effect of domain aspect ratio on the velocity-temperature correlation in Rayleigh-Benard Convection

In Rayleigh-Bénard convection, the turbulent convective heat flux 〈wθ〉 is a key contributor to the Nusselt number (Nu), yet the scale-by-scale dynamics governing its evolution, particularly under varying domain geometries, require further clarification. This study investigates the spectral budget of 〈wθ〉 across a range of aspect ratios (Γ) to elucidate how production, transport, and dissipation mechanisms vary with Γ across spatial scales and wall-normal positions. Direct numerical simulations of planar Rayleigh-Bénard convection are conducted at three Rayleigh numbers (Ra = 105, 6 × 106, and 4 × 108), each computed for three aspect ratios: Γ = 5π/16 (small), 5π/4 (medium), and 5π (large). Our results reveal that large-scale thermal structures dominate the production and redistribution terms in the 〈wθ〉 budget, particularly in large-Γ domains. However, these structures remain confined to the bulk region while small-sclae thermal structures govern heat transport in the near-wall regions. Consequently, even in wider domains, the contribution of large-scale structures to Nu scaling stays limited, revealing a fundamental separation between bulk and boundary-layer dynamics.