2025/12/01 by Joo, Da-Sol
#FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn)
paper · doi:10.48550/arxiv.2512.01308
The representation of buoyancy-driven turbulence in Reynolds-averaged Navier--Stokes models remains unresolved, with no widely accepted standard formulation. A key difficulty is the lack of analytical guidance for incorporating buoyant effects, particularly under unstable stratification. This study derives an analytical solution of the standard k--ω model for Rayleigh--Bénard convection in an infinite layer, where turbulent kinetic energy is generated solely by buoyancy. The solution provides explicit scaling relations among the Rayleigh (\Ra), Prandtl (\Pran), and Nusselt (\Nu) numbers that capture the simulation trends: \Nu ∼ \Ra1/3\Pran1/3 for \Pran ≪ 1 and \Nu ∼ \Ra1/3\Pran-0.415 for \Pran ≫ 1. This framework quantifies the discrepancies in the conventional buoyancy treatment and clarifies their origin. Informed by this analysis, the buoyancy-related modelling terms are reformulated to recover the measured \Nu--\Ra--\Pran trends. Only two dimensionless algebraic functions are introduced, which vanish in the absence of buoyancy, ensuring full compatibility with the standard closure. The corrected model is validated across a range of buoyancy-driven flows, including two-dimensional Rayleigh--Bénard convection, internally heated convection in two configurations, unstably stratified Couette flow, and vertically heated natural convection with varying aspect ratios. Across all cases, it provides highly accurate predictions.