In this work, we report a comprehensive study of turbulent compressible convection through two-dimensional (2D) and three-dimensional (3D) numerical simulations spanning a wide range of Prandtl numbers (${10}^{-2}\le \mathrm{Pr}\le {10}^2$) and Rayleigh numbers (Ra $={10}^7, {10}^8, {10}^9$). The total temperature exhibits adiabatic cooling in the bulk, with minimal variation across Pr. For Pr $<1$ and $>1$, the Nusselt number scales as ${\mathrm{Ra}}^{0.22}{\mathrm{Pr}}^{0.04}$ and ${\mathrm{Ra}}^{0.28}{\mathrm{Pr}}^{0.02}$ in 2D, and as ${\mathrm{Ra}}^{0.27}{\mathrm{Pr}}^{0.16}$ and ${\mathrm{Ra}}^{0.27}{\mathrm{Pr}}^{0.03}$ in 3D. The corresponding variations for the Reynolds number are ${\mathrm{Ra}}^{0.51}{\mathrm{Pr}}^{-0.78}$ and ${\mathrm{Ra}}^{0.60}{\mathrm{Pr}}^{-0.99}$ in 2D, and ${\mathrm{Ra}}^{0.45}{\mathrm{Pr}}^{-0.64}$ and ${\mathrm{Ra}}^{0.51}{\mathrm{Pr}}^{-0.91}$ in 3D. Top-bottom asymmetry persists in both the thermal and viscous boundary layers, with thicker top layers. As Pr increases, thermal boundary layers become thinner while viscous boundary layers thicken, with distinct scaling near the top and bottom boundaries.

Close

PrevNext

View figure in article

• Compressible boundary layers
• Compressible flows
• Compressible turbulence
• Turbulence simulations
• Turbulent convection
• Direct numerical simulations