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Prandtl number dependence in turbulent compressible convection

Lekha Sharma*, Mayank Pathak†, and Harshit Tiwari‡

Mahendra K. Verma§

  • *Contact author: lekhas@iitk.ac.in
  • †Contact author: mpathak@iitk.ac.in
  • ‡Contact author: tharshit@iitk.ac.in
  • §Contact author: mkv@iitk.ac.in
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Phys. Rev. Fluids 10, 114611 – Published 19 November, 2025

DOI: https://doi.org/10.1103/vkvv-l3m4

Abstract

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≤Pr≤102) and Rayleigh numbers (Ra =107, 108, 109). The total temperature exhibits adiabatic cooling in the bulk, with minimal variation across Pr. For Pr <1 and >1, the Nusselt number scales as Ra0.22Pr0.04 and Ra0.28Pr0.02 in 2D, and as Ra0.27Pr0.16 and Ra0.27Pr0.03 in 3D. The corresponding variations for the Reynolds number are Ra0.51Pr−0.78 and Ra0.60Pr−0.99 in 2D, and Ra0.45Pr−0.64 and Ra0.51Pr−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.

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Phys. Rev. Fluids 10, 114611– Published 19 November, 2025
  • Received 6 July 2025
  • Accepted 16 October 2025
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