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Total enthalpy transformation in compressible turbulence recovering the incompressible law of the wall

Xianliang Chen1,2, Zhiye Zhao3, Jianping Gan1,2, and Lin Fu1,3,*

  • *Contact author: linfu@ust.hk
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Phys. Rev. Fluids 11, 084608 – Published 17 August, 2026

DOI: https://doi.org/10.1103/p2jq-t1gn

Abstract

Accurate scaling of heat energy is critical for compressible turbulence modeling. In addition to the temperature-velocity relation, temperature transformations have received increasing interest recently, but their overall accuracy is still inferior to the velocity counterparts. In this work, we propose to use total enthalpy H instead of temperature to construct the compressible law of the wall for heat energy. A critical justification is the structural resemblance between the equations of compressible H and incompressible passive scalars. Also, H reduces to static enthalpy at zero Mach number, meeting the requirement of self-consistency for transformations. To build the transformation, we first define and uncover the scalings of laminar and turbulent Prandtl numbers for H, and then reveal the strong analogy of heat flux budgets between compressible H and incompressible passive scalars. Finally, a semilocal total enthalpy transformation of no fitted parameters is constructed for channel flows, which is structurally analogous and comparable in accuracy to the Trettel-Larsson velocity transformation. This new transformation can potentially serve as a wall model for energy equations to accurately predict the enthalpy or temperature in compressible turbulence.

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Information

Phys. Rev. Fluids 11, 084608– Published 17 August, 2026
  • Received 21 January 2026
  • Accepted 22 July 2026
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