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Wall-modelled large-eddy simulation of turbulent channel flow with unstable stratification

  • Li-Sheng Jiang
  • Ao Xu
  • Heng-Dong Xi
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Abstract

Unstable thermal stratification modifies near-wall momentum and heat transport, causing the mean velocity profile to depart from the classical logarithmic law and complicating wall modelling for turbulent mixed convection. We develop a buoyancy-modified logarithmic-quadratic wall model for incompressible Poiseuille--Rayleigh--Bénard flow. The model combines an approximately linear relation between the near-wall mean temperature and mean streamwise velocity with a thermally modified mean-gradient representation inspired by mixing-length scaling. A priori assessments using wall quantities from the direct numerical simulation (DNS) database show that the calibrated wall law reconstructs near-wall velocity and wall-function-equivalent eddy-viscosity profiles. We implement the wall model in wall-modelled large-eddy simulations (WMLES) at friction Reynolds numbers up to Reτ≈6000 and Rayleigh numbers up to Ra=1010. For cases with DNS reference profiles at Ra=108 and 109, the maximum pointwise absolute relative errors are 3.6% for the mean velocity and 1.9% for the mean temperature. For cases with available DNS global-transport data, the maximum relative deviations in the Nusselt number Nu and skin-friction coefficient Cf are 11.7% and 15.9%, respectively. The WMLES reduces the mesh count by factors of approximately $195−−542$ relative to the corresponding DNS meshes. For the Ra=1010 and Rib=0.1 case, extrapolation of reference DNS resolution strategies gives a mesh count of order 1011, approximately three orders of magnitude larger than the present WMLES mesh count. We also examine how the balance between shear and buoyancy reorganises flow structure, and we identify signatures consistent with the coexistence of streamwise-elongated motions resembling very-large-scale motions and buoyancy-associated streamwise rolls.

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Cite

BibTeXRIS
BibTeX
@misc{jiang2026wallmodelled,
  title = {{Wall-modelled large-eddy simulation of turbulent channel flow with unstable stratification}},
  author = {Li-Sheng Jiang and Ao Xu and Heng-Dong Xi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.23311},
  eprint = {2609.23311},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.23311},
}
RIS
TY  - UNPB
TI  - Wall-modelled large-eddy simulation of turbulent channel flow with unstable stratification
AU  - Li-Sheng Jiang
AU  - Ao Xu
AU  - Heng-Dong Xi
PY  - 2026
DA  - 2026/09/20
PB  - arXiv
DO  - 10.48550/arxiv.2609.23311
UR  - https://arxiv.org/abs/2609.23311
AB  - Unstable thermal stratification modifies near-wall momentum and heat transport, causing the mean velocity profile to depart from the classical logarithmic law and complicating wall modelling for turbulent mixed convection. We develop a buoyancy-modified logarithmic-quadratic wall model for incompressible Poiseuille--Rayleigh--Bénard flow. The model combines an approximately linear relation between the near-wall mean temperature and mean streamwise velocity with a thermally modified mean-gradient representation inspired by mixing-length scaling. A priori assessments using wall quantities from the direct numerical simulation (DNS) database show that the calibrated wall law reconstructs near-wall velocity and wall-function-equivalent eddy-viscosity profiles. We implement the wall model in wall-modelled large-eddy simulations (WMLES) at friction Reynolds numbers up to Re_τ≈6000 and Rayleigh numbers up to Ra=10^10. For cases with DNS reference profiles at Ra=10^8 and 10^9, the maximum pointwise absolute relative errors are 3.6% for the mean velocity and 1.9% for the mean temperature. For cases with available DNS global-transport data, the maximum relative deviations in the Nusselt number Nu and skin-friction coefficient C_f are 11.7% and 15.9%, respectively. The WMLES reduces the mesh count by factors of approximately $195−−542$ relative to the corresponding DNS meshes. For the Ra=10^10 and Ri_b=0.1 case, extrapolation of reference DNS resolution strategies gives a mesh count of order 10^11, approximately three orders of magnitude larger than the present WMLES mesh count. We also examine how the balance between shear and buoyancy reorganises flow structure, and we identify signatures consistent with the coexistence of streamwise-elongated motions resembling very-large-scale motions and buoyancy-associated streamwise rolls.
ER  -