Self-scaling tensor basis neural network for Reynolds stress modeling of wall-bounded turbulence
Authors:
Zelong Yuan,
Yuzhu Pearl Li
Abstract:
Recent advances in data-driven turbulence modeling have established tensor basis neural networks (TBNN) as a physically grounded framework for Reynolds-stress closure in Reynolds-averaged Navier-Stokes (RANS) simulations. However, their robustness in wall-bounded turbulent flows remains limited across Reynolds numbers and geometries due to the lack of an intrinsic scaling mechanism. In this work,…
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Recent advances in data-driven turbulence modeling have established tensor basis neural networks (TBNN) as a physically grounded framework for Reynolds-stress closure in Reynolds-averaged Navier-Stokes (RANS) simulations. However, their robustness in wall-bounded turbulent flows remains limited across Reynolds numbers and geometries due to the lack of an intrinsic scaling mechanism. In this work, we propose a self-scaling tensor basis neural network (STBNN) for Reynolds-stress modeling of wall-bounded turbulence. The model incorporates an invariant velocity-gradient normalization derived from the first two invariants of the velocity-gradient tensor, providing an intrinsic and geometry-independent scale that balances strain and rotation effects without relying on empirical coefficients or wall-distance inputs. Owing to its frame-indifferent formulation, the approach preserves Galilean and rotational invariance while maintaining a physically interpretable representation of Reynolds-stress anisotropy. STBNN is evaluated through a priori and a posteriori studies using direct numerical simulation (DNS) data of canonical wall-bounded flows, including plane channel and periodic hill flows. In a priori tests, the model accurately reproduces Reynolds-stress anisotropy, with correlation coefficients exceeding 99% and relative errors below 10%, while capturing near-wall scaling and logarithmic-layer behavior. In a posteriori RANS simulations, STBNN predicts mean velocity profiles in close agreement with DNS and improves prediction of separation and reattachment compared with linear and quadratic eddy-viscosity models and the baseline TBNN. Notably, a model trained at low Reynolds numbers generalizes to higher Reynolds numbers and unseen geometries. These results demonstrate the effectiveness of the proposed framework for data-driven Reynolds-stress modeling in wall-bounded turbulent flows.
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Submitted 10 April, 2026; v1 submitted 31 March, 2026;
originally announced March 2026.
Classical effect for enhanced high harmonic yield in ultrashort laser pulses with a moderate laser intensity
Authors:
Y. Z. Shi,
F. L. Dong,
Y. P. Li,
S. Wang,
Y. J. Chen
Abstract:
We study the influence of the pulse duration on high harmonic generation (HHG) with exploring a wide laser-parameter region theoretically. Previous studies have showed that for high laser intensities near to the saturation ionization intensity, the HHG inversion efficiency is higher for shorter pulses since the ground-state depletion is weaker in the latter. Surprisingly, our simulations show this…
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We study the influence of the pulse duration on high harmonic generation (HHG) with exploring a wide laser-parameter region theoretically. Previous studies have showed that for high laser intensities near to the saturation ionization intensity, the HHG inversion efficiency is higher for shorter pulses since the ground-state depletion is weaker in the latter. Surprisingly, our simulations show this high efficiency also appears even for a moderate laser intensity at which the ionization is not strong. A classical effect relating to shorter travel distances of the rescattering electron in shorter pulses, is found to contribute importantly to this high efficiency. The effect can be amplified significantly as a two-color laser field is used, suggesting an effective approach for increasing the HHG yield.
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Submitted 15 September, 2015;
originally announced September 2015.