A method for evaluating relations of turbulent normal-stresses by experimental data over a wide range of Reynolds numbers

Hassan Nagib; Ivan Marusic

Home/Archive/arXiv

arXiv · 2410.23669

A method for evaluating relations of turbulent normal-stresses by experimental data over a wide range of Reynolds numbers

Hassan Nagib·Ivan Marusic

View original source ↗Read source document ↗Export metadata ↓

Abstract

Recently, Nagib et al (2024} utilized indicator functions of profiles of the streamwise normal stress to reveal the ranges of validity, in wall distance and Reynolds number, for each of two proposed models in DNS of channel and pipe flows. A method more suited to experimental data is proposed here, as establishing accurate indicator functions is a challenge. The new method is outlined and used with the two leading models that propose either a logarithmic or power trend, for the normal stresses of turbulence in a fitting region of wall-bounded flows. The method, which is simple and robust, is used to evaluate each model over a wide range of Reynolds numbers by applying it to two of the prominent experimental data sets in zero-pressure-gradient boundary layers (ZPG) and pipe flows. A somewhat larger exponent for the power trend equal to 0.28, instead of 0.25, is found to slightly extend its range of validity. Correcting for outer intermittency in ZPG data also extends validity of the power trend to around half the boundary layer thickness. Projecting near-wall peak normal-stress values using both models based on data from locations in the fitting region, yields nearly identical results up to the highest Re available from these two experiments.Neither model directly represents the inner peak values and differ by as much as 30%. However, the two relations provide projected values at Re=10M with a relative difference of approximately 6.2%; distinguishing between these values would require measurement accuracy well beyond our capabilities. Current results and those of Monkewitz and Nagib (2023) on the mean flow, suggest that considerations of nonlinear growth of eddies from the wall and accounting for some viscous effects, are important for modeling wall-bounded flows. Such effects also apply to potential refinements of the logarithmic trend along ideas advanced by Deshpande et al. (2021).

Explore related subjects

physics.flu-dyn

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Hassan Nagib, Ivan Marusic. 2024-11-19. A method for evaluating relations of turbulent normal-stresses by experimental data over a wide range of Reynolds numbers. https://arxiv.org/abs/2410.23669

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Kinetic closure of turbulence

This letter presents a kinetic closure of the filtered Boltzmann--BGK equation, paving the way toward an alternative description of turbulence. The closure retains the turbulent subfilter stress tensor without a separate Smagorinsky-type ansatz for its structure, unlike classical filtered Navier--Stokes closures. In contrast, it accounts for the subfilter turbulent diffusion in the nonconserved moments by generalizing the BGK collision operator. The model does not require scale separation between resolved and unresolved scales. The Chapman--Enskog analysis shows how its hydrodynamic limit can converge to the filtered Navier--Stokes equations, with velocity gradients isolating subfilter contributions. Numerical tests on the Taylor--Green vortex and the turbulent mixing layer show improved stability and reduced dissipation in the reported cases, benchmarked against the Smagorinsky model.

physics.flu-dyn↗

arXiv2026

Kinetic closure of turbulence: collision-side modeling beyond the filtered Boltzmann equation

This article extends a recently introduced kinetic closure of turbulence by developing its theoretical framework, operational realizations, and validation. In contrast with filtered Navier--Stokes formulations, filtering the Boltzmann equation retains subgrid transport under the linear streaming operator, so that unresolved physics is concentrated on the collision side. We show that in dilute-gas large-eddy simulation, the main limitation of Bhatnagar--Gross--Krook (BGK)-type collision models is not the breakdown of molecular chaos, but the retention of a Markovian collision at a scale where filtering can induce finite temporal correlations in the collision product. In a BGK-type framework, the closure problem is dual: one must infer the filtered fine-grained equilibrium, not computable from filtered moments alone, and model the non-Markovian collision dynamics generated by the collision-product covariance. The present framework makes this dual structure explicit and represents the resulting collision-covariance source term through a BGK-like closure built from the equilibrium commutation residual, with the turbulent relaxation frequency given by a first phenomenological realization. The framework relies on a Chapman--Enskog analysis organized by the reference timescale ratio emerging from the nondimensionalization of the kinetic equation, performed in the classical sense, thereby avoiding artificial turbulent scale separations. We show that the Chapman--Enskog structure is not a pure one-parameter Knudsen scaling: the primary ordering is set by the kinetic-to-macroscopic timescale ratio, while higher moments retain an additional Mach dependence through the mixed scaling of particle velocity. The resulting kinetic closures are validated through lattice Boltzmann simulations and compared with the Smagorinsky model and regularization-based collision models.

physics.flu-dyn↗

arXiv2026

Deep Koopman Sensing

Real-time reconstruction of fluid flows from sparse sensor measurements is important for both physical understanding and flow control. When first-principles models are too expensive for online data assimilation (DA), learned reduced-order models provide an efficient alternative, but are commonly optimized for forward prediction rather than state estimation. We propose Deep Koopman Sensing, a data-driven reduced-order DA framework that combines a nonlinear autoencoder with parameter-conditioned linear latent dynamics approximating the Koopman operator. We compare the proposed model with parametric dynamic mode decomposition (pDMD), a multilayer perceptron (MLP), and xLSTM across four benchmarks: 1D viscous Burgers, 2D flow past a cylinder, 2D dambreak, and 3D flow past a sphere. Our results reveal a marked distinction between forecasting and sensing: open-loop accuracy does not reliably predict assimilation performance, while Deep Koopman Sensing achieves the lowest assimilation error across all four benchmarks. More importantly, with an extended Kalman filter, incorporating sensor measurements improves the estimates of both linear latent models across all four benchmarks, whereas it degrades the nonlinear models, despite their strong open-loop performance. With ensemble filtering, the nonlinear models are no longer degraded by assimilation, while the Koopman model still attains the lowest assimilation error. These results show that latent dynamics should be designed for the downstream estimation task rather than selected solely for forecast accuracy, and demonstrate Koopman-based reduced-order modeling as an effective approach for real-time flow reconstruction from sparse, streaming measurements.

physics.flu-dyn↗