Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1710.01199

Two-dimensional dynamics of elasto-inertial turbulence and its role in polymer drag reduction

S. Sid·Y. Dubief·V. E. Terrapon
View original source ↗Read source document ↗Export metadata ↓

Abstract

The goal of the present study is: (i) to demonstrate the two-dimensional nature of the elasto-inertial instability in elasto-inertial turbulence (EIT), (ii) to identify the role of the bi-dimensional instability in three-dimensional EIT flows and (iii) to establish the role of the small elastic scales in the mechanism of self-sustained EIT. Direct numerical simulations of FENE-P fluid flows are performed in two- and three-dimensional channels. The Reynolds number is set to $\mathrm{Re}_τ= 85$ which is sub-critical for 2D flows but beyond transition for 3D ones. The polymer properties correspond to those of typical dilute polymer solutions and two moderate Weissenberg numbers, $\mathrm{Wi}_τ= 40, 100$, are considered. The simulation results show that sustained turbulence can be observed in 2D sub-critical flows, confirming the existence of a bi-dimensional elasto-inertial instability. The same type of instability is also observed in 3D simulations where both Newtonian and elasto-inertial turbulent structures co-exist. Depending on the Wi number, one type of structure can dominate and drive the flow. For large Wi values, the elasto-inertial instability tends to prevail over the Newtonian turbulence. This statement is supported by (i) the absence of the typical Newtonian near-wall vortices and (ii) strong similarities between two- and three-dimensional flows when considering larger Wi numbers. The role of the small elastic scales is investigated by introducing global artificial diffusion in the hyperbolic transport equation for polymers. The study results show that the introduction of large polymer diffusion in the system strongly damps a significant part of the elastic scales that are necessary to feed turbulence, eventually leading to the flow laminarization. A sufficiently high Schmidt number is necessary to allow self-sustained turbulence to settle.

Explore related subjects

physics.flu-dyn

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

S. Sid, Y. Dubief, V. E. Terrapon. 2017-10-03. Two-dimensional dynamics of elasto-inertial turbulence and its role in polymer drag reduction. https://doi.org/10.1103/physrevfluids.3.011301

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↗