On the role of inertia and self-sustaining mechanism in two-dimensional elasto-inertial turbulence

TL;DR

This study investigates how fluid inertia influences two-dimensional elasto-inertial turbulence through direct numerical simulations, revealing inertia's role in structure dynamics, energy transfer, and statistical properties.

Contribution

It provides new insights into the effect of inertia on EIT, including scaling laws and the robustness of statistical self-similarity across different Reynolds numbers.

Findings

Inertia enhances turbulence fluctuations and wallward migration of structures.

The elastic shear stress peak follows a $y^+ \, \propto \, Re_\tau^{1/2}$ scaling law.

Velocity and elastic stress PDFs show exponential heavy tails and collapse across Re.

Abstract

Elasto-inertial turbulence (EIT) is primarily driven by polymer elasticity, yet the modulating role of fluid inertia is non-negligible and remains largely unexplored. To investigate the effect of inertia, we perform direct numerical simulations of two-dimensional EIT in channel flow over a wide range of Reynolds numbers ($Re$). We show that increasing inertia promotes both the enhancement of dynamic amplitudes and the wallward migration of core structures. Specifically, inertia intensifies the turbulent fluctuations, facilitates the fragmentation of large-scale structures, and amplifies statistical quantities such as the root-mean-square of velocity fluctuations and polymer extension. The peak location of nonlinear elastic shear stress follows a scaling law $y^+ \propto Re_\tau^{1/2}$, closely resembling that of Reynolds shear stress in Newtonian turbulence, indicating a change of the momentum transfer mechanism. Meanwhile, the peak location of energy conversion between elastic and turbulent kinetic energies exhibits a $y^+ \propto Re_\tau^{0.1}$ scaling law migration, remaining mostly confined to the near-wall region. Remarkably, despite the inertial modulation, the probability density functions (PDFs) of velocity and elastic stress fluctuations extracted at the energy-conversion peak collapse convincingly over the range of $Re$ investigated. This reveals a robust statistical self-similarity across a wide range of inertia magnitude. Furthermore, the PDFs of wall-normal velocity and elastic stress fluctuations exhibit pronounced exponential heavy tails.