Distinct Lifetime Scaling Laws of Turbulent Puff in Duct Flow

TL;DR

This study investigates the lifetime scaling laws of turbulent puffs in duct flow, revealing distinct regimes and bifurcations, with findings applicable across different geometries due to geometric invariance in decay mechanisms.

Contribution

It introduces a theoretical framework explaining puff lifetime scaling laws via a noisy saddle-node bifurcation model, extending understanding of transitional turbulence in confined geometries.

Findings

Puff lifetimes follow a square-root scaling law below Re_c.

Lifetimes exhibit super-exponential scaling above Re_c.

Decay mechanisms are geometrically invariant across different flow configurations.

Abstract

The spatio-temporal dynamics of localized turbulent puffs $-$ the characteristic transitional structures in square duct flows $-$ are investigated through direct numerical simulations and theoretical analyses. It is revealed that the turbulent puffs are transient structures, exhibiting distinct relaminarization regimes bifurcated at a critical Reynolds number $Re_c\simeq1450$. Puff's mean lifetimes at the subcritical regime ($Re<Re_c$) follow a square-root scaling law with increasing $Re$, transitioning to a super-exponential scaling in the supercritical regime ($Re > Re_c$). By implementing pattern preservation approximation, the Reynolds-Orr kinetic energy equation is reduced to a noisy saddle-node bifurcation equation, which explains the observed scaling laws in terms of the deterministic decay governed by the critical slowing down at the subcritical regime, and the abrupt decay activated by the stochastic fluctuations. Despite geometric confinement inducing unique secondary flows, e.g., corner-localized streamwise vortex pairs, corner-aligned high-speed streaks, and forked low-speed streaks, the puff lifetime statistics remain analogous to those in pipe flows, suggesting geometric invariance in decay mechanisms for transitional wall-surrounded turbulence.