Distinct Lifetime Scaling Laws of Turbulent Puff in Duct Flow

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.