On the Markovian assumption in near-wall turbulence: The case of particle resuspension

TL;DR

This study examines the validity of the Markovian assumption in near-wall turbulence modeling, revealing that flow memory effects are significant in certain regimes and affect the accuracy of classical stochastic models.

Contribution

It introduces a coupled simulation approach showing the limitations of Markovian models and identifies a critical decay rate governing flow memory effects.

Findings

Wall shear stress events follow Poissonian statistics.

Flow exhibits strong temporal persistence with Hurst exponent ~0.84.

A critical decay rate (λ ≈ 0.2) separates regimes of flow memory and randomness.

Abstract

We investigate the validity of the Markovian assumption in modeling near-wall turbulence by analyzing the detachment of micron-sized particles from the viscous sublayer. By coupling direct numerical simulations with a fractional Ornstein-Uhlenbeck process, we demonstrate that while wall shear stress events follow Poissonian occurrence statistics, their internal dynamics exhibit strong temporal persistence (Hurst exponent $H \approx 0.84$), indicating non-Markovian memory. We reveal that the successful predictions of Markovian resuspension models stems from their free parameter acting as a phenomenological surrogate for flow memory. We further identify a critical regime transition governed by a wall shear stress events decay rate, $\lambda$. We identify a strong intermittency regime ($\lambda < 0.2$), where coherent structures exhibit extended temporal correlations that cannot be mimicked by white noise. Conversely, rapid decays ($\lambda > 0.2$) generate quasi-random fluctuations that justify the Markovian approximation. These findings offer a new perspective on the physical validity of classical stochastic modeling in wall-bounded flows.