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

Stochastic models of near-wall turbulence commonly rely on the Markovian assumption, despite evidence that coherent structures induce long-lived temporal correlations. Here, we test the validity of this assumption using micron-sized particle resuspension from the viscous sublayer. Analysis of direct numerical simulation (DNS) data reveals that while high- and low-drag events occur with Poissonian statistics, their internal dynamics is strongly persistent, with a Hurst exponent $H \approx 0.84$ , indicating intrinsic non-Markovian behaviour. We therefore develop a non-Markovian resuspension model based on a fractional Ornstein–Uhlenbeck process, with physical parameters extracted directly from the DNS flow. Comparative simulations show that the empirical success of classical Markovian models arises not from an accurate description of the near-wall dynamics, but from their free parameter $C_{0}$ acting as a phenomenological surrogate for unresolved flow memory. We further identify a critical regime transition controlled by the event decay rate $\lambda$ : strong intermittency ( $\lambda \lt 0.2$ ) invalidates the Markovian approximation, whereas weak intermittency ( $\lambda \gt 0.2$ ) renders it physically justifiable. These results define quantitative limits on stochastic modelling in near-wall turbulence.