Structural Boundary State Transitions in Turbulent Pipe Flow

Abstract

Extensive optical measurements of canonical turbulent pipe flows have revealed the existence of structural boundary states (SBSs) -- near-wall low-speed streaks strongly correlated with pairs of counter-rotating quasi-streamwise vortices. In this study, we investigate the number fluctuations of these structures within the framework of statistical mechanics. Specifically, we introduce reduced degrees of freedom to model the low-speed streaks as a dilute lattice gas of hard-core particles. The Metropolis stochastic evolution provides, furthermore, a simple yet effective two-parameter model for describing SBS transitions. The lattice gas approach enables us to derive both the probability of SBS occurrence and the peculiar self-similar correlations that these structures exhibit along the streamwise direction. Our findings give additional support to the idea that the statistically stationary regimes of wall-bounded turbulent flows can be understood as Markov chains of coherent dynamical states in reduced-dimensional phase spaces.