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 quasistreamwise 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.

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• Classical statistical mechanics
• Structure & turbulence of boundary layers
• Turbulence
• Coherent structures