Stochastic Model of Organizational State Transitions in a Turbulent Pipe Flow

TL;DR

This paper develops a probabilistic Markovian model to describe the non-Markovian organizational state transitions in turbulent pipe flow, revealing that these states are statistically correlated packets of vortical structures.

Contribution

It introduces a novel Markovian model that captures the complex, power-law decay of correlations in turbulent pipe flow OS transitions, linking them to vortical structures.

Findings

OS transitions exhibit power-law decay in correlations

A Markovian model accurately reproduces OS transition behavior

OSs are statistically correlated packets of vortical structures

Abstract

Turbulent pipe flows exhibit organizational states (OSs) that are labelled by discrete azimuthal wavenumber modes and are reminiscent of the traveling wave solutions of low Reynolds number regimes. The discretized time evolution of the OSs, obtained through stereoscopic particle image velocimetry, is shown to be non-Markovian for data acquisition carried out at a structure-resolved sampling rate. In particular, properly defined time-correlation functions for the OS transitions are observed to decay as intriguing power laws, up to a large-eddy time horizon, beyond which they decorrelate at much faster rates. We are able to establish, relying upon a probabilistic description of the creation and annihilation of streamwise streaks, a lower-level {\it{Markovian}} model for the OS transitions, which reproduces their time-correlated behavior with meaningful accuracy. These findings indicate that the OSs are distributed along the pipe as statistically correlated packets of quasi-streamwise vortical structures.