Spectral entropy-based metric for evaluating flow states in circular pipe flows

The flow regime in complex configurations cannot always be reliably identified alone by the Reynolds number Re. While Re as a single quantity should describe the overall flow state, the essential features describing the flow may vary in both space and time. This study is to present a detailed analysis of the circular pipe flow across a wide range of bulk Reynolds numbers (Reb = 2000–5300) using spectral entropy, providing a direct framework for identifying flow regimes (laminar, transitional, turbulent). Spectral entropy is derived from either individual velocity components or their combinations. The pipe flow simulations are carried out using a high-fidelity lattice Boltzmann method. The turbulent flow statistics, including mean and root mean square velocities, are validated against both experimental and numerical data at a friction Reynolds number of 180, confirming the accuracy of the in-house solver. The further analysis of the results reveals distinctive spectral entropy characteristics for laminar, transitional, and turbulent flows. A sharp increase in the spectral entropy values appears within the transitional range (Reb = 3000–3800). At higher Reynolds number (Reb≥3800), the spectral entropy values plateau, indicating a fully developed turbulent energy cascade. Compared to classical turbulence diagnostics, spectral entropy offers a straightforward and computationally efficient metric that reflects both inter-component interactions and multi-scale energy distribution. This proposed approach is applicable to various geometries and can be used with both numerical simulations and experimental datasets, which offers promising potential for detecting turbulence as well as to drive reduced-order modeling.