Effects of thermodynamic states on a pipe flow

This is the authors' abstract. We don't add key points for this paper.

The influence of thermodynamic states on turbulent pipe flow is investigated by examining the interaction between dissipative and nondissipative motions. The proposed framework hypothesizes that when it locally reaches the boundary of the second law of thermodynamics, a fluid parcel undergoes a transient transition from a dissipative to a nondissipative state. The transition spontaneously starts local resonance, whose interaction with the surrounding dissipative flow governs the formation and evolution of coherent structures. Based on this framework, analytical solutions are derived for the resonant velocity field together with the corresponding initial and boundary conditions, spatiotemporal correlation functions, and coherent spatial topologies. The analysis demonstrates that the transitions modify the spatial organization of turbulent pipe flow while preserving a common resonant correlation kernel. In isotropic turbulence, the theory recovers the observed temporal correlation and associated scaling laws. For wall-bounded pipe flow, the interaction leads to localized antinodal tunneling, which provides the excitation boundary. The empirical fitted tunneling boundary accurately predicts experimentally observed spatial correlation isocontours with the same scaling kernel. Comparisons with measurements for azimuthal wavenumbers k = 2–7 at Re = 17 800 yield an average root-mean-squared error below 0.6% for spatial correlations and below 2.6% overall. The reconstructed velocity field further illustrates how the coexistence of dissipative and nondissipative states produces paired coherent structures, localized through-flow, bifurcation, and vortical motions. These demonstrate that thermodynamic state transitions fundamentally alter the spatial organization of turbulent pipe flow and provide a unified physical framework for interpreting coherent structures and nonlinear turbulent dynamics.