Coherent Structures and Lattice-Boltzmann Hydrodynamics in Turbulent Pipe Flows

Abstract

Coherent structures (CS) are known to be part of the foundations of turbulent flow dynamics. For a long time, their appearance was believed to be chaotic and unorganized. However, it has been demonstrated through numerical simulations and experiments that a high degree of organization of CS could be attributed to the constitution of a turbulent state. Understanding these organizational dynamics promises to bring valuable theoretical and applied predictions, such as the average lifetime of turbulent structures and understanding the role of CS in particulate transport. The identification of CS was achieved by selecting the most energetic mode in the flow direction within a specified reference shell. Furthermore, the transition dynamics between the identified CS was investigated as a stochastic process, revealing a non-Markovian effect through an algebraic decay of the temporal self-correlation of the identified CS. Finally, the non-Markovian behavior observed between the transitions of CS was reproduced by a low-level Markovian model, which takes into account the degeneracy effects in the definition of the identified CS. In order to obtain an algorithm capable of simulating the quasi-static regime in magnetohydrodynamic (MHD) flows a multiple-relaxation-time (MRT) model and a distance-dependent boundary condition were introduced for the lattice Boltzmann method (LBM) associated with the induction equation for MHD flows. Finally, a turbulent pipe flow simulation was performed by the LBM with a MRT model for hydrodynamic distributions. The identification of CS revealed a non-trivial memory effect with respect to the force that triggered the turbulent state. The transition dynamics of CS revealed a Markovian behavior for finely resolved time data, indicating that experimental behavior could be recovered for larger time separations and, consequently, a larger dataset.