Statistical Characterization of the Time-reversible Navier-Stokes Equation

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How irreversible macroscopic behavior arises from time-reversible microscopic dynamics in complex systems with infinitely many degrees of freedom has been intensely studied in the field of non-equilibrium statistical mechanics. However, in the context of turbulence we still lack a fundamental understanding of the time irreversibility. The presence of a viscous term in the Navier-Stokes equations explicitly breaks the time-reversal invariance, which is not restored in the limit of vanishing viscosity (high Reynolds numbers) in a three-dimensional fully developed turbulence because of the dissipative anomaly. Therefore, it is a priori not clear how to distinguish the role of viscous dissipation from that of the energy cascade coming from the nonlinear, non-equilibrium nature of the dynamics in contributing to the irreversibility in turbulent flows. We propose to study this problem using an alternative approach, based on the idea of equivalence of non-equilibrium ensembles put forth by G. Gallavotti. We use governing equations with built-in time-reversibility and study whether these can reproduce the features of irreversibility, as observed in turbulence. The proposed study is interdisciplinary in nature, as it borrows ideas from statistical physics and applies them to the problem of turbulence, while taking advantage of advanced high-performance computing.