Cocciaglia Niccolò, Cencini Massimo, Vulpiani Angelo
Dipartimento di Fisica, Università degli Studi di Roma "Sapienza," P. le Aldo Moro 5, 00185 Rome, Italy.
Istituto dei Sistemi Complessi, CNR, Via dei Taurini 19, 00185 Rome, Italy.
Phys Rev E. 2024 Jan;109(1-1):014113. doi: 10.1103/PhysRevE.109.014113.
The statistical properties of turbulent flows are fundamentally different from those of systems at equilibrium due to the presence of an energy flux from the scales of injection to those where energy is dissipated by the viscous forces: a scenario dubbed "direct energy cascade." From a statistical mechanics point of view, the cascade picture prevents the existence of detailed balance, which holds at equilibrium, e.g., in the inviscid and unforced case. Here, we aim at characterizing the nonequilibrium properties of turbulent cascades in a shell model of turbulence by studying an asymmetric time-correlation function and the relaxation behavior of an energy perturbation, measured at scales smaller or larger than the perturbed one. We contrast the behavior of these two observables in both nonequilibrium (forced and dissipated) and equilibrium (inviscid and unforced) cases. Finally, we show that equilibrium and nonequilibrium physics coexist in the same system, namely, at scales larger and smaller, respectively, of the forcing scale.
由于存在从注入尺度到粘性力耗散能量尺度的能量通量，湍流的统计特性与平衡态系统的统计特性有着根本的不同：这种情况被称为“直接能量串级”。从统计力学的角度来看，串级图景阻止了在平衡态成立的细致平衡的存在，例如在无粘和无外力的情况下。在这里，我们旨在通过研究一个非对称时间关联函数以及在小于或大于受扰尺度处测量的能量扰动的弛豫行为，来刻画湍流壳层模型中湍流串级的非平衡特性。我们对比了这两个可观测量在非平衡（有外力和耗散）和平衡（无粘和无外力）情况下的行为。最后，我们表明平衡物理和非平衡物理在同一系统中共存，即在分别大于和小于外力尺度的尺度上。
