A landmark of turbulence is the emergence of universal scaling laws, such as Kolmogorov’s E(q) ~ q^−5∕3 scaling of the kinetic energy spectrum of inertial turbulence with the wavevector q. In recent years, active fluids have been shown to exhibit turbulent-like flows at low Reynolds number. However, the existence of universal scaling properties in these flows has remained unclear. To address this issue, here we propose a minimal defect-free hydrodynamic theory for two-dimensional active nematic fluids at vanishing Reynolds number. By means of large-scale simulations and analytical arguments, we show that the kinetic energy spectrum exhibits a universal scaling E(q) ~ q⁻¹ at long wavelengths. We find that the energy injection due to activity has a peak at a characteristic length scale, which is selected by a nonlinear mechanism. In contrast to inertial turbulence, energy is entirely dissipated at the scale where it is injected, thus precluding energy cascades. Nevertheless, the non-local character of the Stokes flow establishes long-range velocity correlations, which lead to the scaling behaviour. We conclude that active nematic fluids define a distinct universality class of turbulence at low Reynolds number.

动荡的地标是普遍的缩放的法律，如柯尔莫哥洛夫的出现ë（q）〜q ^-5/3与波矢惯性湍流的动能谱的比例q。近年来，已经证明活性流体在低雷诺数下表现出湍流状的流动。但是，尚不清楚这些流中是否存在通用缩放属性。为了解决这个问题，在这里我们提出了二维零雷诺数下的二维活性向列流体的最小无缺陷流体力学理论。通过大规模的模拟和分析论证，我们表明动能谱具有普遍的标度E（q）〜在长波长处q ^-1。我们发现，由于活动引起的能量注入在特征长度尺度上具有一个峰值，这是通过非线性机制选择的。与惯性湍流相反，能量在其注入的尺度上完全消散，因此排除了能量级联。然而，斯托克斯流的非局部特征建立了长距离的速度相关性，这导致了结垢行为。我们得出结论，在低雷诺数下，活性向列流体定义了独特的湍流普遍性类别。