Active fluids exhibit complex turbulentlike flows at low Reynolds number. Recent work predicted that 2D active nematic turbulence follows scaling laws with universal exponents. However, experimentally testing these predictions is conditioned by the coupling to the 3D environment. Here, we measure the spectrum of the kinetic energy $E(q)$ in an active nematic film in contact with a passive oil layer. At small and intermediate scales, we find the scaling regimes $E(q)\sim q^{-4}$ and $E(q)\sim q^{-1}$, respectively, in agreement with the theoretical prediction for 2D active nematics. At large scales, however, we find a new scaling $E(q)\sim q$, which emerges when the dissipation is dominated by the 3D oil layer. In addition, we derive an explicit expression for the spectrum that spans all length scales, thus explaining and connecting the different scaling regimes. This allows us to fit the data and extract the length scale that controls the crossover to the new large-scale regime, which we tune by varying the oil viscosity. Overall, our work experimentally demonstrates the emergence of scaling laws with universal exponents in active turbulence, and it establishes how the spectrum is affected by external dissipation.

中文翻译：

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具有外部耗散的主动湍流的标度制度

活性流体在低雷诺数下表现出复杂的湍流。最近的工作预测，二维主动向列湍流遵循具有通用指数的标度定律。然而，对这些预测的实验测试取决于与 3D 环境的耦合。在这里，我们测量动能谱$乙(q)$在与被动油层接触的主动向列膜中。在中小规模上，我们找到了缩放机制$乙(q)～q^{-4}$ 和 $乙(q)～q^{-1}$，分别与二维活性向列的理论预测一致。然而，在大尺度上，我们发现了一个新的尺度$乙(q)～q$，当耗散由 3D 油层主导时出现。此外，我们推导出了跨越所有长度尺度的频谱的明确表达式，从而解释和连接了不同的尺度机制。这使我们能够拟合数据并提取控制交叉到新的大尺度区域的长度尺度，我们通过改变油的粘度来进行调整。总的来说，我们的工作通过实验证明了在主动湍流中出现了具有通用指数的标度定律，并确定了光谱如何受到外部耗散的影响。