Title: Universal scaling laws of boundary-driven turbulence Show Chinese title

Title: 边界驱动湍流的普遍标度定律

Abstract: Turbulence is a fundamental flow phenomenon, typically anisotropic at large scales and approximately isotropic at small scales. The classical Kolmogorov scaling laws (2/3, -5/3 and 4/5) have been well-established for turbulence without small-scale body forcing, describing second-order velocity structure functions, energy spectra, and third-order velocity structure functions in an intermediate small-scale range. However, their validity boundary remains unclear. Here, we identify new 1 and -2 scaling laws (replacing 2/3 and -5/3 laws) alongside the unchanged 4/5 law in the core region of boundary-driven turbulence, where energy is injected solely through viscous friction at moving boundaries. Local isotropy is recovered after high-pass filtering. Notably, odd-order velocity structure functions with and without absolute value exhibit distinct scaling exponents. A characteristic speed in the inertial range, derived from the constant ratio of third- to second-order structure functions, quantifies the time-averaged projectile speed at the bulk interface. Based on energy dissipation rate and the characteristic speed, a phenomenological framework for structure functions is developed together with a model for probability distributions of velocity increment at distinct small-scales. The universal scaling laws formulated can produce the full set of scaling exponents for low- and high-order velocity structure functions, including both the odd-orders' with and without absolute value, which are validated by direct numerical simulations and experimental datasets. Show Chinese abstract

Abstract: 湍流是一种基本的流动现象，在大尺度上通常各向异性，而在小尺度上近似各向同性。经典的Kolmogorov标度定律（2/3，-5/3和4/5）已为无小尺度体力的湍流建立起来，描述了中间小尺度范围内的二阶速度结构函数、能量谱和三阶速度结构函数。然而，它们的有效边界仍然不清楚。在这里，我们在边界驱动湍流的核心区域识别出新的1和-2标度定律（取代2/3和-5/3定律），同时保持4/5定律不变，在该区域中能量仅通过移动边界处的粘性摩擦注入。经过高通滤波后恢复局部各向同性。值得注意的是，带有绝对值和不带绝对值的奇数阶速度结构函数表现出不同的标度指数。惯性范围内一个特征速度，由三阶与二阶结构函数的恒定比值得出，量化了整体界面处的时间平均弹道速度。基于能量耗散率和特征速度，提出了结构函数的唯象框架，并建立了不同小尺度速度增量概率分布的模型。制定的普遍标度定律可以产生低阶和高阶速度结构函数的完整标度指数集，包括带有绝对值和不带绝对值的奇数阶，这些已被直接数值模拟和实验数据集验证。