Understanding and predicting turbulent flow phenomena remain a challenge for both theory and applications. The nonlinear and nonlocal character of small-scale turbulence can be comprehensively described in terms of the velocity gradients, which determine fundamental quantities like dissipation, enstrophy, and the small-scale topology of turbulence. The dynamical equation for the velocity gradient succinctly encapsulates the nonlinear physics of turbulence; it offers an intuitive description of a host of turbulence phenomena and enables establishing connections between turbulent dynamics, statistics, and flow structure. The consideration of filtered velocity gradients enriches this view to express the multiscale aspects of nonlinearity and flow structure in a formulation directly applicable to large-eddy simulations. Driven by theoretical advances together with growing computational and experimental capabilities, recent activities in this area have elucidated key aspects of turbulence physics and advanced modeling capabilities.

中文翻译：

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湍流中的多尺度速度梯度


理解和预测湍流现象对于理论和应用来说仍然是一个挑战。小尺度湍流的非线性和非局部特征可以用速度梯度来综合描述，速度梯度决定了耗散、熵和湍流小尺度拓扑等基本量。速度梯度的动力学方程简洁地概括了湍流的非线性物理学；它提供了对许多湍流现象的直观描述，并能够在湍流动力学、统计和流动结构之间建立联系。对滤波速度梯度的考虑丰富了这一观点，以直接适用于大涡模拟的公式表达非线性和流动结构的多尺度方面。在理论进步以及不断增长的计算和实验能力的推动下，该领域最近的活动阐明了湍流物理和高级建模能力的关键方面。