Turbulent fluid flows are ubiquitous in nature and technology, and are mathematically described by the incompressible Navier-Stokes equations (INSE). A hallmark of turbulence is spontaneous generation of intense whirls, resulting from amplification of the fluid rotation-rate (vorticity) by its deformation-rate (strain). This interaction, encoded in the non-linearity of INSE, is non-local, i.e., depends on the entire state of the flow, constituting a serious hindrance in turbulence theory and in establishing regularity of INSE. Here, we unveil a novel aspect of this interaction, by separating strain into local and non-local contributions utilizing the Biot-Savart integral of vorticity in a sphere of radius R. Analyzing highly-resolved numerical turbulent solutions to INSE, we find that when vorticity becomes very large, the local strain over small R surprisingly counteracts further amplification. This uncovered self-attenuation mechanism is further shown to be connected to local Beltramization of the flow, and could provide a direction in establishing the regularity of INSE.

中文翻译：

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纳维-斯托克斯湍流中极端事件的自衰减

湍流在自然界和技术中无处不在，并且可以通过不可压缩的 Navier-Stokes 方程 (INSE) 进行数学描述。湍流的一个标志是自发产生强烈的漩涡，这是由于流体旋转速度（涡度）被其变形速度（应变）放大所致。这种以 INSE 非线性编码的相互作用是非局部的，即取决于流动的整个状态，构成了湍流理论和建立 INSE 规律性的严重障碍。在这里，我们揭示了这种相互作用的一个新方面，通过利用半径为 R 的球体中的 Biot-Savart 涡度积分将应变分离为局部和非局部贡献。 分析 INSE 的高分辨率数值湍流解，我们发现当涡度变得非常大，小 R 上的局部应变令人惊讶地抵消了进一步的放大。这种未被发现的自衰减机制进一步显示出与流动的局部 Beltramization 相关，并且可以为建立 INSE 的规律性提供一个方向。