论文标题
Navier-Stokes湍流中极端事件的自我融入
Self-attenuation of extreme events in Navier-Stokes turbulence
论文作者
论文摘要
湍流流本质和技术无处不在，并且由不可压缩的Navier-Stokes方程（INSE）数学描述。湍流的标志是由于流体旋转率（涡度）的变形率（应变）的放大而产生的强烈旋转。这种相互作用是在INSE的非线性中编码的，是非本地的，即取决于流动的整个状态，这构成了湍流理论的严重障碍和建立INSE的规律性。在这里，我们通过将应变分离为局部和非本地贡献，利用Radius R的涡度涡流积分的局部和非本地贡献。分析对INSE的高度分解的数值湍流解决方案，我们发现，当涡流变得很大时，涡度就会变得很大，而质量很大。这种未透明的自我侵入机制进一步证明与流动的局部贝尔特拉伸相关，并可以为建立INSE的规律性提供一个方向。
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.
