论文标题
可压缩的涡旋结构及其在流体动力湍流发作中的作用
Compressible vortex structures and their role in the onset of hydrodynamic turbulence
论文作者
论文摘要
我们研究了三维流中的准二维（薄煎饼）涡流结构的形成，以及二维流体动力学中的准一维结构。当欧拉方程以理想不可压缩的流体描述它们的领先顺序上，这些结构在高雷诺数下形成。我们在数值和分析上表明，这些结构的压缩以及其幅度的增加与流体中冷冻领域的可压缩性有关：在三维情况下连续分布的涡流线和涡旋转子（差异）中连续分布的涡流线的领域，以进行两大效果。我们发现，涡度和差异性的生长可以视为断裂相应场的过程。在高强度下，该过程表明了kolmogorov型缩放尺度，该缩放与结构的特征宽度有关。在二维湍流的情况下，分析了这些相干结构的可能作用，分析在湍流kolmogorov光谱的形成中，以及对应于恒定的endrophophy恒定通量的kraichnan光谱。
We study formation of quasi two-dimensional (thin pancakes) vortex structures in three-dimensional flows, and quasi one-dimensional structures in two-dimensional hydrodynamics. These structures are formed at high Reynolds numbers, when their evolution is described at the leading order by the Euler equations for an ideal incompressible fluid. We show numerically and analytically that the compression of these structures and, as a consequence, the increase in their amplitudes is related to the compressibility of the frozen-in-fluid fields: the field of continuously distributed vortex lines in the three-dimensional case and the field of vorticity rotor (divorticity) for two-dimensional flows. We find that the growth of vorticity and divorticity can be considered as a process of breaking of the corresponding fields. At high intensities, the process demonstrates a Kolmogorov-type scaling relating the maximum amplitude with the characteristic width of the structures. The possible role of these coherent structures is analyzed in the formation of the turbulent Kolmogorov spectrum, as well as the Kraichnan spectrum corresponding to a constant flux of enstrophy in the case of two-dimensional turbulence.
