Vortex properties of two-dimensional turbulence
Vortex properties of two-dimensional turbulence
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二维湍流的涡旋特性
DOI：
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发表时间：
1993
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通讯作者：
D. Dritschel
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作者：
D. Dritschel
提出了近无粘、非受迫二维（2-D）湍流的新物理空间涡特性。它们是从一个大的合奏的计算分析，所有开始与一个随机分布的涡补丁等涡量大小的球面。数值方法（MACS）是轮廓动力学/外科手术（CD/CS）和用于计算分离涡相互作用的力矩展开的组合。该方法的计算速度比CD/CS快约100倍，从而可以形成一个大型数据库，以获得有意义的统计数据。数值方法可以解决一个更广泛的空间尺度比传统的（伪谱）的方法，它被发现，产生的统计涡属性不同的显着方面，从以前获得的。这一结论不仅是根据一组计算得出的，而是根据三组不同空间分辨率的计算得出的。虽然基本流统计的代数衰减（例如，涡度拟能，涡量）在后期观测到，衰减指数比以前得到的要小，而且不符合最近提出的“普适标度理论”所建议的比率。此外，涡数密度分布没有发现是自相似的，但随着涡尺寸的减小而连续且明显地变陡。这迫使我们重新评估无粘极限下二维湍流的性质。对这一极限的正确描述需要关于最可能的涡相互作用的（更多）定量信息。这样的相互作用不会像通常认为的那样只发生在两个旋涡之间。
Novel physical‐space vortex properties of nearly inviscid, unforced two‐dimensional (2‐D) turbulence are presented. They are obtained from the analysis of a large ensemble of calculations all beginning with a random distribution of vortex patches of equal vorticity magnitude on a spherical surface. The numerical method (MACS) is a combination of contour dynamics/surgery (CD/CS) and a moment expansion for calculating separated vortex interactions. This method calculates approximately 100 times faster than CD/CS thereby permitting the formation of a large database for obtaining meaningful statistics. The numerical method can resolve a much wider range of spatial scales than conventional (pseudospectral) methods, and it is found that the statistical vortex properties produced differ in significant respects from those obtained previously. This conclusion is drawn from not just one set of calculations, but three at different spatial resolutions. While algebraic decay of basic flow statistics (e.g., enstrophy, vortex population) is observed at late times, the decay exponents are smaller than previously obtained and furthermore do not come in the ratios suggested by the recently proposed ‘‘universal scaling theory.’’ In addition, the vortex number density distribution is not found to be self‐similar but steepens continuously and appreciably with decreasing vortex size. This forces a reevaluation of the nature of 2‐D turbulence in the inviscid limit. A proper description of this limit needs (more) quantitative information concerning the most probable vortex interactions. Such interactions will not be between just two vortices, as is commonly supposed.