arXiv 2102.012662021-02-28physics.flu-dyn

承受更一般应变的粘性涡层和各向同性turbulence的比较

Viscous vortex layers subject to more general strain and comparison to isotropic turbulence

Karim Shariff, Gerrit Elsinga

备注：: 16 pages, 4 figures
DOI：: 10.1063/5.0045243

摘要：

粘性涡层受到更普遍的均匀应变被认为是。它们包括汤森的平面应变定常解（对应于参数$a = 1$），其中层平面内的所有应变都朝向涡量拉伸，以及米格达尔最近的轴对称应变定常非对称解（$a = 1/2$），其中一半应变进入涡量拉伸。除了考虑非对称、对称和反对称定常解$\forall a \ge 0$外，还证明了对于$a < 1$，即，如果不是汤森德的情况，涡量本身随时间衰减：只有在一端或两端保持涡量供应的边界条件才导致非零稳态。对于超汤森情况$a > 1$，定常状态有一个相反符号的涡鞘。与各向同性湍流的比较，在这种情况下的平均涡的应变本征框架是层状的，有翅膀相反的涡，和应变配置被发现是超级汤森。只有零积分扰动的$a > 1$稳定的解决方案是稳定的，否则，解决方案的增长。最后，附录表明，应变本征框架中的平均流动（除了一个附加项）是雷诺平均的纳维-斯托克斯方程。

英文摘要：

Viscous vortex layers subject to a more general uniform strain are considered. They include Townsend's steady solution for plane strain (corresponding to a parameter $a = 1$) in which all the strain in the plane of the layer goes toward vorticity stretching, as well as Migdal's recent steady asymmetric solution for axisymmetric strain ($a = 1/2$) in which half of the strain goes into vorticity stretching. In addition to considering asymmetric, symmetric and antisymmetric steady solutions $\forall a \ge 0$, it is shown that for $a < 1$, i.e., anything less than the Townsend case, the vorticity inherently decays in time: only boundary conditions that maintain a supply of vorticity at one or both ends lead to a non-zero steady state. For the super-Townsend case $a > 1$, steady states have a sheath of opposite sign vorticity. Comparison is made with homogeneous-isotropic turbulence in which case the average vorticity in the strain eigenframe is layer-like, has wings of opposite vorticity, and the strain configuration is found to be super-Townsend. Only zero-integral perturbations of the $a > 1$ steady solutions are stable; otherwise, the solution grows. Finally, the appendix shows that the average flow in the strain eigenframe is (apart from an extra term) the Reynolds-averaged Navier-Stokes equation.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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