Helical invariant flows: New conservation laws and their importance for 2 1/2D turbulence

螺旋不变流：新守恒定律及其对 2 1/2D 湍流的重要性

• 批准号: 270556741
• 负责人: Professor Dr.-Ing. Martin Oberlack
• 金额: --
• 依托单位: Fachgebiet Strömungsdynamik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2015
• 资助国家: 德国
• 起止时间: 2014-12-31 至 2019-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/270556741?language=en
• 关键词: Helical; invariant; flows; New; conservation

The principal starting point of the proposal is the recent breakthrough of finding new conservation laws for viscid and inviscid helical flows in the group of the applicant, most probably for the first time after the discovery of helicity in the 60th. This, in fact, comprised new conservation laws for plane and axisymmetric flows. In the present proposal the application to turbulence is in the foreground. In view of the turbulence application helically symmetric turbulence is placed between the fully 3D turbulence, which determines our classical knowledge of turbulence, and plane 2D turbulence, which is rather distinct. Similar to 3D turbulence, helical turbulence admits a three-dimensional velocity field and, most important, the vortex stretching term in the vorticity transport equation responsible for the generation of small scales can be identified. Nevertheless, helical flows live on a 2D manifold, somewhat analogous to plane 2D turbulence. Employing a simulation code especially designed for simulating helical flows we intend to answer exactly the key question in how far helical turbulence is closer to 2D or to 3D turbulence or in other words if helical flows have a preferential to transfer energy from small to large scales or vice versa.

该提案的主要起点是最近在申请人组中找到有关粘性和无粘性螺旋流的新保护法的突破，这很可能是60年代发现螺旋性后的第一次。实际上，这包括针对平面和轴对称流的新保护定律。在本提案中，湍流的应用在前景中。鉴于湍流的应用，将螺旋对称性湍流放置在完全3D湍流之间，这决定了我们对湍流的经典知识，而平面2D湍流则是相当不同的。与3D湍流相似，螺旋湍流承认可以识别出负责产生小尺度的涡度传输方程中的三维速度场，最重要的是，涡流拉伸项。然而，螺旋流居住在2D歧管上，有点类似于平面2D湍流。采用专门为模拟螺旋流而设计的模拟代码，我们打算在螺旋湍流之间或近距离湍流更接近螺旋湍流或换句话说，如果螺旋流有优先地将能量从小规模转移到大型或反之亦然，则打算准确地回答关键问题。

项目成果

Euler and Navier–Stokes equations in a new time-dependent helically symmetric system: derivation of the fundamental system and new conservation laws

新的瞬态螺旋对称系统中的欧拉和纳维斯托克斯方程：基本系统和新守恒定律的推导

• DOI: 10.1017/jfm.2017.74
• 发表时间: 2017
• 期刊: Journal of Fluid Mechanics
• 影响因子: 3.7
• 作者: Dierkes;Oberlack
• 通讯作者: Oberlack

New similarity reductions and exact solutions for helically symmetric viscous flows

螺旋对称粘性流的新相似性约简和精确解

• DOI: 10.1063/5.0005423
• 发表时间: 2020
• 期刊: Physics of Fluids
• 影响因子: 4.6
• 作者: Dierkes;Dominik;Cheviakov;Alexei;Oberlack;Martin
• 通讯作者: Martin