Asymptotic Suction Boundary Layer: Alternative Linear and Weakly Non-Modal Stability Modes - a New Route to Large-Scale Turbulent Structures

渐进吸力边界层：替代线性和弱非模态稳定模式 - 大规模湍流结构的新途径

• 批准号: 316376675
• 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: Priority Programmes
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/316376675?language=en
• 关键词: Asymptotic; Suction; Boundary; Layer; Alternative

Turbulent simulations of asymptotic suction boundary layer (ASBL) have shown that very large-scale motion are observed being rather different e.g. from roles in turbulent Couette flow. The structures of ASBL have a very strong influence even on the mean velocity and seem to be responsible for effects such as significant change of the von Karman constant or the wake region.Presently a combined theoretical and numerical approach is proposed. In part A, new symmetry based non-modal (NM) linear and weakly non-linear stability modes will be computed analytically and, thereafter, in part B validated numerically. Further, the purpose of the numerical simulation is to track the stability modes beyond their theoretical basis up into a fully non-linear regime, where in particular two key questions are to be answered (i) if modes may persist even in a fully non-linear regime, and (ii) if they correspond to the large-scales expected from previous investigations.For the theoretical part A, stability theory, it is to note, that the modal Ansatz of stability theory rests on three symmetries, i.e. translation in space and time and scaling of the dependent variable. In a series or publications, the applicant has shown that for a broad variety of canonical shear flows such as Couette, Poiseuille, pipe or Taylor-Couette flow the linearized Navier-Stokes equations admit at least one additional symmetry, which, in turn, results in very different NM type of eigenfunctions. Most of the new NM eigenfunctions exhibit algebraic behavior in time, though not limited to the initial state as in transient growth theory.Specifically for the ASBL a new symmetry has been derived, which results in new NM type of eigenfunctions with a stability/instability behavior which is double exponential in time. In particular, the interplay of NM eigenfunctions will be investigated employing Fokas method. In recent years this method has experienced an impressive growth as it comprehensively extends classical methods to solve linear partial differential equations.Further, a weakly non-linear stability analysis based on approximate groups is intended, which rests on the idea of merging symmetry analysis and perturbation theory. Compared to the classical approaches, the major advantage of using approximate groups is, that the employed perturbative series is not assumed a priori. However, it is an outcome of the analysis, and results in a tailor-made series for the problem under investigation. The objective is to understand the non-linear structures, which are expected to be responsible for some of the results observed in simulations.The objective of the final step of the stability part of the proposal will be to numerically track the theoretical findings beyond its theoretical limits. This, however, is not only to push theoretical results beyond its limits but also to numerically follow the computed modes and resulting linear/non-linear structures deep into a fully non-linear regime.

渐近吸力边界层（ASBL）的湍流模拟表明，观察到非常大的运动是相当不同的，例如从湍流中的角色。 ASBL的结构即使对平均速度也具有很强的影响，并且似乎是诸如von Karman常数或唤醒区域的显着变化之类的效果。提出了一种合并的理论和数值方法。在A部分中，基于新的对称性的非模式（NM）线性和弱的非线性稳定性模式将通过分析进行计算，此后，在B部分验证了数值。此外，数值模拟的目的是将稳定模式超出其理论基础之外的稳定模式，直至完全非线性的制度，特别是要回答两个关键问题（i），如果模式甚至可以在完全非线性的状态下持续存在，并且（ii）是否与先前的调查中的大范围相对应。在三个对称性上，即相关变量的时空翻译以及缩放。在一系列或出版物中，申请人表明，对于各种规范的剪切流，例如couette，poiseuille，pipe或taylor-couette流动，线性化的navier-stokes方程将至少另外一种对称性承认，这反过来又导致了非常不同的NM NM类型的特征性特征函数。大多数新的NM本征函数在时间上表现出代数行为，尽管不仅限于瞬态生长理论的初始状态。对于Asbl而言，已得出了新的对称性，这导致了新的NM类型的具有稳定性/不稳定性行为的NM类型的特征函数，其稳定性/不稳定性行为是及时双重指数的。特别是，将使用FOKAS方法研究NM本征函数的相互作用。近年来，这种方法经过了令人印象深刻的增长，因为它全面扩展了求解线性偏微分方程的经典方法。FURTHER是打算基于近似群体的弱非线性稳定性分析，这取决于合并对称性分析和扰动理论的想法。与经典方法相比，使用近似基团的主要优点是，使用的扰动序列不是先验的。但是，这是分析的结果，并为正在研究的问题提供了量身定制的系列。目的是理解非线性结构，这些结构应负责模拟中观察到的某些结果。提案的稳定部分的最后一步的目的将是数值跟踪理论上的理论发现超出其理论限制。但是，这不仅是将理论结果推向超越其限制，而且还要遵循计算的模式，并遵循导致的线性/非线性结构，深入到完全非线性的状态。