Stability, nolinear regimes and transport properties of viscous flows subject to spatially inhomogeneous forcing: theory and applications.

空间非均匀强迫下粘性流的稳定性、非线性状态和输运特性：理论与应用。

• 批准号: 430085491
• 负责人: Privatdozent Dr. Michael Zaks
• 金额: --
• 依托单位: Institut für Physik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/430085491?language=en
• 关键词: Stability; nolinear; regimes; transport; properties

Recently, fluid mechanics has witnessed a raise of interest to multi-vortex patterns, characterized by spatial regularity and featuring periodic, quasiperiodic or chaotic temporal dynamics. Created either by the instability of primary uniform flows or as a result of direct external influence, such patterns are encountered in a variety of setups from the cosmological and large-scale atmospheric phenomena to vortical flows in microfluidics; in the industry they have applications e.g., in metallurgy and chemical technologies. Experimentally, such patterns have been reproduced in liquid metals and other conducting media by the action of electric currents, periodic in space. In theoretical analysis, a canonical example is the seminal Kolmogorov flow, excited by the spatially periodic force and serving as a model for inferring the mechanisms of instability and for understanding the cascade energy transfer at the turbulent stage. As demonstrated by further studies (in particular, by researchers, participating in this Project), generalizations of the Kolmogorov setup to the case of flows with mean drift, and extension from one-dimensional forcing to stationary forces that are doubly periodic in space, lead to a dynamically new class of flows. These flows occupy a certain intermediate position between laminar and turbulent ones and feature unusual properties: fractal power spectra of Lagrangian observables and anomalies in the transport of passive admixtures. Another mechanism for the formation of multi-vortex quasi-two-dimensional patterns, studied by the participants of the project, is the Marangoni convection near the localized heat source or the surface-active substance. Within the Project, we aim at further research of these phenomena, focusing, along with conventional hydrodynamical characteristics, at spectral and transport properties of various stationary and time-dependent flow patterns with vortices. We will investigate the dependence of these properties on the configuration of the flow pattern, on the relative intensity of the vortices and the mean drift, on the geometry of the setup and on the symmetry-breaking effects. Additional factors: onset of three-dimensionality in the flow as a result of the fluid rotation or due to the action of electromagnetic forces upon electroconductive liquids, will be taken into account as well. We expect that various modifications in the problem setup should eventually destabilize the stationary flow patterns, lead, first, to formation of regular eddies on different scales, to their nonlinear interaction, further, to the onset of time-dependence in the flow and, finally, to the growth of spatial disorder and the onset of turbulence. In this way, our research will deepen the theoretical knowledge about the mechanisms that generate turbulence in vortical streams, and, on the practical side, contribute to the more efficient usage of such flows in applications.

近年来，流体力学对具有空间规律性和时间动力学特性的多涡模式的研究越来越受到重视。这种模式是由主要均匀流动的不稳定性或直接外部影响造成的，在从宇宙学和大规模大气现象到微流体中的涡流的各种设置中都会遇到这种模式;在工业中，它们具有应用，例如，冶金和化学技术。在实验上，这种模式已经在液态金属和其他导电介质中通过空间周期性电流的作用复制出来。在理论分析中，一个典型的例子是开创性的柯尔莫哥洛夫流，激发的空间周期性的力，并作为一个模型，用于推断不稳定的机制，并了解在湍流阶段的级联能量传递。正如进一步的研究（特别是参与该项目的研究人员）所证明的那样，将Kolmogorov设置推广到具有平均漂移的流动的情况，并从一维强迫扩展到空间中具有双重周期性的固定力，导致动态的新一类流动。这些流量占据了一定的层流和湍流之间的中间位置，并具有不寻常的属性：分形功率谱的拉格朗日观测值和异常的被动混合物的运输。该项目参与者研究的另一种形成多涡准二维模式的机制是局部热源或表面活性物质附近的马兰戈尼对流。在该项目中，我们的目标是进一步研究这些现象，重点是，沿着传统的流体动力学特性，在频谱和传输特性的各种固定和随时间变化的流动模式与旋涡。我们将研究这些特性对流型结构、涡的相对强度和平均漂移、装置的几何形状和湍流破碎效应的依赖性。其他因素：由于流体旋转或由于电磁力作用在液体上而产生的三维流动也将被考虑在内。我们预计，在问题设置的各种修改应最终稳定的流动模式，导致，首先，形成规则的涡流在不同的尺度上，他们的非线性相互作用，进一步，发病的时间依赖性的流动，最后，增长的空间无序和湍流的发病。通过这种方式，我们的研究将深化有关在涡流中产生湍流的机制的理论知识，并且在实践方面，有助于在应用中更有效地使用这种流动。