Controlling Turbulence as a Chaotic System

将湍流作为混沌系统进行控制

• 批准号: 9729189
• 负责人: Robert Moser
• 金额: $ 24万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-08-01 至 2002-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9729189&HistoricalAwards=false
• 关键词: Controlling; Turbulence; Chaotic; System

ABSTRACT Proposal Number: CTS 9729189 Principal Investigator: Moser This is a grant to explore a particularly promising technique for controlling turbulence by exploiting its chaotic nature. In particular, the details of the evolution of the turbulence are highly sensitive to small perturbations. Thus, judiciously chosen small control inputs can in principle produce large changes in the evolution of the flow. In most situations it is important that the control input require very little energy so that the benefits of modifying the flow are not out-weighed by the cost of the control. Several schemes have been developed to control low dimensional chaotic systems using very small control inputs. In the research proposed here, these schemes will be applied to a simple turbulent fluid flow (the minimal turbulent channel), in which drag reduction will be the objective. In these control techniques, one selects as the goal dynamics for the system, one of the presumably infinite number of unstable periodic trajectories that are expected to be embedded in the chaotic attractor of the system. Since this is a natural, although unstable, system trajectory, controlling to this goal dynamic just requires stabilizing it, which can be done with very small control inputs.

摘要 提案编号：CTS 9729189 首席研究员：Moser 这是一项拨款，旨在探索一种特别有前途的技术，通过利用其混沌性质来控制湍流。 特别是，湍流演化的细节对小扰动高度敏感。 因此，明智地选择小的控制输入原则上可以在流动的演变中产生巨大的变化。 在大多数情况下，重要的是控制输入需要很少的能量，这样改变流量的好处就不会被控制成本所抵消。 已经开发了几种方案来使用非常小的控制输入来控制低维混沌系统。 在这里提出的研究中，这些方案将应用于简单的湍流流体流动（最小湍流通道），其中减阻将是目标。 在这些控制技术中，人们选择预计嵌入系统混沌吸引子中的无限数量的不稳定周期轨迹之一作为系统的目标动力学。 由于这是一个自然但不稳定的系统轨迹，因此控制该目标动态只需要稳定它，这可以通过非常小的控制输入来完成。