Controlling Turbulence as a Chaotic System

摘要 提案编号：CTS 9729189 主要研究者：Moser 这是一个赠款，以探索一个特别有前途的技术，通过利用其混沌性质控制湍流。 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，原则上可以产生大的变化，在流动的演变。 在大多数情况下，重要的是，控制输入需要非常少的能量，使得改变流量的益处不被控制的成本超过。 已经开发了几种方案来控制低维混沌系统使用非常小的控制输入。 在这里提出的研究中，这些计划将被应用到一个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，一个选择作为系统的目标动力学，一个大概是无限数量的不稳定的周期性轨迹，预计将嵌入在系统的混沌吸引子。 由于这是一个自然的，虽然不稳定的系统轨迹，控制到这个目标动态只需要稳定它，这可以用非常小的控制输入来完成。

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.