Controlling Turbulence as a Chaotic System

摘要申请号：CTS 9729189项目负责人：Moser这是一项通过利用湍流的混沌特性来探索一种特别有前途的控制湍流的技术的资助。特别是，湍流演变的细节对微小的扰动非常敏感。因此，明智地选择小的控制输入原则上可以在流的演变中产生大的变化。在大多数情况下，重要的是控制输入需要很少的能量，以便改变流量的好处不会被控制的成本所抵消。已经开发了几种方案来控制使用非常小的控制输入的低维混沌系统。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），其中减少阻力将是目标。在这些控制技术中，人们选择一个作为系统的目标动力学，可能是无限数量的不稳定周期轨迹中的一个，这些轨迹预计将嵌入系统的混沌吸引子中。由于这是一个自然的，虽然不稳定的系统轨迹，控制这个动态目标只需要稳定它，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.