The dynamics and control of a vortex pair in ground effect are investigated in a planar, incompressible and laminar setting. The evolution of the vortices obtained numerically shows vortex rebound as a consequence of the separation of the boundary layer induced at the wall by the vortices. An optimal control approach is developed and employed for vortex Reynolds numbers of 200 and 1000 in order to identify the optimal Dirichlet boundary condition at the wall to counteract this rebound and allow for an increased lateral displacement of the vortex, similarly to the inviscid evolution of the flow, which features hyperbolic trajectories. The work is primarily a conceptual approach to deal with aircraft separation distances in airport airspace by moving the vortices laterally, away from the runway but may also apply to the control of coherent structures in wall bounded turbulence. The most efficient control is able to double the lateral position and yields mostly vertical in and outflow at the wall. An optimal horizon time is found, equal to 5 characteristic time units of the vortex system, beyond which control is not able to further displace the vortices. The control is shown to delay the separation of the boundary layer at the origin of vortex rebound by applying suction ahead of the vortex, and to generate a vorticity flux at the wall, leading to a pusher vortex of sign opposite to that of the primary vortex, that attenuates the effect of the no-slip boundary condition at the wall by pushing the vortex outward.

中文翻译：

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地面效应、动力学和优化控制中的涡旋对

在平面、不可压缩和层流环境中研究了地面效应中涡对的动力学和控制。数值上获得的涡旋的演变表明涡旋反弹是由于涡旋在壁上引起的边界层分离的结果。为涡流雷诺数为 200 和 1000 开发并采用了最佳控制方法，以确定壁处的最佳狄利克雷边界条件以抵消这种回弹并允许涡流的横向位移增加，类似于无粘性演化流动，具有双曲线轨迹。这项工作主要是一种通过横向移动涡流来处理机场空域中飞机间隔距离的概念方法，远离跑道，但也可能适用于壁面湍流中相干结构的控制。最有效的控制能够使横向位置加倍，并在壁上产生大部分垂直流入和流出。找到了一个最佳水平时间，等于涡流系统的 5 个特征时间单位，超过这个时间控制将无法进一步移动涡流。控制显示通过在涡流前面施加吸力来延迟涡流回弹起点处边界层的分离，并在壁上产生涡量通量，导致与主涡流符号相反的推进涡流，通过向外推动涡流来减弱壁上无滑移边界条件的影响。最有效的控制能够使横向位置加倍，并在壁上产生大部分垂直流入和流出。找到了一个最佳水平时间，等于涡流系统的 5 个特征时间单位，超过这个时间控制将无法进一步移动涡流。控制显示通过在涡流前面施加吸力来延迟涡流回弹起点处边界层的分离，并在壁上产生涡量通量，导致与主涡流符号相反的推进涡流，通过向外推动涡流来减弱壁上无滑移边界条件的影响。最有效的控制能够使横向位置加倍，并在壁上产生大部分垂直流入和流出。找到了一个最佳水平时间，等于涡流系统的 5 个特征时间单位，超过这个时间控制将无法进一步移动涡流。控制显示通过在涡流前面施加吸力来延迟涡流回弹起点处边界层的分离，并在壁上产生涡量通量，导致与主涡流符号相反的推进涡流，通过向外推动涡流来减弱壁上无滑移边界条件的影响。