Harnessing the Kelvin-Helmholtz Instability: Feedback Stabilization of an Inviscid Vortex Sheet. (arXiv:1711.03249v1 [physics.flu-dyn])

In this investigation we use a simple model of the dynamics of an inviscid vortex sheet given by the Birkhoff-Rott equation to obtain fundamental insights about the potential for stabilization of shear layers using feedback. First, we demonstrate using analytical computations that the Birkhoff-Rott equation linearized around the flat-sheet configuration is in fact controllable when a pair of point vortices located on both sides of the sheet is used as actuation. On the other hand, this system is not controllable when the actuation has the form of a pair of sinks/sources with zero net mass flux. Next we design a state-based LQR stabilization strategy where the key difficulty is the numerical solution of the Riccati equation in the presence of severe ill-conditioning resulting from the properties of the Birkhoff-Rott equation and the chosen form of actuation, an issue which is overcome by performing computations with a suitably increased arithmetic precision. Analysis of the linear close 查看全文>>