NONLINEAR MODELING OF VORTEX SHEDDING CONTROL IN CYLINDER WAKES

Karman vortex shedding behind a cylinder placed at right angles to a u niform flow is known to be a limit cycle oscillation that results from the saturation of a global instability of the wake flow. In this pape r we study the feedback control of Karman vortex shedding for Reynolds numbers (based an cylinder diameter) close to the critical value of R e-c approximate to 47 using ''single input-single output'' (SISO) prop ortional control. A model is presented that combines the linear stream wise global mode amplitude equation and the nonlinear spanwise Ginzbur g-Landau equation and correctly models the three-dimensional effects o bserved In the controlled wake of finite length cylinders. In particul ar it is demonstrated that for long cylinders vortex shedding can only be suppressed at the spanwise location of the sensor even though the actuation occurs uniformly over the entire span. At a fixed streamwise position the spanwise variation of the shedding angle is thereby give n by the ''hole solution'' of Nozaki and Bekki, J. Phys. Sec. Jpn. 53 (1984) 1581.