A theoretical approach for analyzing the restabilization of wakes

A linear stability analysis provides the basis for an analysis of the effects of prescribed changes upon the global stability characteristics of a bluff body wake. The analysis is applied in particular to the problem of placing a small cylinder in the wake of a larger one in order to suppress the vortex street. A prediction of the alteration in the critical Reynolds number of the system as a function of the location of the second cylinder relative to the first is presented and is shown to compare favorably with experimental results. The effect upon shedding frequency is also considered. The approach relies on the solution of an adjoint eigenvalue problem and an inhomogeneous adjoint boundary value problem. These adjoint solutions are shown to be a key component in the analysis of a variety of wake control strategies.