Effect of unsteady forcing on the sinusoidal instability of vortex wakes

An analytical model of the vortex wake instability subject to forcing by unsteady lift fluctuations has been developed. These lift fluctuations can be caused either by variations in angle of attack or by flying through atmospheric turbulence. The effect of turbulence in the fluid itself, already studied by Crow and Bate, has been reviewed and incorporated into the analysis. A simple procedure is provided to estimate the time at which contact occurs between the two wake vortices as a function of certain characteristics of the forcing inputs. The behavior of the instability is somewhat altered by these forcing terms. In particular, it was found that contact between vortices can occur at much shorter wavelengths than predicted for the unforced case. Furthermore, in the presence of forcing, the minimum completion time for the instability does not correspond to the wavenumber for which the amplification rate is a maximum because the length of the vortex trajectories is also an important factor. Finally, the stability boundary is extended to larger wavenumbers by the presence of forcing, and the boundary location depends on the forcing level. © 1982 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

Duke Scholars

Author Donald B. Bliss Thomas Lord Department of Mechanical Engineering and Materia ...