Excitation of vortex meandering in shear flow

Kurzfassung

This paper investigates the evolution of a streamwise aligned columnar vortex with vorticity ω in an axial background shear of magnitude Ω by means of linear stability analysis and numerical simulations. A long wave mode of vorticity normal to the plane spanned by the background shear vector Ω and the vorticity of the vortex are excited by an instability. The stationary wave modes of the vertical and lateral vorticity are amplified. In order to form a helical vortex, the lateral and vertical vorticity can be phase shifted by half a wavelength. The linear and nonlinear evolutions of the vortex in the shear flow are studied numerically. Linearized simulations confirm the results of the stability analysis. The nonlinear simulations reveal further evolution of the helix in the shear flow. The linearly excited mode persists in co-existence with evolving smaller scale instabilities until the flow becomes fully turbulent at the time of O(100 Ω−1). Turbulent mixing dampens the amplifying mode. The described phenomenon of vortex meandering may serve as an alternative explanation for the excitation of wind turbine wake meandering in the atmospheric boundary layer.