Nonlinear processes of short-wave instabilities growing in a helical vortex: saturation and turbulent transition

Wind turbines are known to produce helical vortices as tip vortices. If these helical vortices persist over a long distance, wake recovery can be severely hindered, resulting in a significant reduction in power generation in large-scale wind farms. Therefore, the turbulent transition process of helical vortices has attracted much attention. It is known that there are two types of instabilities depending on the wavelength scale: the long-wave instability and the short-wave instability. Although both instabilities are considered to play important roles in the turbulent transition of helical vortices, the nonlinear process of the short-wave instability is not sufficiently understood for helical vortices. Therefore, this presentation investigates the nonlinear effects of the short-wave instabilities in a helical vortex. Here, direct numerical simulations of a helical vortex disturbed by the short-wave instability are performed. This confirms that there are several possible states that the short-wave instability leads to. In particular, in addition to cases where the short-wave instability directly leads to the collapse of the vortex core, the saturation of the growth due to viscosity and nonlinear effects is identified. The possibility of secondary instability after saturation is also discussed. It is found that the energy of some specific wavenumbers, besides the instability mode and its harmonics, grows, developing characteristic mode structures, which is most likely due to the triadic resonance.