Amplitude effects of initial perturbations on nonlinear transient growth dynamics for a vortex column

Nonlinear dynamics present in the evolution of finite amplitude perturbations to a vortex column are discussed, where the initial perturbations are designed to optimize transient energy gain for a linearized Navier-Stokes system. Previous studies of linear transient growth speculated that nonlinear saturation played an important role in the limitation of perturbation energy growth and in causing substantial distortion to the base vortex. New results show that there is no set saturation amplitude, suggesting that the nonlinear dynamics responsible for the distortion of the column change depending on the initial perturbation amplitude. A range of amplitudes and linear transient growth optimals are explored, ranging from nearly linear dynamics for all times to strongly nonlinear at early times, and the resulting differences in the evolution are discussed with a focus on understanding vortex breakup. Additionally, superposition of multiple linear transient growth modes are explored to assess the potential in computing nonlinear optimal perturbations.