Global sensitivity explaining atmospheric shear layer transition

As small vortices appearing within a mixing layer in the atmosphere often shake airplanes dangerously, a better understanding of its transition process is necessary to improve current turbulence forecasts provided by meteorological organizations. There is little meteorological knowledge of that phenomenon because it often happens above the atmospheric boundary layer where weather forecasting models are solved on coarse grids and intensive turbulence observations are usually difficult. We investigated a secondary rib-like structure growing on the primary Kelvin-Helmholtz (KH) vortices in a realistic atmospheric shear profile, which was simulated by a weather forecasting model. By using a three-dimensional Euler computation, we obtained global sensitivities to the primary vortex by measuring kinetic energies of superimposed sinusoidal velocity and vortex disturbances. We concluded the growth of the rib-like structures was explained by the vortex stretching mechanism due to a strong strain between two KH vortices, which was not obtained by the conventional linear stability analysis.