| Popis: |
We investigate the three-dimensional temporal non-modal stability of viscous round jets subject to the primary Kelvin-Helmholtz instability. Non-modal linear stability analysis is based on a direct-adjoint technique which enables to determine the fastest growing perturbation, or optimal perturbation, over a single period of the time-evolving two-dimensional base flow during a given time interval, [t0; T]. We explore the sensitivity of the optimal perturbation to the following parameters: • the azimuthal wavenumber of the mode, m; • the injection time, t0; • the horizon time, T; • the aspect ratio, α = R/θ, where R and θ are respectively the jet radius and the shear layer momentum thickness; • the Reynolds number, Re = UjR/ν, where Uj is jet center-line velocity and ν the kinematic viscosity. In particular, we focus on the influence of the azimuthal wavenumber, m, on the optimal energy gain as a function of the horizon time, T. In this context, for Re = 1000 and α = 10, the helical perturbations experience the highest energy growth. The short time dynamics of the perturbations, i.e. T < 5, are driven by the so-called Orr mechanism whatever the azimuthal wavenumber. For larger horizon times, the optimal perturbation leads to the development of an elliptic instability located within the vortex core for low values of the azimuthal wavenumber. When m is increased, the location of the optimal perturbation progressively moves towards the braid region, which is characteristic of an hyperbolic instability. Finally, we also consider the impact of the injection time on the contribution of the Orr mechanism to transient dynamics. |
