an author's https://oatao.univ-toulouse.fr/21534
Nastro, Gabriele and Fontane, Jérôme and Joly, Laurent Optimal perturbations in a time-dependent round jet. (2018) In: 71st Annual Meeting of the American Physical Society, Division of Fluid Dynamics (DFD), 18 November 2018 - 20 November 2018 (Atlanta, United States).
Optimal perturbations in a time-dependent round jet Gabriele Nastro1, Jérôme Fontane1 and Laurent Joly1
1 Institut Supérieur de l'Aéronautique et de l'Espace (ISAE-SUPAERO), Université de Toulouse,
10 avenue Édouard Belin - BP 54032 - 31055 Toulouse CEDEX 4, France
We analyse the in uence of the speci c features of a time-dependent round jet undergoing the Kelvin-Helmholtz instability on the development of three-dimensional secondary instabilities. We proceed to a non-modal linear stability analysis based on a direct-adjoint approach in order to de-termine the fastest growing perturbation over a single period of the time-evolving two-dimensional base ow during a given time interval, [t0, T ]. An optimisation loop allows to adapt the control criteria depending on the quantity we want to maximise. In particular, it enables to explore the sensitivity of the optimal perturbation to the azimuthal periodicity of the mode, m, as well as the Reynolds number, Re. We focus on the in uence of the azimuthal wavenumber, m, on the optimal energy gain as a function of the horizon time, T . We also consider the impact of the injection time, t0, on the transient dynamics of the optimal perturbation and, in particular, on the contribution of the Orr mechanism. Through a detailed analysis of the kinetic energy budget, we identify the dierent types of instability (elliptical, hyperbolic) and their coexistence associated with the three-dimensionalisation process of the round jet.
key words: instability, round jet, non modal, direct-adjoint method, optimal perturbation
