Using nonlinear optimization to understand coherent structures in turbulence and transition

Abstract : This thesis aims at unraveling the main mechanisms involved in transitional and turbulent flows. The central idea is that of using a nonlinear optimization technique to investigate the origin and role of coherent structures usually observed in these flows. This method has been used in three different contexts. First, a linearly stable laminar flow has been considered and the optimization has been used to compute the most amplified perturbations among all disturbances able to trigger transition to turbulence. Once turbulence is well established, a fully 3D nonlinear optimization maximizing the turbulent kinetic energy is used to study coherent structures populating turbulent shear flow as well as investigate the mechanisms responsible for the energy (optimally) growth and exchange. Then, a dynamical system approach is applied to fluid flow equations. The geometry of the state space is investigated by using transient growth theory to reveal the importance of the stable and unstable manifold. In the same framework, a nonlinear minimization algorithm is used to compute heteroclinic connections among invariant solutions of the Navier-Stokes equations.
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Mirko Farano. Using nonlinear optimization to understand coherent structures in turbulence and transition. Fluids mechanics [physics.class-ph]. Ecole nationale supérieure d'arts et métiers - ENSAM, 2017. English. ⟨NNT : 2017ENAM0047⟩. ⟨tel-01881360⟩

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