%0 Journal Article
%T Optimal Transient Growth in an Incompressible Flow past a Backward-Slanted Step
%A Eric Serre
%A Marco Martins Afonso
%A Philippe Meliga
%J -
%D 2019
%R https://doi.org/10.3390/fluids4010033
%X Abstract With the aim of providing a first step in the quest for a reduction of the aerodynamic drag on the rear-end of a car, we study the phenomena of separation and reattachment of an incompressible flow by focusing on a specific aerodynamic geometry, namely a backward-slanted step at 25 ¡ã of inclination. The ensuing recirculation bubble provides the basis for an analytical and numerical investigation of streamwise-streak generation, lift-up effect, and turbulent-wake and Kelvin¨CHelmholtz instabilities. A linear stability analysis is performed, and an optimal control problem with a steady volumic forcing is tackled by means of a variational formulation, adjoint methods, penalization schemes, and an orthogonalization algorithm. Dealing with the transient growth of spanwise-periodic perturbations, and inspired by the need of physically-realizable disturbances, we finally provide a procedure attaining a kinetic-energy maximal gain on the order of 10 6 , with respect to the power introduced by the external forcing. View Full-Tex
%K linear stability analysis
%K separation and reattachment
%K optimal control
%K streak lift-up
%K turbulent-wake and Kelvin¨CHelmholtz instabilities
%K incompressibility
%K 3D perturbations of 2D steady base flow
%K structural sensitivity
%K recirculation bubble
%K 25¡ã backward-slanted step
%U https://www.mdpi.com/2311-5521/4/1/33