Optimal streaks in 2D wakes and their stabilizing effect on local and global instabilities

By Prof. Carlo Cossu
Directeur de recherche CNRS, Institut de mécanique des fluides (IMFT) – Toulouse


Monday 26th of May 2014 – 15:00 / Room BM 1130



This talk will summarize recent results obtained on the forcing of optimal perturbations in wakes and on their stabilizing action on local and global wake instabilities.
In the first part of the talk, parallel wakes are considered. Optimal temporal transient energy growths of  streamwise uniform perturbations are computed.
Optimal initial conditions consist in streamwise vortices and the optimally amplified perturbations are streamwise streaks. It is shown that, when forced at finite
amplitude in absolutely unstable wakes, optimal streaks can completely suppress the absolute instability converting it into a convective instability.
Next, a synthetic non-parallel and the circular cylinder wakes are considered.
Optimal spatial energy amplifications of steady disturbances are computed, finding again that streamwise streaks are the most amplified structures. It is shown that global
instabilities can be stabilized by optimal streaks of sufficiently large amplitude.
We also show that the amplitude of optimal spanwise periodic (3D) perturbations of the basic flow required to stabilize the global instability is smaller than the one required by
spanwise uniform (2D) perturbations despite the fact that the first order sensitivity of the global eigenvalue to basic flow modifications is zero for 3D spanwise periodic modifications and non-zero for 2D modifications.
We therefore conclude that first-order sensitivity analyses can be misleading if used far from the instability threshold, where higher order terms are the most relevant.




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