Adjoint Equations in Stability Analysis: Supplemental Video 1

A supplemental video from the 2014 review by Paolo Luchini and Alessandro Bottaro, "Adjoint Equations in Stability Analysis," from the Annual Review of Fluid Mechanics. 

Spatial evolution of the minimal seed in a boundary layer. The structure evolves with the initial downstream tilting of the low streamwise velocity region (in light blue) by the Orr mechanism, the formation of a Λ structure, and the subsequent creation of a hairpin vortex (visualized in gray through isosurfaces of the Q-criterion). This hairpin can rapidly induce downstream a train of smaller-scale hairpin vortices which display, embedded within, further small minimal seeds; this leads to a repeated sequence of the same events taking place over shorter length scales and timescales, until turbulence (Cherubini et al. 2011, 2012).