Stability of streaks in shear flows

The stability of streaks, generated by vortices in wall-bounded shear flows, is studied analytically, numerically and experimentally. A novel analytical approximation of the linear transient growth in Couette flow allows investigating the secondary stability of spanwise periodic streaks using Floquet theory. The optimal parameters for instability correspond to the strongest inflection points, those having maximal shear, rather than initial conditions maximizing the energy growth. For the symmetric transient growth the most dangerous secondary disturbances are sinuous, associated with spanwise inflection points having a spanwise wavenumber of β = 3.6 (as opposed to β = 1.67 which maximizes energy growth) and the varicose instabilities are associated with spanwise inflection points as well. For the antisymmetric transient growth both sinuous and varicose instabilities are observed, associated with spanwise and wall-normal inflection points, respectively. The theoretical results are verified by obtaining transition in a direct numerical simulation (DNS) initiated by the corresponding analytical expressions. The rapid evolution of the secondary disturbance on top of the slowly evolving transient growth enables us to use the multiple time scales method to follow the evolution of the secondary disturbance. The very good agreement between the DNS and analytical expressions verifies the theoretical predictions. Finally, the above results are discussed with respect to previous transitional pipe and Poiseuille flow experiments.