Secondary optimal growth and subcritical transition in the plane Poiseuille flow
2010 (English)In: 7th IUTAM Symposium on Laminar-Turbulent Transition, Springer Netherlands, 2010, 129-134 p.Conference paper (Refereed)
Nonlinear optimal perturbations leading to subcritical transition with minimum threshold energy are searched in the plane Poiseuille flow at Re = 1500. To this end we proceed in two steps. First a family of optimally growing primary streaks U issued by the optimal vortices of the Poiseuille laminar solution is computed by direct numerical simulation for a set of finite amplitudes AI of the primary vortices. An adjoint technique is then used to compute the maximum growth and the finite time Lyapunov exponents of secondary perturbations growing on top of these primary base flows. The secondary optimals take into full account the non-normality and the local instabilities of the tangent operator all along the temporal evolution of the primary flows. The most amplified optimal perturbations are sinuous and realized in correspondence of streaks that are locally unstable. The combinations of primary and secondary perturbations optimal for transition are then explored using direct numerical simulations. It is shown that the minimum initial energy is realized by a large set of these combinations, revealing new paths to transition. Surprisingly we find that transition can be efficiently obtained even using secondary perturbations alone, in the absence of primary optimal vortices.
Place, publisher, year, edition, pages
Springer Netherlands, 2010. 129-134 p.
, IUTAM Bookseries, ISSN 1875-3507 ; 18
Adjoint techniques, Baseflows, Finite amplitude, Finite-time Lyapunov exponent, Initial energy, Local instability, Non-normality, Nonlinear optimal, Optimal growth, Optimal perturbation, Plane Poiseuille flow, Primary flow, Primary vortex, Subcritical transition, Tangent operators, Temporal evolution, Threshold energy, Direct numerical simulation, Vortex flow, Optimization
IdentifiersURN: urn:nbn:se:kth:diva-150304DOI: 10.1007/978-90-481-3723-7-19ISI: 000277097200019ScopusID: 2-s2.0-84862279531ISBN: 978-90-481-3722-0OAI: oai:DiVA.org:kth-150304DiVA: diva2:742549
7th IUTAM Symposium on Laminar-Turbulent Transition; Stockholm; Sweden; 23 June 2009 through 26 June 2009
QC 201409022014-09-022014-09-012014-09-02Bibliographically approved