Towards minimal perturbations in transitional plane Couette flow
2010 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, Vol. 82, no 2, 026316- p.Article in journal (Refereed) Published
For parallel shear flows, transition to turbulence occurs only for perturbations of sufficiently large amplitude. It is therefore relevant to study the shape, amplitude, and dynamics of the least energetic initial disturbances leading to transition. We suggest a numerical approach to find such minimal perturbations, applied here to the case of plane Couette flow. The optimization method seeks such perturbations at initial time as a linear combination of a finite number of linear optimal modes. The energy threshold of the minimal perturbation for a Reynolds number Re=400 is only 2% less than for a pair of symmetric oblique waves. The associated transition scenario shows a long transient approach to a steady state solution with special symmetries. Modal analysis shows how the oblique-wave mechanism can be optimized by the addition of other oblique modes breaking the flow symmetry and whose nonlinear interaction generates spectral components of the edge state. The Re dependence of energy thresholds is revisited, with evidence for a O(Re(-2))-scaling for both oblique waves and streamwise vortices scenarios.
Place, publisher, year, edition, pages
2010. Vol. 82, no 2, 026316- p.
Fusion, Plasma and Space Physics
IdentifiersURN: urn:nbn:se:kth:diva-46630DOI: 10.1103/PhysRevE.82.026316ISI: 000281228700003ScopusID: 2-s2.0-77956106395OAI: oai:DiVA.org:kth-46630DiVA: diva2:455137
QC 201111082011-11-082011-11-042011-11-08Bibliographically approved