Towards the foundation of a global modes concept

Daniel Rodríguez, Anatoli Tumin, Vassilis Theofilis

Research output: Chapter in Book/Report/Conference proceedingConference contribution

11 Scopus citations


A contribution is presented, intended to provide theoretical foundations for the ongoing efforts to employ global instability theory for the analysis of the classic boundary-layer flow, and address the associated issue of appropriate inflow/outflow boundary conditions to close the PDE-based global eigenvalue problem in open flows. Starting from a theoretically clean and numerically simple application, in which results are also known analytically and thus serve as a guidance for the assessment of the performance of the numerical methods employed herein, a sequence of issues is systematically built into the target application, until we arrive at one representative of open systems whose instability is presently addressed by global linear theory applied to open flows, the latter application being neither tractable theoretically nor straightforward to solve by numerical means. Experience gained along the way is documented. It regards quantification of the departure of the numerical solution from the analytical one in the simple problem, the generation of numerical boundary layers at artificially truncated boundaries, no matter how far the latter are placed from the region of highest flow gradients and, ultimately the impracti-cally large number of (direct and adjoint) modes necessary to project an arbitrary initial perturbation and follow its temporal evolution by a global analysis approach, a finding which may question the purported robustness reported in the literature of the recovery of optimal perturbations as part of global analyses yielding under-resolved eigenspectra.

Original languageEnglish (US)
Title of host publication6th AIAA Theoretical Fluid Mechanics Conference
StatePublished - 2011
Event6th AIAA Theoretical Fluid Mechanics Conference - Honolulu, HI, United States
Duration: Jun 27 2011Jun 30 2011

Publication series

Name6th AIAA Theoretical Fluid Mechanics Conference


Other6th AIAA Theoretical Fluid Mechanics Conference
Country/TerritoryUnited States
CityHonolulu, HI

ASJC Scopus subject areas

  • Fluid Flow and Transfer Processes


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