Worst-case amplification of disturbances in inertialess flows of viscoelastic fluids

Binh K. Lieu, Mihailo R. Jovanović, Satish Kumar

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

1 Scopus citations


Amplification of deterministic disturbances in inertialess channel flows of viscoelastic fluids is studied by analyzing the frequency responses from spatio-temporal body forces to the velocity fluctuations. In strongly elastic flows, we show that velocity fluctuations can exhibit significant amplification even in the absence of inertia. Our analysis demonstrates that streamwise-constant disturbances are the most amplified. Explicit expressions are established for the worst-case amplification of velocity fluctuations arising from different components of the body forces. These show that amplification from the wall-normal and spanwise forces to the streamwise velocity component scales quadratically with the Weissenberg number. The underlying physical mechanism involves stretching of polymer stress fluctuations by a background shear, which is a close analog of the vortex titling mechanism that is responsible for amplification in inertial flows of Newtonian fluids.

Original languageEnglish (US)
Title of host publicationProceedings of the 18th IFAC World Congress
PublisherIFAC Secretariat
Number of pages6
Edition1 PART 1
ISBN (Print)9783902661937
StatePublished - 2011

Publication series

NameIFAC Proceedings Volumes (IFAC-PapersOnline)
Number1 PART 1
ISSN (Print)1474-6670

Bibliographical note

Funding Information:
★ This work was supported in part by the National Science Foundation under CAREER Award CMMI-06-44793 (to M. R. J.), by the Department of Energy under Award DE-FG02-07ER46415 (to S. K.), and by the University of Minnesota Digital Technology Center’s 2010 Digital Technology Initiative Seed Grant (to M. R. J. and S. K.).


  • Elastic turbulence
  • Frequency responses
  • Inertialess flows
  • Infinite dimensional systems
  • Polymer stretching
  • Robustness analysis
  • Viscoelastic fluids
  • Worst-case amplification


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