Frequency domain analysis of the linearized Navier-Stokes equations

Mihailo R. Jovanović, Bassam Bamieh

Research output: Contribution to journalConference articlepeer-review

8 Scopus citations


We study the Linearized Navier-Stokes (LNS) equations from an input-output point of view by analyzing their spatio-temporal frequency responses. We show how the relative roles of Tollmien-Schlichting (TS) waves and streamwise vortices and streaks can be explained as input-output resonances of the spatio-temporal frequency responses. Furthermore, we derive important conclusions about the effectiveness of input field components, and the contributions of the stream-wise, wall-normal, and spanwise velocity perturbations to the kinetic energy density. In particular, we show that the wall-normal and spanwise forces have much stronger influence on the velocity field than the stream-wise force. On the other hand, the velocity perturbations in the direction of a nominal flow achieve much bigger magnitudes than the perturbations in the other two spatial directions.

Original languageEnglish (US)
Pages (from-to)3190-3195
Number of pages6
JournalProceedings of the American Control Conference
StatePublished - Nov 6 2003
Event2003 American Control Conference - Denver, CO, United States
Duration: Jun 4 2003Jun 6 2003

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