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Effect of base-flow variation in noise amplifiers: the flat-plate boundary layer
KTH, Skolan för teknikvetenskap (SCI), Mekanik, Stabilitet, Transition, Kontroll. KTH, Skolan för teknikvetenskap (SCI), Centra, Linné Flow Center, FLOW.ORCID-id: 0000-0002-4346-4732
2011 (Engelska)Ingår i: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 687, s. 503-528Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

Non-modal analysis determines the potential for energy amplification in stable flows. The latter is quantified in the frequency domain by the singular values of the resolvent operator. The present work extends previous analysis on the effect of base-flow modifications on flow stability by considering the sensitivity of the flow non-modal behaviour. Using a variational technique, we derive an analytical expression for the gradient of a singular value with respect to base-flow modifications and show how it depends on the singular vectors of the resolvent operator, also denoted the optimal forcing and optimal response of the flow. As an application, we examine zero-pressure-gradient boundary layers where the different instability mechanisms of wall-bounded shear flows are all at work. The effect of the component-type non-normality of the linearized Navier-Stokes operator, which concentrates the optimal forcing and response on different components, is first studied in the case of a parallel boundary layer. The effect of the convective-type non-normality of the linearized Navier-Stokes operator, which separates the spatial support of the structures of the optimal forcing and response, is studied in the case of a spatially evolving boundary layer. The results clearly indicate that base-flow modifications have a strong impact on the Tollmien-Schlichting (TS) instability mechanism whereas the amplification of streamwise streaks is a very robust process. This is explained by simply examining the expression for the gradient of the resolvent norm. It is shown that the sensitive region of the lift-up (LU) instability spreads out all over the flat plate and even upstream of it, whereas it is reduced to the region between branch I and branch II for the TS waves.

Ort, förlag, år, upplaga, sidor
2011. Vol. 687, s. 503-528
Nyckelord [en]
boundary layer receptivity, control theory
Nationell ämneskategori
Maskinteknik
Identifikatorer
URN: urn:nbn:se:kth:diva-58821DOI: 10.1017/jfm.2011.382ISI: 000297930400019Scopus ID: 2-s2.0-84855497397OAI: oai:DiVA.org:kth-58821DiVA, id: diva2:474184
Forskningsfinansiär
Swedish e‐Science Research Center
Anmärkning
QC 20120109Tillgänglig från: 2012-01-09 Skapad: 2012-01-09 Senast uppdaterad: 2017-12-08Bibliografiskt granskad

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Brandt, Luca

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Stabilitet, Transition, KontrollLinné Flow Center, FLOW
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