Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Non-linear wave interactions from transient growth in plane-parallel shear flows
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
2009 (English)In: European journal of mechanics. B, Fluids, ISSN 0997-7546, E-ISSN 1873-7390, Vol. 28, no 3, p. 420-429Article in journal (Refereed) Published
Abstract [en]

Based on the normal velocity-normal vorticity (v - η) formulation for the development of 3D disturbances in plane-parallel shear flows, the non-linear terms in the governing equations are derived as convolution integrals of the Fourier-transformed variables. They are grouped in three categories: v - v, v - η and η - η terms, and are expressed in a simple geometric form using the modulus of the two wave-vectors (k′ and k″) appearing in the convolution integrals, and their intervening angle (χ). The non-linear terms in the v-equation involving η are all weighted by sin χ (or sin2 χ). This confirms the known result that non-linear regeneration of normal velocity, necessary for a sustained driving of 3D disturbances, is not possible for stream-wise elongated structures (α = 0), only. It is therefore suggested how transiently amplified η can interact with decaying 2D waves to activate (oblique) waves which may be less damped than the 2D wave. This is shown to be possible for Blasius flow. In the η-equation, non-linear effects are possible for elongated structures resulting in shorter spanwise scales appearing at a shorter time-scale than the (linear) transient growth. A numerical example shows the details of this process in plane Poiseuille flow. From an inspection of the y-dependency (wall-normal direction) of the non-linear terms it is suggested that higher y-derivatives may give rise to non-linear effects in the inviscid development of perturbations. Also, a result for the y-symmetry of the non-linear terms is derived, applicable to plane Poiseuille flow.

Place, publisher, year, edition, pages
2009. Vol. 28, no 3, p. 420-429
Keywords [en]
Engineering mechanics - Fluid mechanics
Keywords [sv]
Teknisk mekanik - Strömningsmekanik
National Category
Fluid Mechanics and Acoustics
Research subject
Fluid Mechanics
Identifiers
URN: urn:nbn:se:ltu:diva-9201DOI: 10.1016/j.euromechflu.2008.10.001ISI: 000265341500007Scopus ID: 2-s2.0-62349087017Local ID: 7c3a19b0-29b7-11de-adf6-000ea68e967bOAI: oai:DiVA.org:ltu-9201DiVA, id: diva2:982139
Note
Validerad; 2009; 20090415 (ysko)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full textScopus

Authority records BETA

Gustavsson, Håkan

Search in DiVA

By author/editor
Gustavsson, Håkan
By organisation
Fluid and Experimental Mechanics
In the same journal
European journal of mechanics. B, Fluids
Fluid Mechanics and Acoustics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 213 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf