Change search
ReferencesLink to record
Permanent link

Direct link
Receptivity, instability and breakdown of Görtler flow
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0002-4346-4732
Department of Mechanical Engineering, Imperial College.
2011 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 682, 362-396 p.Article in journal (Refereed) Published
Abstract [en]

Receptivity, disturbance growth and breakdown to turbulence in Gortler flow are studied by spatial direct numerical simulation (DNS). The boundary layer is exposed to free-stream vortical modes and localized wall roughness. We propose a normalization of the roughness-induced receptivity coefficient by the square root of the Gortler number. This scaling removes the dependence of the receptivity coefficient on wall curvature. It is found that vortical modes are more efficient at generating Gortler vortices than localized roughness. The boundary layer is most receptive to zero- and low-frequency free-stream vortices, exciting steady and slowly travelling Gortler modes. The associated receptivity mechanism is linear and involves the generation of boundary-layer streaks, which soon evolve into unstable Gortler vortices. This connection between transient and exponential amplification is absent on flat plates and promotes transition to turbulence on curved walls. We demonstrate that the Gortler boundary layer is also receptive to high-frequency free-stream vorticity, which triggers steady Gortler rolls via a nonlinear receptivity mechanism. In addition to the receptivity study, we have carried out DNS of boundary-layer transition due to broadband free-stream turbulence with different intensities and frequency spectra. It is found that nonlinear receptivity dominates over the linear mechanism unless the free-stream fluctuations are concentrated in the low-frequency range. In the latter case, transition is accelerated due to the presence of travelling Gortler modes.

Place, publisher, year, edition, pages
2011. Vol. 682, 362-396 p.
Keyword [en]
boundary layer receptivity, transition to turbulence
National Category
Physical Sciences
URN: urn:nbn:se:kth:diva-25488DOI: 10.1017/jfm.2011.229ISI: 000294775800016ScopusID: 2-s2.0-80052174354OAI: diva2:358788
Swedish Research CouncilSwedish e‐Science Research Center
QC 20101025. Updated from submitted to published.Available from: 2010-10-25 Created: 2010-10-25 Last updated: 2012-05-24Bibliographically approved
In thesis
1. Receptivity of Boundary-Layer Flows over Flat and Curved Walls
Open this publication in new window or tab >>Receptivity of Boundary-Layer Flows over Flat and Curved Walls
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Direct numerical simulations of the receptivity and instability of boundary layers on flat and curved surfaces are herein reported. Various flow models are considered with the aim to capture aspects of flows over straight and swept wings such as wall curvature, pressure variations, leading-edge effects, streamline curvature and crossflow. The first model problem presented, the flow over a swept flat plate, features a crossflow inside the boundary layer. The layer is unstable to steady and traveling crossflow vortices which are nearly aligned with the free stream. Wall roughness and free-stream vortical modes efficiently excite these crossflow modes, and the associated receptivity mechanisms are linear in an environment of low-amplitude perturbations. Receptivity coefficients for roughness elements with various length scales and for free-stream vortical modes with different wavenumbers and frequencies are reported. Key to the receptivity to free-stream vorticity is the upstream excitation of streamwise streaks evolving into crossflow modes. This mechanism is also active in the presence of free-stream turbulence.

The second flow model is that of a Görtler boundary layer. This flow type forms on surfaces with concave curvature, e.g. the lower side of a turbine blade. The dominant instability, driven by a vertically varying centrifugal force, appears as pairs of steady, streamwise counter-rotating vortical rolls and streamwise streaks. The Görtler boundary layer is in particular receptive to free-stream vortical modes with zero and low frequencies. The associated mechanism builds on the excitation of upstream disturbance streaks from which the Görtler modes emerge, similar to the mechanism in swept-plate flows. The receptivity to free-stream vorticity can both be linear and nonlinear. In the presence of free-stream turbulence, nonlinear receptivity is more likely to trigger steady Görtler vortices than linear receptivity unless the frequencies of the free-stream fluctuations are very low.

The third set of simulations considers the boundary layer on a flat plate with an elliptic leading edge. This study aims to identify the effect of the leading edge on the boundary-layer receptivity to impinging free-stream vortical modes. Three types of modes with streamwise, vertical and spanwise vorticity are considered. The two former types trigger streamwise disturbance streaks while the latter type excites Tollmien-Schlichting wave packets in the shear layer. Simulations with two leading edges of different bluntness demonstrate that the leading-edge shape hardly influences the receptivity to streamwise vortices, whereas it significantly enhances the receptivity to vertical and spanwise vortices. It is shown that the receptivity mechanism to vertical free-stream vorticity involves vortex stretching and tilting - physical processes which are clearly enhanced by blunt leading edges.

The last flow configuration studied models an infinite wing at 45 degrees sweep. This model is the least idealized with respect to applications in aerospace engineering. The set-up mimics the wind-tunnel experiments carried out by Saric and coworkers at the Arizona State University in the 1990s. The numerical method is verified by simulating the excitation of steady crossflow vortices through micron-sized roughness as realized in the experiments. Moreover, the receptivity to free-stream vortical disturbances is investigated and it is shown that the boundary layer is most receptive, if the free-stream modes are closely aligned with the most unstable crossflow mode

Place, publisher, year, edition, pages
Stockholm: KTH, 2010. vii, 50 p.
Trita-MEK, ISSN 0348-467X ; 2010:08
Boundary-layer receptivity, laminar-turbulent transition, swept-plate boundary layer, Görtler flow, leading-edge effects, swept-wing flow, crossflow vortices, Görtler rolls, disturbance streaks, wall roughness, free-stream turbulence
National Category
Fluid Mechanics and Acoustics
urn:nbn:se:kth:diva-25439 (URN)978-91-7415-779-6 (ISBN)
Public defence
2010-11-12, F 3, Lindstedtsvägen 26, KTH, Stockholm, 10:00 (English)
QC 20101025Available from: 2010-10-25 Created: 2010-10-21 Last updated: 2010-10-25Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textScopus

Search in DiVA

By author/editor
Schrader, Lars-UveBrandt, Luca
By organisation
MechanicsLinné Flow Center, FLOW
In the same journal
Journal of Fluid Mechanics
Physical Sciences

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 74 hits
ReferencesLink to record
Permanent link

Direct link