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MODAL ANALYSIS OF ROUGHNESS-INDUCED CROSSFLOW VORTICES IN A FALKNER−SKAN−COOKE BOUNDARY LAYER

Mattias Brynjell-Rahkola
Linne FLOW Centre and Swedish e-Science Research Centre (SeRC) KTH Mechanics, Royal Institute of Technology SE-100 44 Stockholm, Sweden

Phillipp Schlatter
Linne FLOW Centre and Swedish e-Science Research Centre (SeRC) KTH Mechanics, Royal Institute of Technology SE-100 44 Stockholm, Sweden

Ardeshir Hanifi
Linne FLOW Centre and Swedish e-Science Research Centre (SeRC) KTH Mechanics, Royal Institute of Technology SE-100 44 Stockholm, Sweden; Swedish Defence Research Agency, FOI, SE-164 90 Stockholm, Sweden

Dan S. Henningson
Linne FLOW Centre and Swedish e-Science Research Centre (SeRC) KTH Mechanics, Royal Institute of Technology SE-100 44 Stockholm, Sweden

Abstract

A three-dimensional global stability analysis using high-order direct numerical simulations is performed to investigate the effect of surface roughness with Reynolds number (based on roughness height) Rek above and below the critical value for transition, on the eigenmodes of a Falkner−Skan−Cooke boundary layer. The surface roughness is introduced with the immersed boundary method and the eigenvalues and eigenfunctions are solved using an iterative time-stepper method. The study reveals a global instability for the case with higher Reynolds number that causes the flow in the non-linear simulations to break down to turbulence shortly downstream of the roughness. Examination of the unstable linear global modes show that these are the same modes that are observed in experiments immediately before breakdown due to secondary instability, which emphasizes the importance of these modes in transition.