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Feedback Instability in a Boundary‐Layer Flow Over Roughness
Author(s) -
Timoshin S. N.
Publication year - 2005
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300000437
Subject(s) - instability , mathematics , flow (mathematics) , boundary layer , mechanics , surface finish , compressibility , surface roughness , geometry , physics , materials science , quantum mechanics , composite material
Abstract Linear stability of an incompressible triple‐deck flow over a wall roughness is considered for disturbances of high frequency. The wall roughness consists of two relatively short obstacles placed far apart on an otherwise flat surface. It is shown that the flow is unstable to feedback or global mode disturbances. The feedback loop is formed by algebraically decaying disturbances propagating upstream and weakly growing Tollmien‐Schlichting waves travelling downstream and as such represents an interaction between modes from continuous and discrete spectra of the corresponding parallel‐flow problem. An example of growth rate calculation for a specific roughness is considered.