Secondary Instabilities of Three-Dimensional Inflectional Velocity Profiles Resulting from Longitudinal Vorticity Elements in Boundary Layers
We consider the problem of “high frequency” secondary instability of nonlinearly developed and strongly modified Gortler vortices initiated at finite Gortler and wave numbers in the amplified region. Local linear stability analyses of relevant cross-sectional planes show that secondary instabilities are more correlated with the vertical vorticity and that they would originate in two regions: (1) in the outer region of the boundary layer at the “shoulders” on either side of the peak region and (2) in the lower regions at about y+≈30, on either side but more concentrated about the peak region. For the same frequency and strcamwise wave number found in experiments, the sinuous type disturbance would prevail over the varicose; disturbances in lower region near the wall have the largest amplification rate.
KeywordsPeak Region Secondary Instability Longitudinal Vortex Vertical Vorticity Concave Wall
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