On the connection between cross-flow vortices and attachment-line instabilities

  • Fabio P. Bertolotti
Conference paper
Part of the IUTAM Symposia book series (IUTAM)


The connection between cross-flow vortices and attachment-line instabilities is identified in the swept Hiemenz flow. Starting from an exact description of the perturbation vorticity field in the free-stream based on confluent hypergeometric functions, we derive an eigenvalue problem that yields a more complete set of the attachment-line instabilities than previously possible. For eigenvalues of the form −n/2, n an integer, the hypergeometric functions reduce to Hermite polynomials that fully describe the previously known instabilities, which, however, do not connect to the cross-flow vortices. For eigenvalues with both real and imaginary parts, a new family of attachment-line instabilities appears, having members that connect to the cross-flow modes. (Supported by DFG project Da 183/3-2)


Neutral Curve Neutral Stability Curve Confluent Hypergeometric Function Attachment Line Parabolized Stability Equation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Fabio P. Bertolotti
    • 1
  1. 1.DLR, Institute of Fluid MechanicsGöttingenGermany

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