The Mack’s amplitude method revisited

Alexander Fedorov, Anatoli Tumin

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Mack (1977) criticized methods referring to a single frequency perturbation for correlation of transition prediction because the external disturbance source (like free stream turbulence) should have a broadband spectrum. Delta-correlated perturbations are characterized by the mean square of physical amplitude, which is expressed as a double integral of the power spectral density in frequency and the spanwise wave number. It is suggested to evaluate this integral asymptotically. The results obtained using the asymptotic method and direct numerical integration are compared with ad hoc approaches for high speed and moderate supersonic boundary layers. This allows us to suggest recommendations on rational usage of the amplitude method with avoiding unconfirmed simplifications while reducing the computational effort to the level affordable for engineering practice.

Original languageEnglish (US)
Pages (from-to)9-24
Number of pages16
JournalTheoretical and Computational Fluid Dynamics
Issue number1
StatePublished - Feb 2022


  • Amplitude method
  • Boundary layer
  • Laminar-turbulent transition

ASJC Scopus subject areas

  • Computational Mechanics
  • Condensed Matter Physics
  • Engineering(all)
  • Fluid Flow and Transfer Processes


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