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The Mack’s amplitude method revisited

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Abstract

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.

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Notes

  1. Such factors like temperature spottiness or particulates in atmosphere may vary from region to region, seasons, day time, etc. and hardly are predictable. It means that, finally, a designer has to make a decision on the scenario and design point choice.

  2. See a clarification of the terminology in Ref. [15]

  3. In the variable \(e^N\) method [11], which deals with the spectral lines, the bandwidth factor \(A_F\) is not taken into account at all.

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Acknowledgements

The authors thank Ms. Michelle Bailey for assistance in the computations. A. Fedorov (Sect. 3) was supported by the Russian Scientific Foundation (project No. 19-19-00470). A. Tumin was supported by ONR Grant N00014-20-1-2502 monitored by Dr. E. Marineau.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology, Dolgoprudny, Russian Federation, 141701

    Alexander Fedorov

  2. The University of Arizona, 1130 N. Mountain Ave, Tucson, AZ, 85721, USA

    Anatoli Tumin

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  1. Alexander Fedorov
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  2. Anatoli Tumin
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Correspondence to Anatoli Tumin.

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Communicated by Vassilios Theofilis.

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Fedorov, A., Tumin, A. The Mack’s amplitude method revisited. Theor. Comput. Fluid Dyn. 36, 9–24 (2022). https://doi.org/10.1007/s00162-021-00575-x

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