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Development of Initial Disturbances in the Circulating Flow with Variable Vorticity around the Free Cylinder

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Abstract

A two-dimensional system consisting of a circular cylinder placed in a circulating flow of an inviscid incompressible fluid with variable vorticity is considered. The processes in the critical layers of vortex flows (the region in which the phase velocity of disturbances coincides with the velocity of the mean flow) are investigated using the example of a problem with an exact analytical solution. Previously, for such a system, the discrete part of the spectrum was considered and described; i.e., individual natural oscillations are obtained and it is shown that, in a certain range of parameters, the system exhibits shear instability. The features of the system dynamics related to a continuous spectrum are considered. For this purpose, the initial problem is solved, and an analysis of the growth of large vorticity disturbances in the vicinity of the critical layer from a state with smooth initial conditions is made.

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REFERENCES

  1. V. F. Kopiev, S. A. Chernyshev, and M. A. Yudin, Appl. Math. Mech. 81, 148 (2017).

    Article  MathSciNet  Google Scholar 

  2. V. F. Kopiev, S. A. Chernyshev, and M. A. Yudin, Fluid Dyn. 54, 812 (2019).

    Article  ADS  MathSciNet  Google Scholar 

  3. L. A. Dikii, Hydrodynamic Stability and Atmospheric Dynamics (Gidrometeoizdat, Leningrad, 1976) [in Russian].

    Google Scholar 

  4. V. F. Kop’ev and S. A. Chernyshev, Izv. Akad. Nauk, Mekh. Zhidk. Gaza, No. 6, 78 (2000).

  5. V. F. Kop’ev and S. A. Chernyshev, Phys. Usp. 43, 663 (2000).

    Article  ADS  Google Scholar 

  6. V. F. Kopiev and S. A. Chernyshev, J. Fluid Mech. 341, 19 (1997).

    Article  ADS  MathSciNet  Google Scholar 

  7. S. Chandrasekhar, Ellipsoidal Figures of Equilibrium (Yale Univ. Press, New Haven, CT, 1969).

    MATH  Google Scholar 

  8. P. G. Drazin and W. H. Reid, Hydrodynamic Stability (Cambridge Univ. Press, Cambridge, 1981).

    MATH  Google Scholar 

  9. V. I. Arnol’d, Dokl. Akad. Nauk 162, 975 (1965).

    Google Scholar 

  10. V. I. Arnol’d, Prikl. Mat. Mekh. 29, 846 (1965).

    Google Scholar 

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Funding

This work was supported by the Russian Science Foundation, grant no. 21-71-30016 and initiated by the results of experimental studies performed on the the basis of the TsAGI “Anechoic chamber with AC-2 flow,” modernized with the support of the Ministry of Science and Higher Education of the Russian Federation under agreement no. 075-11-2021-066..

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Authors and Affiliations

  1. Moscow Research Complex Central Aerohydrodynamic Institute, 107005, Moscow, Russia

    M. A. Yudin, V. F. Kopiev & S. A. Chernyshev

Authors
  1. M. A. Yudin
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  2. V. F. Kopiev
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  3. S. A. Chernyshev
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Correspondence to M. A. Yudin.

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Translated by V. Bukhanov

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Yudin, M.A., Kopiev, V.F. & Chernyshev, S.A. Development of Initial Disturbances in the Circulating Flow with Variable Vorticity around the Free Cylinder. Dokl. Phys. 67, 289–295 (2022). https://doi.org/10.1134/S1028335822090142

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  • DOI: https://doi.org/10.1134/S1028335822090142

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