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Zh. Vychisl. Mat. Mat. Fiz., 2013, Volume 53, Number 3, Pages 433–441 (Mi zvmmf9889)  

This article is cited in 9 scientific papers (total in 9 papers)

Numerical simulation of the three-dimensional Kolmogorov flow in a shear layer

S. V. Fortova

Institute for Computer Aided Design of RAS, Moscow

Abstract: Numerical simulation is used to study the Kolmogorov flow in a shear layer of a compressible inviscid medium. A periodic permanent force applied to the flow gives rise to a vortex cascade of instabilities. The influence exerted by the size of the computational domain, the initial conditions, and the amplitude of the force on the formation of an instability cascade and the transition to turbulence is studied. It is shown that the mechanism of the onset of turbulence has an essentially three-dimensional nature. For the turbulent flows computed, the classical Kolmogorov $-5/3$ power law holds in the inertial range.

Key words: Kolmogorov flow, three-dimensional inviscid compressible flows, onset of turbulence, instability cascade, power spectrum, numerical simulation.


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English version:
Computational Mathematics and Mathematical Physics, 2013, 53:3, 311–319

Bibliographic databases:

UDC: 519.634
MSC: 76F06
Received: 05.04.2012

Citation: S. V. Fortova, “Numerical simulation of the three-dimensional Kolmogorov flow in a shear layer”, Zh. Vychisl. Mat. Mat. Fiz., 53:3 (2013), 433–441; Comput. Math. Math. Phys., 53:3 (2013), 311–319

Citation in format AMSBIB
\by S.~V.~Fortova
\paper Numerical simulation of the three-dimensional Kolmogorov flow in a shear layer
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2013
\vol 53
\issue 3
\pages 433--441
\jour Comput. Math. Math. Phys.
\yr 2013
\vol 53
\issue 3
\pages 311--319

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    This publication is cited in the following articles:
    1. S. V. Fortova, “Eddy cascade of instabilities and transition to turbulence”, Comput. Math. Math. Phys., 54:3 (2014), 553–560  mathnet  crossref  crossref  isi  elib  elib
    2. D. Lucas, R. Kerswell, “Spatiotemporal dynamics in two-dimensional kolmogorov flow over large domains”, J. Fluid Mech., 750 (2014), 518–554  crossref  mathscinet  isi  elib  scopus
    3. S. Musacchio, G. Boffetta, “Turbulent channel without boundaries: the periodic kolmogorov flow”, Phys. Rev. E, 89:2 (2014), 023004  crossref  mathscinet  isi  elib  scopus
    4. S. V. Fortova, “Comparative analysis of eddy cascade formation in various turbulent problems”, Comput. Math. Math. Phys., 55:2 (2015), 298–304  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    5. A. N. Doludenko, S. V. Fortova, “Numerical simulation of Rayleigh–Taylor instability in inviscid and viscous media”, Comput. Math. Math. Phys., 55:5 (2015), 874–882  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. M. S. Belotserkovskaya, A. P. Pronina, S. V. Fortova, V. V. Shepelev, “Application of the program package TURBO problem solver for some fluid dynamics problems”, Comput. Math. Math. Phys., 56:6 (2016), 1162–1173  mathnet  crossref  crossref  isi  elib
    7. S. V. Revina, “Stability of the Kolmogorov flow and its modifications”, Comput. Math. Math. Phys., 57:6 (2017), 995–1012  mathnet  crossref  crossref  mathscinet  isi  elib
    8. M. Kalashnik, M. Kurgansky, “Nonlinear dynamics of long-wave perturbations of the Kolmogorov flow for large Reynolds numbers”, Ocean Dyn., 68:8 (2018), 1001–1012  crossref  isi  scopus
    9. S. V. Fortova, P. S. Utkin, A. P. Pronina, T. S. Narkunas, V. V. Shepelev, “Improvement of three-dimensional mathematical model for the simulation of impact of high-speed metallic plates”, XXXII International Conference on Interaction of Intense Energy Fluxes With Matter (ELBRUS 2017), Journal of Physics Conference Series, 946, IOP Publishing Ltd, 2018, 012052  crossref  mathscinet  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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