Journal of Applied Mechanics and Technical Physics

, Volume 59, Issue 7, pp 1279–1287 | Cite as

Direct Numerical Simulation of Homogeneous Isotropic Helical Turbulence with the TARANG Code

  • A. S. TeimurazovEmail author
  • R. A. Stepanov
  • M. K. Verma
  • S. Barman
  • A. Kumar
  • S. Sadhukhan


The problem of taking into account the influence of turbulence comes up while solving both fundamental questions of geo- and astrophysics and applied problems arising in the development of new engineering solutions. Difficulties in applying the standard propositions of the theory appear when considering flows with a special spatial structure, for example, helical flows. The flow helicity determines the topology of vortices and is conserved in the process of energy transfer in a turbulent flow. In this paper we suggest an approach for numerical simulation of homogeneous isotropic helical turbulence aimed at detecting characteristic signatures of the inertial range and finding the distributions of the spectral energy and helicity densities. In this approach we use the TARANG code designed to numerically solve various problems of fluid dynamics in the regime of a developed turbulent flow and to study hydrodynamic instability phenomena of a different physical nature (thermal convection, advection of passive and active scalars, magnetohydrodynamics, and the influence of Coriolis forces). TARANG is an open source code written in the object-oriented C++ language with a high efficiency of computation on multiprocessor computers. Particular attention in the paper is given to the application of the tool kit from the package to analyze the solutions obtained. The spectral distributions and fluxes of energy and helicity have been computed for Reynolds numbers of 5700 and 14 000 on 5123 and 10243 grids, respectively. We have checked whether the –5/3 spectral law is realizable and estimated the universal Kolmogorov and Batchelor constants in the inertial range. An analysis of the energy and helicity transfer functions between the selected scales (shell-to-shell transfer) shows a significant contribution of nonlocal interactions to the cascade process.

Key words

helical turbulence direct numerical simulation pseudospectral method TARANG code 


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  1. 1.
    Kolmogorov, A.N., The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers, Dokl. Akad. Nauk SSSR, 1941, vol. 30, no. 4, pp. 301–304.ADSMathSciNetGoogle Scholar
  2. 2.
    Schlichting, H., Boundary-Layer Theory, New York: McGraw-Hill, 1955.zbMATHGoogle Scholar
  3. 3.
    Scheeler, M.W., van Rees, W.M., Kedia, H., Kleckner, D., and Irvine, W.T.M., Complete measurement of helicity and its dynamics in vortex tubes, Science (Washington, DC, U. S.), 2017, vol. 357, no. 6350, pp. 487–490. Google Scholar
  4. 4.
    Moffatt, H.K., Helicity-invariant even in a viscous fluid, Science (Washington, DC, U. S.), 2017, vol. 357, no. 6350, pp. 448–449. ADSCrossRefGoogle Scholar
  5. 5.
    Ferziger, J.H. and Peric, M., Computational Methods for Fluid Dynamics, Berlin: Springer, 2002.CrossRefzbMATHGoogle Scholar
  6. 6.
    Verma, M.K., Chatterjee, A.G., Reddy, S., Yadav, R.K., Paul, S., Chandra, M., and Samtaney, R., Benchmarking and scaling studies of pseudospectral code Tarang for turbulence simulations, Pramana-J. Phys., 2013, vol. 81, no. 4, pp. 617–629. ADSCrossRefGoogle Scholar
  7. 7.
    Canuto, C., Hussaini, M.Y., Quarteroni, A., and Zhang, T.A., Spectral Methods in Fluid Turbulence, Berlin: Springer, 1988.CrossRefzbMATHGoogle Scholar
  8. 8.
    Boyd, J.P., Chebyshev and Fourier Spectral Methods, 2nd ed., New York: Dover, 2001.zbMATHGoogle Scholar
  9. 9.
    Alvelius, K., Random forcing of three-dimensional homogeneous turbulence, Phys. Fluids, 1999, vol. 11, no. 7, pp. 1880–1889. ADSCrossRefzbMATHGoogle Scholar
  10. 10.
    Kessar, M., Plunian, F., Stepanov, R., and Balarac, G., Non-Kolmogorov cascade of helicity-driven turbulence, Phys. Rev. E, 2015, vol. 92, p. 031004(R). ADSCrossRefGoogle Scholar
  11. 11.
    Stepanov, R., Plunian, F., Kessar, M., and Balarac, G., Systematic bias in the calculation of spectral density from a three-dimensional spatial grid, Phys. Rev. E, 2014, vol. 90, no. 5, p. 053309. ADSCrossRefGoogle Scholar
  12. 12.
    McKay, M.E., Linkmann, M., Clark, D., Chalupa, A.A., and Berera, A., Comparison of forcing functions in magnetohydrodynamics, Phys. Rev. Fluids, 2017, vol. 2, no. 11, p. 114604. ADSCrossRefGoogle Scholar
  13. 13.
    Stepanov, R., Teimurazov, A., Titov, V., Verma, M.K., Barman, S., Kumar, A., and Plunian, F., Direct numerical simulation of helical magnetohydrodynamic turbulence with TARANG code, 2017 Ivannikov ISPRAS Open Conference (ISPRAS), Moscow, 2017, pp. 90–96. CrossRefGoogle Scholar
  14. 14.
    Verma, M.K., Statistical theory of magnetohydrodynamic turbulence: recent results, Phys. Rep., 2004, vol. 401, no. 5, pp. 229–380. ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    Donzis, D.R. and Sreenivasan, A.K., The bottleneck effect and the Kolmogorov constant in isotropic turbulence, J. Fluid Mech., 2010, vol. 657, pp. 171–188. ADSCrossRefzbMATHGoogle Scholar
  16. 16.
    Yeung, P.K. and Zhou, Y., Universality of the Kolmogorov constant in numerical simulations of turbulence, Phys. Rev. E, 1997, vol. 56, no. 2, pp. 1746–1752. ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2018

Authors and Affiliations

  • A. S. Teimurazov
    • 1
    Email author
  • R. A. Stepanov
    • 1
  • M. K. Verma
    • 2
  • S. Barman
    • 2
  • A. Kumar
    • 2
  • S. Sadhukhan
    • 2
  1. 1.Institute of Continuous Media MechanicsRussian Academy of Sciences, Ural BranchPermRussia
  2. 2.Department of PhysicsIndian Institute of TechnologyKanpurIndia

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