Theoretical and Computational Fluid Dynamics

, Volume 31, Issue 2, pp 211–220 | Cite as

Influence of molecular diffusion on alignment of vector fields: Eulerian analysis

Original Article

Abstract

The effect of diffusive processes on the structure of passive vector and scalar gradient fields is investigated by analyzing the corresponding terms in the orientation and norm equations. Numerical simulation is used to solve the transport equations for both vectors in a two-dimensional, parameterized model flow. The study highlights the role of molecular diffusion in the vector orientation process and shows its subsequent action on the geometric features of vector fields.

Keywords

Passive vector Scalar gradient Molecular diffusion Alignment properties 

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References

  1. 1.
    Lüthi, B., Tsinober, A., Kinzelbach, W.: Lagrangian measurements of vorticity dynamics in turbulent flow. J. Fluid Mech. 528, 87–118 (2005)CrossRefMATHGoogle Scholar
  2. 2.
    Favier, B., Bushby, P.J.: Small-scale dynamo action in rotating compressible convection. J. Fluid Mech. 690, 262–287 (2012)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Diamessis, P.J., Nomura, K.K.: Interaction of vorticity, rate-of-strain, and scalar gradient in stratified homogeneous sheared turbulence. Phys. Fluids 12, 1166–1188 (2000)CrossRefMATHGoogle Scholar
  4. 4.
    Brethouwer, G., Hunt, J.C.R., Nieuwstadt, F.T.M.: Micro-structure and Lagrangian statistics of the scalar field with a mean gradient in isotropic turbulence. J. Fluid Mech. 474, 193–225 (2003)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Holzner, M., Guala, M., Lüthi, B., Liberzon, A., Nikitin, N., Kinzelbach, W., Tsinober, A.: Viscous tilting and production of vorticity in homogeneous turbulence. Phys. Fluids 22, 061701 (2010)CrossRefMATHGoogle Scholar
  6. 6.
    Kida, S., Takaoka, M.: Breakdown of frozen motion of vorticity field and vorticity reconnection. J. Phys. Soc. Jpn. 60, 2184–2196 (1991)CrossRefGoogle Scholar
  7. 7.
    Constantin, P., Procaccia, I., Segel, D.: Creation and dynamics of vortex tubes in three-dimensional turbulence. Phys. Rev. E 51, 3207–3222 (1995)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Lapeyre, G., Hua, B.L., Klein, P.: Dynamics of the orientation of active and passive scalars in two-dimensional turbulence. Phys. Fluids 13, 251–264 (2001)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Protas, B., Babiano, A., Kevlahan, N.K.-R.: On geometrical alignment properties of two-dimensional forced turbulence. Phys. D 128, 169–179 (1999)CrossRefMATHGoogle Scholar
  10. 10.
    Vedula, P., Yeung, P.K., Fox, R.O.: Dynamics of scalar dissipation in isotropic turbulence: a numerical and modelling study. J. Fluid Mech. 433, 29–60 (2001)CrossRefMATHGoogle Scholar
  11. 11.
    Brandenburg, A., Procaccia, I., Segel, D.: The size and dynamics of magnetic flux structures in magnetohydrodynamic turbulence. Phys. Plasmas 2, 1148–1156 (1995)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Jeong, E., Girimaji, S.S.: Velocity-gradient dynamics in turbulence: effect of viscosity and forcing. Theor. Comput. Fluid Dyn. 16, 421–432 (2003)CrossRefMATHGoogle Scholar
  13. 13.
    Meneveau, C.: Lagrangian dynamics and models of the velocity gradient tensor in turbulent flows. Annu. Rev. Fluid Mech. 43, 219–245 (2011)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Gonzalez, M.: Kinematic properties of passive scalar gradient predicted by a stochastic Lagrangian model. Phys. Fluids 21, 055104 (2009)CrossRefMATHGoogle Scholar
  15. 15.
    Moffat, K.: The amplification of a weak applied magnetic field by turbulence in fluids of moderate conductivity. J. Fluid Mech. 11, 625–635 (1961)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Lapeyre, G., Klein, P., Hua, B.L.: Does the tracer gradient align with strain eigenvectors in 2D turbulence? Phys. Fluids 11, 3729–3737 (1999)CrossRefMATHGoogle Scholar
  17. 17.
    Garcia, A., Gonzalez, M., Paranthoën, P.: On the alignment dynamics of a passive scalar gradient in a two-dimensional flow. Phys. Fluids 17, 117102 (2005)CrossRefMATHGoogle Scholar
  18. 18.
    Garcia, A., Gonzalez, M.: Analysis of passive scalar gradient alignment in a simplified three-dimensional case. Phys. Fluids 18, 058101 (2006)CrossRefGoogle Scholar
  19. 19.
    Tanner, S.E.M., Hughes, D.W.: Fast-dynamo action for a family of parameterized flows. Astrophys. J. 586, 685–691 (2003)CrossRefGoogle Scholar
  20. 20.
    Galloway, D.J., Proctor, M.R.E.: Numerical calculations of fast dynamos in smooth velocity fields with realistic diffusion. Nature 356, 691–693 (1992)CrossRefGoogle Scholar
  21. 21.
    Childress, S., Soward, A.M.: Scalar transport and alpha-effect for a family of cat’s-eye flows. J. Fluid Mech. 205, 99–133 (1989)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Galloway, D.J.: ABC flows then and now. Geophys. Astrophys. Fluid Dyn. 106, 450–467 (2012)CrossRefGoogle Scholar
  23. 23.
    Courvoisier, A., Gilbert, A.D., Ponty, Y.: Dynamo action in flows with cat’s-eyes. Geophys. Astrophys. Fluid Dyn. 99, 413–429 (2005)MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Gonzalez, M.: Effect of orientation dynamics on the growth of a passive vector in a family of model flows. Fluid Dyn. Res. 46, 015510 (2014)MathSciNetCrossRefMATHGoogle Scholar
  25. 25.
    Lele, S.K.: Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103, 16–42 (1992)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.CNRS, UMR 6614/CORIASaint-Etienne du RouvrayFrance

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