Skip to main content
SpringerLink
Log in

Micromorphic theory of turbulence

  • Published:
Zeitschrift für angewandte Mathematik und Physik Aims and scope Submit manuscript

Abstract

Based on the theory of micromorphic fluid dynamics (MMF), a new theory of turbulence is introduced. The law of conservation of microinertia of MMF is replaced by a balance law of microinertia, with all other laws remaining unchanged, the theory is called, “extended micromorphic fluid dynamics”. The present theory of turbulence is founded on the extended theory. Thus, a new theory of turbulence, is founded on the first principles, not using any a priori closure assumptions or semi-empirical hypothesis. Field equations are solved for the two-dimensional steady channel flow. The mean velocity turbulent shear stress and all turbulent velocities are in remarkably good agreement with the experimentally observed turbulent velocities.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Schlichting H.: Boundary Layer Theory, p 383. McGraw-Hill, New York (1957)

    Google Scholar 

  2. Speziale C.G., So R.M.C.: Turbulence modeling simulation. In: Johnson, R.W. (eds) Handbook of Fluid Dynamics, CRS Press, Boston (1988)

    Google Scholar 

  3. Heinz S.: Statistical Mechanics of Turbulent Flows. Springer, Berlin (2003)

    Google Scholar 

  4. Laufer, J.: Investigation of turbulent flow in two-dimensional channel. N.A.C.A. Report 1053 (1949)

  5. Eringen, A.C.: Simple microfluids. Int. J. Eng. Sci. 2, 205–217 (1964); See also Microcontinuum Field Theories II, Fluent Media. Springer, New York (2001), sections 17.4 and 17.9

    Google Scholar 

  6. Oevel W., Schröter J.: Balance equations for micromorphic materials. J. Stat. Phys. 25(4), 645–661 (1981)

    Article  Google Scholar 

  7. Eringen, A.C.: Microcontinuum Field Theories I, Foundations and Solids, pp. 42–47. Springer, New York (1999)

  8. Prandl L.: Über die ausgebildete turbulenz. ZAMM 5, 136 (1925)

    Google Scholar 

  9. Taylor G.I.: The transport of vorticity and heat through fluids in turbulent motion. Proc. R. Soc. A 135, 685 (1932)

    Article  Google Scholar 

  10. von Kármán T.: Mechanische Ähnlichkeit und Turbulenz Nachr. Ges. Wiss. Göttinger. Math. Phys. Klasse 5, 58 (1930)

    Google Scholar 

  11. Eringen A.C.: On a rational theory of turbulence. Int. J. Eng. Sci. 43, 209–221 (2005)

    Article  MathSciNet  Google Scholar 

  12. Eringen A.C.: Continuum theory of dense rigid suspensions. Rheol. Acta 30, 23–32 (1991)

    Article  MATH  Google Scholar 

  13. Eringen A.C.: A continuum theory of dense suspensions. Z. Angew. Math. Phys. 56, 529–547 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  14. Aşkar A.: Molecular crystals and polar theories of continua. Int. J. Eng. Sci. 10, 293–300 (1972)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Princeton University, 15 Red Tail Drive, Littleton, CO, 80126-5001, USA

    A. Cemal Eringen

Authors
  1. A. Cemal Eringen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Cemal Eringen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cemal Eringen, A. Micromorphic theory of turbulence. Z. Angew. Math. Phys. 61, 119–132 (2010). https://doi.org/10.1007/s00033-009-0002-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00033-009-0002-6

Keywords

Search

Navigation