Advertisement

Characteristic Functionals for Incompressible Turbulent Flows

  • Wolfgang KollmannEmail author
Chapter

Abstract

The Fourier transform of a finite-dimensional Pdf is the characteristic function, hence contains probabilistic information equivalent to the Pdf/Cdf. The main difference to the Pdfs is its relation to statistical moments, which follow from the characteristic function by differentiation at the origin of the argument space \(\mathcal{N}\).

References

  1. 1.
    Hosokawa, I.: A functional treatise on statistical hydromechanics with random force action. J. Physical Soc. Jpn 25, 271–278 (1968)ADSCrossRefGoogle Scholar
  2. 2.
    Lewis, R.M., Kraichnan, R.H.: A Space-Time Functional Formalism for Turbulence. Comm. Pure Appl. Math. XV, 397–411 (1962)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Conway, J.: A Course in Functional Analysis. Springer, New York (1990)Google Scholar
  4. 4.
    Hopf, E.: Statistical hydromechanics and functional calculus. J. Rat. Mech. Anal. 1, 87–123 (1952)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Vishik, M.J., Fursikov, A.V.: Mathematical Problems of Statistical Hydromechanics. Kluwer Academic Publication, Dordrecht (1988)CrossRefGoogle Scholar
  6. 6.
    Monin, A.S., Yaglom, A.M.: Statistical Fluid Mechanics: Mechanics of Turbulence, vol. 1. The MIT Press, Cambridge Mass (1975)Google Scholar
  7. 7.
    Monin, A.S., Yaglom, A.M.: Statistical Fluid Mechanics: Mechanics of Turbulence, vol. 2. The MIT Press, Cambridge Mass (1975)Google Scholar
  8. 8.
    Stanisic, M.M.: The Mathematical Theory of Turbulence. Springer, New York (1988)CrossRefGoogle Scholar
  9. 9.
    Gross, L.: Potential theory on hilbert space. J. Funct. Anal. 1, 123–181 (1967)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Cannarso, P., DaPrato, G.: Potential Theory in Hilbert Spaces. Proc, p. 54. Symposia Appl, Math (1998)Google Scholar
  11. 11.
    Feller, M.N.: The Lévy-Laplacian. Cambridge University Press (2005)Google Scholar
  12. 12.
    Klauder, J.R.: A Modern Approach to Functional Integration. Birkhaeuser/Springer, New York (2010)zbMATHGoogle Scholar
  13. 13.
    Simon, B.: Functional Integration and Quantum Physics. AMS Chelsea Publication, Providence, Rhode Island (2004)CrossRefGoogle Scholar
  14. 14.
    Gelfand, I.M., Vilenkin, N.Y.: Generalized Functions, vol. 4. Academic Press, New York (1964)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of California DavisDavisUSA

Personalised recommendations