Skip to main content
SpringerLink
Log in

Incompressible liquid in thermodynamics, new entropy, and the scenario for the occurrence of turbulence for the Navier-Stokes equation

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

In this paper, we propose a new scenario for the occurrence of turbulence on the basis of the new notion of entropy of an ideal liquid and the theory of coherent vortices.

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. G. B. Whitham, “A General Approach to Lineral and Non-lineral Dispersive Waves Using a Lagrangian”, J. FluidMech. 22(2), 273–283 (1965).

    MathSciNet  Google Scholar 

  2. G. B. Whitham, “Non-lineral Dispersion of Water Waves”, J. Fluid Mech. 27(2), 399–412 (1967).

    Article  MATH  MathSciNet  Google Scholar 

  3. G. B. Whitham, “Two-timing, variational principles and Waves”, J. Fluid Mech. 44(2), 373–395 (1970).

    Article  MATH  MathSciNet  Google Scholar 

  4. V. P. Maslov, G. A. Omel’yanov, Geometrical Asymptotics for Nonlinear PDE. I (Translations of Mathematical Monographes. V. 202. American Mathematical Society. Providence, Rhode Island, 2001).

    Google Scholar 

  5. V. P. Maslov, A. I. Shafarevich, “Application of the Canonical Operator to the Description of Self-Focusing Soliton-Like Solutions of the Kadomtsev-Petviashvili Equation”, Russ. J. Math. Phys. 18(4), 510–512 (2011).

    MathSciNet  Google Scholar 

  6. V. P. Maslov and A. I. Shafarevich, “Asymptotic solutions of the Navier-Stokes equations describing periodic systems of localized vortices,” Math. Notes 90(5), 686–700, (2011).

    Article  MathSciNet  Google Scholar 

  7. V. P. Maslov, “Mathematical Conception of “Phenomenological” Equilibrium Thermodynamics”, Russian J. Math. Phys. 18(4), 363–370 (2011).

    Google Scholar 

  8. V. P. Maslov, T. V. Maslova, “Main Axiom of Thermodynamics and Entropy of Number Theory: Tunnel and Ultrasecond Quantization”, Math.Notes 90(3), 385–397 (2011).

    Article  Google Scholar 

  9. T. L. Hill, Statistical Mechanics: Principles and Selected Applications (McGraw-Hill Book Co., Inc., New York-Toronto-London, 1956; IL, Moscow, 1960).

    MATH  Google Scholar 

  10. S M Stishov, “The Thermodynamics of Melting Simple Substances,” Uspekhi Fiz. Nauk 114, 3–40 (1974) [Sov. Phys. Usp. 18, 625–643 (1975)].

    Article  Google Scholar 

  11. R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965 (Dover, Mineola, 2010); Mir, Moscow, 1968).

    MATH  Google Scholar 

  12. A. A. Abrikosov, L. P. Gor’kov, I. E. Dzyaloshinskii, Quantum Field Theoretical Methods in Statistical Physics (2ed., Pergamon, 1965).

  13. V. P. Maslov, “Nonstandard characteristics in asymptotic problems,” Proceedings of the XIX International Mathematical Congress (Warsaw, 1983) [Polish Sci. Press, Warsaw, 1984].

  14. V. P. Maslov, “Nonstandard characteristics in asymptotic problems,” Uspekhi Mat. Nauk 38(6), 3–36 (1983) [Russian Math. Surveys 38 (6), 1–42 (1983)].

    MathSciNet  Google Scholar 

  15. L. D. Landau and E. M. Lifshits, Course of Theoretical Physics, Vol. 3: Quantum Mechanics: Non-Relativistic Theory, 2nd ed. (Nauka, Moscow, 1964; translation of the 1st ed., Pergamon Press, London-Paris and Addison-Wesley Publishing Co., Inc., Reading, Mass., 1958).

    Google Scholar 

  16. V. P. Maslov, Méthodes opératorielles (Mir, Moscow, 1987) [in French].

    MATH  Google Scholar 

  17. V. P. Maslov, “Number-Theoretic Internal Energy for a Gas Mixture”, Russian J. Math. Phys. 18(2), 163–175 (2011).

    Article  Google Scholar 

  18. B. van-der-Pol and H. Bremmer, Operational Calculus, Based on the Two-Sided Laplace Integral (Cambridge, at the University Press, 1950; Izd. Inostr. Lit., Moscow, 1952).

  19. V. P. Maslov, “Tunnel Quantization of Thermodynamics and Critical Exponents”, Math. Notes, v 90(4), 533–547 (2011).

    Article  Google Scholar 

  20. B. D. Summ, Basics of Colloid Chemistry (Academia, Moscow, 2007) [in Russian]

    Google Scholar 

  21. V. G. Baidakov, S. P. Protsenko, “Metastable Extensions of Phase Equilibrium Curves and Singular Points of Simple Substances“, Zh. Éxper. Teoret. Fiz. 130(6), 1014–1026 (2006).

    Google Scholar 

  22. V. E. Vinogradov, P. A. Pavlov, V. G. Baidakov, “Cavitation Strength of an Argon-Helium Solution”, Chemical Physics Letters 474(4–6), 294–296 (2009).

    Article  Google Scholar 

  23. V. P. Maslov, “A New Approach to Phase Transitions, Thermodynamics and Hydrodynamics”, Teoret. Mat. Fiz. 165(3), 543–567 (2010) [Theoret. and Math. Phys. 165 (3), 1699–1720 (2010)].

    Google Scholar 

  24. V. P. Maslov. “Gibbs paradox, liquid phase as an alternative to the Bose condensate and homogeneous mixtures of new ideal gases”, Math. Notes, 89(3), 366–373 (2011).

    Article  MATH  Google Scholar 

  25. V. P. Maslov and A. I. Shafarevich, “Rapidly Oscillating Asymptotic Solutions of the Navier-Stokes Equations, Coherent Structures, Fomenko Invariants, Kolmogorov Spectrum and Flicker Noise”, Russ. J. Math. Phys. 13(4), 414–425 (2006).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    V. P. Maslov

Authors
  1. V. P. Maslov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. P. Maslov.

Additional information

The article was submitted by the author for the English version of the journal.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Maslov, V.P. Incompressible liquid in thermodynamics, new entropy, and the scenario for the occurrence of turbulence for the Navier-Stokes equation. Math Notes 90, 859–866 (2011). https://doi.org/10.1134/S0001434611110253

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0001434611110253

Keywords

Search

Navigation