Skip to main content
SpringerLink
Log in

Probability Distributions of the Riemann Wave and an Integral of It

  • PHYSICS
  • Published:
Doklady Physics Aims and scope Submit manuscript

Abstract

In this paper, we study the statistical characteristics of the Riemann wave and the integral of it. Such problems arise in the physics of fronts’ propagation, in particular, during the wave run-up on the shore, a flame front, and phase surfaces. Using the relation of the Lagrangian and Eulerian statistical descriptions, we obtained general expressions for the probability distributions of the front velocity and its displacement. We show that the joint probabilistic distribution of displacement, velocity, and acceleration at the input of a nonlinear medium are necessary to find the probability distribution of displacement. Based on the idea of probability as the time the signal spent in a certain interval, the characteristics of the waves after their breaking were calculated.

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

Fig. 1.

Similar content being viewed by others

REFERENCES

  1. S. N. Gurbatov and O. V. Rudenko, Nonlinear Acoustics (Academic, San Diego, 1998), Ed. by M.F. Hamilton and D.T. Blackstock, Vol. 13, pp. 377–398.

  2. O. V. Rudenko, S. N. Gurbatov, and C. M. Hedberg, Nonlinear Acoustics through Problems and Examples (Trafford Publishing, 2010).

  3. S. N. Gurbatov, O. V. Rudenko, and A. I. Saichev, Waves and Structures in Nonlinear Nondispersive Media. Application to Nonlinear Acoustics (Springer, Berlin, 2011).

  4. G. F. Carrier and H. P. Greenspan, J. Fluid Mech. 4, 97–109 (1958).

    Article  ADS  MathSciNet  Google Scholar 

  5. I. I. Didenkulova, A. V. Sergeeva, E. N. Pelinovsky, and S. N. Gurbatov, Izvestiya, Atmospheric and Oceanic Physics 246 (4), 530–532 (2010).

  6. A. Rybkin, E. N. Pelinovsky, and I. Didenkulova, J. Fluid Mech. 748, 416–432 (2014).

    Article  ADS  MathSciNet  Google Scholar 

  7. S. N. Gurbatov and E. N. Pelinovsky, NHESS 19, 1925–1935 (2019).

    ADS  Google Scholar 

  8. M. Kardar, G. Parisi, and Y.-C. Zhang, Phys. Rev. Lett. 56 (9), 889–892 (1986).

    Article  ADS  Google Scholar 

  9. E. A. Kuznetsov and S. S. Minaev, Phys. Lett. A 221 (3–4), 187–192 (1996).

    Article  ADS  MathSciNet  Google Scholar 

  10. T. Sasamoto, Prog. Theor. Exp. Phys. 2016, 022A01 (2016).

  11. Ya. B. Zel’dovich, A. V. Mamaev, and S. F. Shandarin, Sov. Phys. Usp. 26, 77–83 (1983) .

  12. S. N. Gurbatov, A. I. Saichev, and S. F. Shandarin, Phys. Usp. 55, 223–249 (2012).

  13. S. N. Gurbatov, A. N. Malakhov, and A. I. Saichev, Nonlinear Random Waves and Turbulence in Nondispersive Media: Waves, Rays, Particles (Manchester University Press, Manchester, 1991).

Download references

Funding

This work was supported by the Russian Science Foundation, project nos. 19-12-00256 (Section 2 CIS) and 16-17-00041 (Section 3 UNR).

Author information

Authors and Affiliations

  1. Lobachevsky State University of Nizhny Novgorod, 603105, Nizhny Novgorod, Russia

    S. N. Gurbatov

  2. Nizhny Novgorod State Technical University n.a. R. Alekseev, 603155, Nizhny Novgorod, Russia

    E. N. Pelinovsky

  3. National Research University Higher School of Economics, 101000, Moscow, Russia

    E. N. Pelinovsky

  4. Institute of Applied Physics, Russian Academy of Sciences, 603155, Nizhny Novgorod, Russia

    E. N. Pelinovsky

Authors
  1. S. N. Gurbatov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. N. Pelinovsky
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to S. N. Gurbatov or E. N. Pelinovsky.

Additional information

Translated by A. Ivanov

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gurbatov, S.N., Pelinovsky, E.N. Probability Distributions of the Riemann Wave and an Integral of It. Dokl. Phys. 65, 269–272 (2020). https://doi.org/10.1134/S1028335820080029

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1028335820080029

Keywords:

Search

Navigation