Skip to main content
SpringerLink
Log in

Modeling Freshwater Ice-Cover Temperature under Varying Atmospheric-Air Temperature

  • Published:
Fluid Dynamics Aims and scope Submit manuscript

Abstract

The process of temperature field formation in the ice-cover thickness is modeled by the heat-conduction equation, the solution of which required parametrization of boundary conditions at the interface with the atmosphere and water mass, allowing for an analytical solution. The most difficult issue in this respect is the condition at the interface with water, where crystallization occurs, as a result of which heat is released and the thickness of the ice increases (Stefan’s condition). This problem was solved by parameterization of the dependence of the ice-freezing rate on air temperature and ice thickness on the basis of observations of the ice cover of Siberian rivers. The obtained analytical solution is compared with field measurements of temperature in the ice cover and the growth rate of its thickness on the Amur River.

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.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.

Similar content being viewed by others

REFERENCES

  1. Donchenko, R.V., Ledovyi rezhim rek SSSR (Ice Mode of the USSR Rivers), Leningrad: Gidrometeoizdat, 1987.

  2. Lepikhin, A.P., To the calculation of the ice cover on fresh water basins, Geogr. Vestn., 2008, no. 1, pp. 1–13.

  3. Krass, M.S. and Merzlikin, V.G., Radiatsionnaya teplofizika snega i l’da (The Radiative Thermophysics of Snow and Ice), Leningrad: Gidrometeoizdat, 1990.

  4. Doronin, Yu.P., Fizika okeana (Physics of the Ocean), St. Petersburg: Russian State Hydrometeorological Univ., 2000.

  5. Leppäranta Matti, Freezing of Lakes and the Evolution of their Ice Cover, Berlin, Heidelberg: Springer-Verlag, 2015.

    Google Scholar 

  6. Voyevodin, A.F. and Grankina, T.B., Mathematical modeling of the ice-thermal regime of water body, Proc. 19th IAHR Int. Symp. on Ice, Vancouver, 2008, vol. 1, pp. 727–735.

  7. Cuffey, K.M. and Paterson, W.S.B., The Physics of Glaciers, Elsevier, 2010.

    Google Scholar 

  8. Goncharov, V.K., Klement’eva, N.Yu., Jianmin Qin, et al., Forecast of the freshwater ice cover thickness increasing, Trudy Mezhdunarodnoi konferentsii po sudostroeniyu i okeanotekhnike NAOE (Proc. Int. Conf. on Naval Architect and Oceantechnics NAOE2016), St. Petersburg, 2016, pp. 219–222.

  9. Goncharov, V.K., Klementeva, N.Yu., Jianmin Qin, et al., Investigation of correlation between the temperature on air-snow and snow-ice interfaces and the atmospheric air temperature, J. Earth Sci. Eng., 2016, vol. 6, no. 5, pp. 245–253.

    Google Scholar 

  10. Chizhov, A.N., Formirovanie ledyanogo pokrova i prostranstvennoe raspredelenie ego tolshchiny (Formation of the Ice Cover and Its Thickness Spatial Distribution), Leningrad: Gidrometeoizdat, 1990.

  11. Zhukov, L.A., Obshchaya okeanologiya (General Oceanology), Leningrad: Gidrometeoizdat, 1976.

  12. Budak, B.M., Samarsky, A.A., and Tikhonov, A.N., Collection of Problems in Mathematical Physics, New York: Dover Publ., 1988.

    Google Scholar 

  13. Tikhonov, A.N. and Samarskii, A.A., Uravneniya matematicheskoi fiziki (Equation of Mathematical Physics), Moscow: Nauka, 1977.

  14. Kreith, F. and Black, W.Z., Basic Heat Transfer, Harper and Row Publ., 1980.

    Google Scholar 

  15. Velikanov, M.A., Dinamika ruslovykh potokov (Dynamics of Streamflows), vol. 1: Struktura potoka (Structure of Flow), Moscow: Gostekhizdat, 1954.

  16. Qin Jianmin, Wang Lijuan, Goncharov, V.K., et al., Realization of the auto-measurement of ice in riverway based on the difference of the air, ice and water, Proc. 23rd IAHR Symp. on Ice, Lahti, 2010, vol. 1, pp. 571–580.

  17. Hammonds, K., Lieb-Lappen, R., Baker, I., and Wang, X., Investigating the thermophysical properties of the ice-snow interface under a controlled temperature and gradient. part i: experiments and observations, Cold Reg. Sci. Technol., 2015, vol. 120, pp. 157–167.

    Article  Google Scholar 

Download references

Funding

This work was supported by the Russian Foundation for Basic Research, project no. 15-58-53013_a National Natural Science Foundation of China.

Author information

Authors and Affiliations

  1. St. Petersburg State Marine Technical University, 190121, St. Petersburg, Russia

    V. K. Goncharov

Authors
  1. V. K. Goncharov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. K. Goncharov.

Ethics declarations

The author declares that he has no conflict of interest.

Additional information

Translated by V. Selikhanovich

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Goncharov, V.K. Modeling Freshwater Ice-Cover Temperature under Varying Atmospheric-Air Temperature. Fluid Dyn 56, 1094–1106 (2021). https://doi.org/10.1134/S0015462821080061

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0015462821080061

Keywords:

Search

Navigation