Some properties of solutions of the equation for oil spills spreading on the sea surface
https://doi.org/10.7868/S2073667319010088
Abstract
The mathematical modeling of oil spills on the sea surface has recently attracted considerable attention of researchers. Despite the fact that a number of approaches for modeling the main processes of oil transport and transformation on the sea surface are proposed in this area, many of them are not satisfactory and do not correspond to the data of observations and/or experiments. The reason for this is the complexity of these processes, which are complex. In the constructed models, a significant number of acting factors are simultaneously considered and a large number of selected constants are introduced in the expressions used, which leads to difficulties in the analysis (interpretation) of the results. In this regard, there is a need to consider independently the individual processes accompanying the transformation of the oil spill. This paper focuses on the process of oil spill spreading and the movement of its boundary. The approach is based on the solution of the system of partial differential equations (PDE) arising from the consideration of the balance of forces acting on the axisymmetric spot. The aim of the work is to construct a method of numerical solution capable of correctly describing the motion of the contact boundary of the spill. The originality of the proposed approach lies in the fact that, on the one hand, it offers boundary conditions specific to each Fay’s stage, and on the other hand, a method of characteristics is considered to numerical solution of the problem considered. It is shown that the resulting numerical solution is consistent with the Fay’s formulas.characteristics is considered to numerical solution of the problem considered. It is shown that the resulting numerical solution is consistent with the Fay’s formulas.
About the Authors
B. V. Arkhipov
Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences (FRC CSC RAS)
Russian Federation
Russian Federation
Moscow
D. A. Shapochkin
Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences (FRC CSC RAS)
Russian Federation
Russian Federation
Moscow
References
1. ASCE Task Committee on Modeling of Oil Spills. State-of-the-art review of modeling transport and fate of oil spills // Journal of Hydraulic Engineering. 1996. V. 122, N 11. P. 594—610.
2. Spaulding M. L. A State-of-the-art review of oil spill trajectory and fate modeling // Oil and Chemical Pollution. 1988. 4. P. 39—55.
3. Reed M., Johansen O., Per Johan Brandvik, Per Daling, Lewis Alun, Fiocco R., Don Mackay, Prentki R. Oil Spill Modeling towards the Close of the 20th Century: Overview of the State of the Art // Spill Science & Technology Bulletin. 1999. V. 5, N 1. P. 3—16.
4. Lehr W. J. Review of modeling procedures for oil spill weathering behavior // Adv. Ecol. Sci. 2001. V. 9. P. 51—90.
5. Fay J. A. The spread of oil slicks on a calm sea // Oil on the Sea. New York: Plenum Press, 1969. P. 53—63.
6. Fay J. A. Physical Processes in the Spread of Oil on a Water Surface // Proceedings of the Joint Conference on Prevention and Control of Oil Spills. Washington D. C., American Petroleum Institute, 1971. P. 463—467.
7. Scory S. Models used by the Belgian authorities in case of accidental spills at sea // Workshop on “Prediction of Short-Term Transport and Dispersion of Accidental Spills from Shipping and Off-Shore Industry”, Hague, Netherlands, 15—17 November 1995. 5 p.
8. Kuipers H. D. A simulation model for oil slicks at sea (SMOSS) // Department of Civil Engineering, Delft University of Technology, North Sea Directorate, National Department of Public Works, Ministry of Transport and Public Works, Rijswijk, Delft, The Netherlands, 1981, 79 p.
9. Kochergin I. E., Bogdanovsky A. A., Budaeva V. D., Makarov V. G., Mishukov V. F., Ovsienko S. N., Putov V. F., Reitsema L. A., Sciallabba J. W., Sergusheva O. O., Yarosh P. V. Modeling of oil spills for the shelf conditions of North-Eastern Sakhalin // Proc. 2nd Workshop on the Okhotsk Sea and Adjacent Areas, Canada, 1999. P. 123—130.
10. Antunes do Carmo1 J., Pinho J. L., Vieira J. P. Oil Spills in Coastal Zones: Predicting Slick Transport and Weathering // The Open Ocean Engineering Journal. 2010. 3. P. 129—142.
11. Архипов Б. В., Шапочкин Д. А. Распространение нефтяных разливов в море // Математическое моделирование. 2018. Т. 30, № 6. С. 39—59.
12. Бровченко И. А., Мадерич В. С. Численный Лагранжевый метод моделирования распространения поверхностных пятен нефти // Прикладна гiдромеханiка. 2002. Т. 4(76), № 4. С. 23—31.
13. Maderich V., Brovchenko I., Jung K. Oil Spreading in instantenious and continious spills on rotational Earth // Envir Fluid Mechanics. 2012. P. 361—378.
14. Ovsienko S., Zatsepa S., Ivchenko A. Study and Modelling of Behavior and Spreading of Oil in Cold Water and in Ice Conditions // Poac 99, Proceedings. 1999. V. 2. P. 848—857.
15. Архипов Б. В., Пархоменко В. А., Солбаков В. В., Шапочкин Д. А. Математическое моделирование распространения нефтяных разливов в морской среде. М.: ВЦРАН, 2001. 53 с.
16. Arkhipov B., Koterov V., Solbakov V., Shapochkin D., Yurezanskaya Y. Numerical Modeling of Pollutant Dispersion and Oil Spreading by the Stochastic Discrete Particles Method // Studies in Applied Mathematics. 2007. 120 (1). P. 87—104.
17. Hoult D. P. Oil spreading on the sea // Annual Review of Fluid Mechanics. 1986. V. 4. P. 341—368.
18. Marius Ungarish. An introduction to gravity currents and intrusions. Department of Computer Sciense Technion. Israel Institute of Technology Haifa. Israel. CRC Press. A Chapman and Hall Book. 2009. 489 p.
19. Friedrichs K. O. On the derivation of the shallow water theory // Comm. Pure and Appl. Math. 1948. V. 1. P. 81—85.
20. Harkins W. D. The physical chemistry of surface films. New York: Reinhold, 1952. 163 p.
21. Foda M., Cox R. G. The spreading of thin liquid films on a water-air interface // J. Fluid Mech. 1980. V. 101 (1). P. 33—51.
22. Loytsiansky L. G. Mechanics of fluid and gas. Second Revised Edition, Pergamon Press, 2014. 688 p.
23. Sedov L. I. Similarity and Dimensional Methods in Mechanics. 10-th ed. CRC Press, 1993. 493 p.
Review
For citations:
Arkhipov B.V., Shapochkin D.A. Some properties of solutions of the equation for oil spills spreading on the sea surface. Fundamental and Applied Hydrophysics. 2019;12(1):62-74. (In Russ.) https://doi.org/10.7868/S2073667319010088
Views:
117
Email this article 