# Pollution of the Black Sea and its Study By Methods of Mathematical Modeling

## Main Article Content

## Abstract

In this study, the articles devoted to simulation of dispersion processes of different substances in the seas and oceans are reviewed. The basic attention is focused on the diffusion mathematical models on spreading of substances of anthropogenic origin in the Black Sea. Numerical models developed at M. Nodia Institute of Geophysics (Tbilisi, Georgia) concerning distribution of different admixtures (oil, Strontium-90, Rioni River alluvium) in the Back Sea basin are described in more details. These models are based on nonstationary 2D and 3D transfer-diffusion equations using annual mean climatic flow field calculated by the barotropic and baroclinic models of the Black Sea dynamics. A theoretical method of determining the pollution source location in a water basin on known pollution concentrations in some points of the upper layer of the sea is also considered. The method is based on a conjugate transfer-diffusion equation. For solution of both the models of dynamics and admixture’s dispersion the two-cycle splitting methods, offered by G. I. Marchuk for solution of problems of atmosphere and ocean dynamics are used.

**Keywords:**

**Published:**Feb 8, 2017

## Article Details

*Journals of Georgian Geophysical Society*,

*14*(2). Retrieved from https://ggs.openjournals.ge/index.php/GGS/article/view/1774

## References

1. Zimakov I. Е. With a thought about tomorrow. Energy: Economy, Techniques, Ecology. М., Mir, 1985, № 4, pp. 2-8 (in Russian).

2. Shnaider C. G. Changing climate. V Mire Nauki, М., Mir, 1989, №11, pp.26-36 (in Russian).

3. Practical Ecology of Marine Regions. The Black Sea. Kiev: Naukovadumka, 1990, 252 p (in Russian).

4. Vinogradov M. Е., Arnautov G. N. Investigation of modern state of the ecosystem of the Black Sea. In: Investigations of Pelagiali of the Ecosystem of the Black Sea. M., 1986, pp. 1-8 (in Russian).

5. Mironescu L. The fight against harm to the environment in the Black Sea. Parliamentary Assembly of Council of Europe. 2008. http://assembly.coe.int

6. Jaoshvili Sh. The river alluvium and the beach formation of the Georgian Black Sea cost. Tbilisi, “CabchotaSakartvelo”, 1986, 155 p (in Russian).

7. Mikhailova M. V., Jaoshvili Sh. V. Hydrological –morphological processes in estuary area of Rioni River and their anthropogenous changes. Vodnieresursi, 1998, t. 25, N 2, pp.152-160 (in Russian).

8. Jaoshvili Sh. The rivers of the Black Sea. Tbilisi, 2003. 186 p

9. Kagan B. A., Ryabchenko V. A. Tracers in the world ocean. Л.: Gidrometeoizdat, 1978, 58 p (in Russian).

10. Marchuk G. I. Mathematical modeling in the Environment Problem. М.: Nauka, 1982, 320 p (in Russian).

11. Ozmidov R. V. Diffusion of Contaminants in the Ocean. L.: Gidrometeoizdat, 1986, 280 p (in Russian).

12. Monin А. С., Ozmidov R. V. Ocean Turbulence. L, Gidrometeoizdat, 1981,319 p. (in Russian).

13. Nelepo B. А. Nuclear Hydrophysics. М., Atomizdat, 1970, 224 p (in Russian).

14. Shtokman V. B. Оn turbulent exchange in the middle and south parts of the Caspian Sea. Izv. AN CCCР, Geogr. iGeofiz., 1940, № 4, pp. 569-592 (in Russian).

15. Shtokman V. B. About pulsations of horizontal component of speed of sea currents owing to turbulence of the big size. Izv. AN CCCР, Geogr. iGeofiz., 1941, № 4, pp.476-486 (in Russian).

16. Richardson L. F., Stommel H. Note on eddy diffusion in the sea. J. Meteorol., 1948, v.5, N 5, pp. 238-240.

Craig H. Abyssal carbon and radiocarbon in the Pacific. J. Geophys. Res., 1969, v. 74, N 23, pp.5491-5506.

17. Munk W. H. Abyssal recipes. Deep-Sea Res., 1966, v.13, N 4, pp. 707-730.

18. Radioactive pollutions of the environment. М., Gosatomizdat, 1962, 275 p (in Russian).

19. Complex researches of the Black Sea. Kiev, “NaukovaDumka”, By eds. B. A. Nelepo,1980, 238 p (in Russian) .

20. Shvedov V. I., Iuzefovich А. А., Еroschev-Shak V. А.et al. Definition of the maintenance of strontium-90 in the Black Sea. In: Radioactive impurity of the seas and oceans. М., Nauka, 1964, pp. 76-80 (in Russian).

21. Beliaev V. I., Kolesnikov А. G., Nelepo B. А. Disposal of radioactive wastes into seas, oceans and surface wasters. JAEA, Vienna, 1966, p. 381-395.

22. Okeanologia. T 1. Hydrophysics of Ocean. Eds V. M. Kamenkovich and A. C. Monin, M., Nauka, 1978, 456 pp (in Russian).

23. Ozmidov P. V., Popov N. I. To studying of vertical water exchange at ocean by data about distribution to him of strontium-90. Izv. AN СССР, Fizikaatmosferyiokeana, 1966, v.2, N 2, pp. 183-190 (in Russian).

24. Vinogradov А. С. Vertical diffusion at ocean of cosmogeneousizotops. Okeanologia, 1978, t. 18, vyp.1, pp 50-57 (in Russian).

25. Vinogradov А. С. Vertical diffusion at ocean of radioactive deposits. Okeanologia, 1979, t. 19, vyp. 2, pp. 239-245 (in Russian).

26. Yakushev Е. М. Mathematical modeling of distributions of phosphates in meridian planes of a southern half of World ocean. Okeanologia, 1984, t. 24, vyp. 2, pp. 277-284 (in Rissian).

27. Yakushev Е. М. Numerical modeling of distribution and Variability of connections Phosphorus at ocean. The author's abstract of Candidate’s thesis in Physics and Mathematics, IOAN, 1984, 16 p (in Russian).

28. Riabchenko V. А. Numerical modeling of distributions of the dissolved oxygen at the World ocean.Okeanologia, 1977, vip. 6, pp.1004-1009 (in Russian).

29. Kogan B. A., Riabchenko V. A. Numerical experiments on seasonal evolution of Carbon cycle at ocean. Izv. СССР, Fizikaatmosferyiokeana, 1982, t.18, N 4, pp. 373-382 (in Russian).

3o. Research of turbulence and solution of problems of transfer of polluting substances in the sea. Proceed. GOIN (Edit. E. B. Borisov), 1977, vyp. 141, 170 p (in Russian).

31. Ozmidov R. V. Horizontal turbulent diffusion of stains of an impurity in the sea. Proceed.IOAN, 1960, t. 37, pp.164-181 (in Russian).

32. Belousova E. I., Latun V. C. Rundown and run-up circulation of waters and impurity distribution in a coastal zone of the sea. Sea hydrophysical researches, 1975, N 3, pp. 54-65(in Russian).

33. Kogan B. А., Oganesian L. А., Riabchenko V. А. Distribution of a passive impurity from an instant point source in the World ocean (Numerical experiment). Izv. AN СССР, Fizikaatmosferyiokeana, 1978, t. 14, N 6, pp. 621-627 (in Russian).

34. Kochergin V. P., Bokovikov A. G. A three-dimensional numerical model of contaminant dispersion in the near-shore zone of a deep basin. Izv. AN СССР, Fizikaatmosferyiokeana, 1980, t. 16, N7, pp.729-737 (in Russian)

35. Kochergin V. P., Bokovikov A. G. Numerical experiments on contaminant dispersion in the sea. MeteorologiaiHidrologia, 1984, N3, pp.73-79 (in Russian).

36. Shkudova G. Ia., Djioev T. Z. Numerical model of water circulation and spreading of admixture in the deep baroclinic sea (on example of the Black Sea). Proceed. GOIN, 1975, vyp.126, pp.92-103 (in Russian).

37. Zhurbas B. M. The principle mechanisms of oil distribution in the sea. Mechanics of fluid and Gas. M.: VINITI, 1978, t. 12, p.144-159 (in Russian).

38. Chemistry of Ocean. Т. 1. (Eds O. K. Bordovski and B. N. Ivanenkov), М.: Nauka, 1979, 518 p (in Russian).

39. Korotenko K. A., Dietrich D. E., Bowman M. J. Modeling Circulation and oil spill transport in the Black Sea.

40. Okeanologia, 2003, t. 43, N 3, p. 367-378 (in Russian).

41. Korotenko K. A., Mamedov R. M., Mooers C. N. K. Prediction of the Dispersal of Oil Transport in the Caspian Sea Resulting from a Continuous Release. Spill Science and Technology Bulletin. 2001, v.6, N 5/6, p. 323-339.

42. Vragov A. V. Methods of detection, estimation and liquidation of emergency floods of oil. Novosibirsk, 2002, 224 p.

43. Korotenko K. A., Mamedov R. M., and Mooers, C. N. K. Prediction of the transport and dispersal of oil in the south Caspian Sea resulting from Blowouts. Environmental Fluid Mechanics 1: 2002, pp. 383-414.

44. Korotenko K. A., and Mamedov R. M.: Modeling of oil slick transport processes in coastal zone of the Caspian Sea. Oceanology, 2001, v. 41, pp.37-48.

45. Reed M., Johansen O., Brandvik P. J., Daling P., Lewis A., Fiocco R., Mackay D., Prentki R. Oil spill modelling toward the close of the 20th century: overview of the state of the art. Spill Science and Tech. Bull. 1999, pp.3-16.

46. Jones B., The use of numerical weather prediction model output in spill modelling, Spill Science and Tech. Bull. 5, 1999, pp.153-159.

47. Christiansen, Bettina M. 3D Oil drift and fate forecast at DMI. Technical Report No 03-36. Danish Meteorological Institute, Denmark, 2003.

48. Brovchenko I., Kuschan A., Maderich V., Shliakhtun M., Yuschenko S., Zheleznyak M. The modeling system for simulation of the oil spills in the Black Sea. Proceed. of the 3rd EuroGOOS Conference, Athens/Greece, 3-6 December, 2002.

49. Daniel P. Numerical simulation of the Aegean Sea oil spill. Proceed. of the 1995 Intern. Oil Spill Conference. American Petrolium Institute, Washington,D.C.,1995, http://www.meteorologie.eu.org/mothy/references/iosc1995.pdf, pp. 894-896.

50. Daniel P. Forecasting oil spill drift at Meteo-France. Proceed. of the 1997 Intern. Oil Spill Conference. American Petrolium Institute, Washington, D. C., 1997, pp. 990-993.

51. Daniel P., Kortchev G., Mungov G. Forecasting oil spill drift in the Black Sea. Proceed. of oil spills in the Mediterranean and Black Sea regions, MEDOSC, University of Manchester, UK, 1998, pp.D011-8.

52. Daniel P., Poitevin J., Tiercelin C., Marchand M. Forecasting accidental marine pollution drift: the French operational plan, oil and hydrocarbon spills, modelling, analysis, and control. Computational Mechanics Publications, WTT Press, 1998, pp. 43-52.

53. Daniel P., Gilbert T., Hackett B., Hines A. Tiercelin C. Operational metocean products and services in support of marine pollution emergency response operations. Proceed. of the 2008 Intern. Oil Spill Conference. American Petrolium Institute, Washington, D. C., 2008.

54. Chune S. L., Drillet Y., Daniel P., Mey P. D. Improving operational oceanography for driftapplicants. 2010 Ocean Sciences Meeting, AGU, Portland, OR, USA, 2010.

55. Grell G., Dudhia A. J., Stauffer D. R. A description of the fifth-generation Penn State/NCAR mesoscale model (MM5). NCAR Technical Note. NCAR/TN-398+STR, 1994.

56. Tolman H. L. User manual and system documentation of WAVEWATCH-III version 1.18. NOAA/NWS/NCEP/OMB Technical Note 166, 1999.

57. Blumberg A. F., Mellor G. L. A. description of a three-dimensional coastal ocean circulation model. AGU, Washington, 1987, DC, 4, 1.

58. Dietrich D. E., Lin C. A., Mestas-Nunez A., Ko D. S. A high resolution numerical study of Gulf of Mexico fronts and eddies. Meteorol. Atmos. Phys. 1997, v. 64, pp. 187-201.

59. Kordzadze A., Kvaratschelia D., Demetrashvili D. On the specification of the eddy viscosity coefficient in the Black Sea dynamics barotropic problem. J. Georgian Geophys. Soc., Tbilisi, v.3B, 1998, pp.59-65.

60. Kordzadze A. A., Demetrashvili D. D. – Numerical modeling of inner-annual variability of the hydrological regime of the Black Sea with taking into account of alternation of different types of the wind above its surface. Proceed. of Intern. Conference: “A year after Johanesburg-Ocean Governance and Sustainable Development: Ocean and Coasts – a Glimpse into the Future”. Kiev, Ukraine, October 27-30, 2003, pp.495-505.

61. Kordzadze А. А., Demetrashvili D. I., Surmava А. А. – Numerical Modeling of hydrophysical fields of the Black Sea under the Conditions of alternation of atmospheric circulation processes. Izv. RAN, FizikaAtmosferyiOkeana, 2008, v. 44, N 2, pp.227- 238 (in Russian).

62. Marchuk G. I. Numerical methods in weather prediction. Leningrad, Gidrometeoizdat, 1967, 353 p (in Russian).

63. Marchuk G. I. The numerical solution of the problems of the atmosphere and the ocean dynamics. L.: Gidrometeoizdat, 1974, 303 p (in Russian).

64. Zilitinkevich C. C., Monin A. C. Turbulence in the dynamical models of the atmosphere. L.: Nauka, 1971, 44 p (in Russian).

65. Kordzadze A., Demetrashvili D. Numerical experiments on the determination of the pollution source location in the Black Sea. 3D problem. J. Georgian Geophys. Soc.,2001, v. 6B, pp.3-12.

66. Kordzadze A., Demetrashvili D. Numerical experiments on the determination of the pollution source location in the Black Sea. 2D problem. J. Georgian Geophys. Soc., 2001, v. 6B, pp.13-22.