Abstract
Propagation of the oil spilling from a damaged oil tanker is considered in a limited sea area. Direct and adjoint estimates of the average oil concentration in special zones are derived by using solutions of the 2-D main and adjoint oil transport problems, respectively. The dual estimates complement each other nicely in studying the oil spill consequences. While the direct estimates are preferable to get a comprehensive idea of the oil spill impact on the whole area, the adjoint ones are specially useful and economical when the accident site-dependence or/and the oil spill rate-dependence of the oil concentration is/are studied only in a few ecologically sensitive zones. Indeed, each adjoint estimate explicitly relates the average oil concentration in a zone to the oil spill rate using the adjoint solution values at the accident site. Being independent of the two parameters (the accident site and oil spill rate), the adjoint solution can be found for each zone regardless of a concrete accident and used repeatedly for various possible values of these parameters. Several examples explain how to decide between two estimates.
Thanks to special boundary conditions, the main and adjoint problems are both well-posed according to Hadamard (1923). The dual estimates can be generalized to the three dimensions. The balanced, absolutely stable and compatibie main and adjoint 3-D numerical algorithms by Skiba (1993) can easily be adapted to the problem discussed here.
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References
ChristensenF. T.: 1994, ‘Management of Oil Spill Risks in Arctic Waters’, J. Mar. Environ. Eng. 1, 131.
ElliottA. J.: 1986, ‘Shear Diffusion and the Spread of Oil in the Surface Layers of the North Sea’, Deutsche Hydrographische Zeitung 39, 113.
ElliottA. J., DaleA. C. and ProctorR.: 1992, ‘Modelling the Movement of Pollutants in the UK Shelf Seas’, Mar. Pollut. Bull. 24, 614.
GodunovS. K.: 1971, Equations of Mathematical Physics, Nauka, Moscow (in Russian).
Hadamard, J.: 1923, Lectures on Cauchy's Problem in Linear Partial Differential Equations, Dover, 316 pp.
KennicuttM. C.II, McDonaldS. J. and SweetS. T.: 1992, ‘The Bahia Paraiso Spill in Arthur Harbor, Anvers Island’, Antarct. J. US 27, 331.
LyusternikL. A. and SobolevV. I.: 1964, Elements of Functional Analysis, Ungar, New York.
MarchukG. I.: 1982, ‘Mathematical Issues of Industrial Effluent Optimization’, J. Meteor. Soc. Japan 60, 481.
MarchukG. I.: 1986, Mathematical models in environmental problems, Elsevier, New York.
MarchukG. I. and SkibaYu. N.: 1976, ‘Numerical Calculation of the Conjugate Problem for a Model of the Thermal Interaction of the Atmosphere with the Oceans and Continents’, Izvestiya, Atmos. Ocean. Physics 12, 279.
PenenkoV. V. and RaputaV. F.: 1982, ‘Experiment Planning in Inverse Problems of Pollutant Transport’, Sov. Meteorol. Hydrology 8, 28.
PenenkoV. V. and RaputaV. F.: 1983, ‘Some Models for Optimizing the Operation of the Atmospehric-Pollution Sources’, Sov. Meteorol. Hydrology, 2, 46.
PoinsotT. J. and LeleS. K.: 1992, ‘Boundary Conditions for Direct Simulations of Compressible Vicous Flows’, J. Comput. Physics 101, 104.
ProctorR., ElliottA. J., DaleA. C. and FlatherR. A.: 1994, ‘Forecast and Hindcast Simulations of the Braer Oil Spill’, Mar. Pollut. Bull. 28, 212.
SchneiderD.: 1993, ‘Oil Spill has Long-Term Effects’, Water Environ. Technol. 5, 30.
SkibaYu. N.: 1993, ‘Balanced and Absolutely Stable Implicit Schemes for the Main and Adjoint Pollutant Transport Equations in Limited Area’, Rev. Int. Contam. Ambient 9, 39.
Skiba, Yu. N.: 1995, ‘Pollution Concentration Estimates in Ecologically Important Zones’, in: Proceedings of X World Clean Air Congress “Growing Challenges-From Local To Global”, May 28 – June 2, 1995, Helsinki, Finland, Vol. 3, paper 525.
SkibaYu. N. and AdemJ.: 1995, ‘A Balanced and Absolute Stable Numerical Thermodynamic Model for Closed and Open Oceanic Basins’, Geofísica Internacional 34, 385.
WolffG. A., PrestonM. R., HarrimanG. and RowlandJ. S.: 1993, ‘Some Preliminary Observations after the Wreck of the Oil Tanker Braer in Shetland’, Mar. Pollut. Bull. 26, 567.
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Skiba, Y.N. Dual oil concentration estimates in ecologically sensitive zones. Environ Monit Assess 43, 139–151 (1996). https://doi.org/10.1007/BF00398604
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DOI: https://doi.org/10.1007/BF00398604