DUAL OIL CONCENTRATION ESTIMATES IN ECOLOGICALLY SENSITIVE ZONES

Propagation of the oil spilling from a damaged oil tanker is considere d in a limited sea area. Direct and adjoint estimates of the average o il concentration in special zones are derived by using solutions of th e 2-D main and adjoint oil transport problems, respectively. The dual estimates complement each other nicely in studying the oil spill conse quences. While the direct estimates are preferable to get a comprehens ive idea of the oil spill impact on the whole area, the adjoint ones a re specially useful and economical when the accident site-dependence o r/and the oil spill rate-dependence of the oil concentration is/are st udied only in a few ecologically sensitive zones. Indeed, each adjoint estimate explicitly relates the average oil concentration in a zone t o 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 regar dless of a concrete accident and used repeatedly for various possible values of these parameters. Several examples explain how to decide bet ween two estimates. Thanks to special boundary conditions, the main an d adjoint problems are both well-posed according to Hadamard (1923). T he dual estimates can be generalized to the three dimensions. The bala nced, absolutely stable and compatible main and adjoint 3-D numerical algorithms by Skiba (1993) can easily be adapted to the problem discus sed here.