Abstract. The processes of transport, diffusion and transformation of surface oil in seawater can be simulated using a Lagrangian model formalism coupled with Eulerian circulation models. This paper describes the formalism and the conceptual assumptions of a Lagrangian marine surface oil slick numerical model and rewrites the constitutive equations in a modern mathematical framework. The Lagrangian numerical representation of the oil slick requires three different state variables: the slick, the particle and the structural state variables. Transformation processes (evaporation, spreading, dispersion and coastal adhesion) act on the slick state variables, while particle variables are used to model the transport and diffusion processes. The slick and particle variables are recombined together to compute the oil concentration in water, a structural state variable. The mathematical and numerical formulation of oil transport, diffusion and transformation processes described in this paper, together with the many simplifying hypothesis and parameterizations, form the basis of a new, open source Lagrangian surface oil spill model, the so-called MEDSLIK-II, based on its precursor MEDSLIK (Lardner et al., 1998Zodiatis et al., 2008a). Part 2 of this paper describes the applications of the model to oil spill simulations that allow the validation of the model results and the study of the sensitivity of the simulated oil slick to different model numerical parameterizations.
Oil spill models are combined with bathymetric, meteorological, oceanographic, and geomorphological data to model a series of oil spill accidents in the Eastern Mediterranean Sea. A total of 104 oil spill simulations, computed for 11 different locations in the Levantine Basin, show that oil slicks will reach the coast of Cyprus in four (4) to seven (7) days in summer conditions. Oil slick trajectories are controlled by prevailing winds and current eddies. Based on these results, we support the use of chemical dispersants in the very few hours after large accidental oil spills. As a corollary, we show shoreline susceptibility to vary depending on: a) differences in coastline morphology and exposure to wave action, b) the existence of uplifted wave-cut platforms, coastal lagoons and pools, and c) the presence of tourist and protected environmental areas. Mitigation work should take into account the relatively high susceptibility of parts of the Eastern Mediterranean.
We present new mathematical and geological models to assist civil protection authorities in the mitigation of potential oil spill accidents in the Eastern Mediterranean Sea. Oil spill simulations for 19 existing offshore wells were carried out based on novel and high resolution bathymetric, meteorological, oceanographic, and geomorphological data. The simulations show a trend for east and northeast movement of oil spills into the Levantine Basin, affecting the coastal areas of Israel, Lebanon and Syria. Oil slicks will reach the coast in 1 to 20 days, driven by the action of the winds, currents and waves. By applying a qualitative analysis, seabed morphology is for the first time related to the direction of the oil slick expansion, as it is able to alter the movement of sea currents. Specifically, the direction of the major axis of the oil spills, in most of the cases examined, is oriented according to the prevailing azimuth of bathymetric features. This work suggests that oil spills in the Eastern Mediterranean Sea should be mitigated in the very few hours after their onset, and before wind and currents disperse them. We explain that protocols should be prioritized between neighboring countries to mitigate any oil spills.
AB S TRACTThe Somigliana formula is used to reduce an arbitrary elastic crack problem to a system of three integral equations for the components of displacement discontinuity. For the case of a penny shaped crack situated in an infinite isotropic medium with the crack faces subjected to arbitrary tractions, the integral equations are solved explicitly. In particular integral formulae are obtained for the stresses on the plane of the crack beyond the crack-tip, and hence for the stress intensity factors. The special case of uni-directional shear traction on the crack is examined.
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