Beyond the parabola: A surface-tension-limited, analytical-numerical extension of Nihoul's oil-slick spreading...

Nihoul's vertically averaged equation remains widely used for operational oil spill modeling because it offers a simple, computationally efficient formulation and an analytical similarity solution that serves as a robust benchmark for validating numerical schemes. However, its reliance on a predefined parabolic slick profile introduces systematic errors at the slick periphery. Relative to laboratory observations, the parabolic profile underestimates the slick radius and overestimates thickness near the tail end. The simulated slick thickness fields, spatial extent, and spreading persistence represent physical hazard-related indicators describing the intensity and footprint of surface contamination. To address these limitations, we enhanced Nihoul's spreading equation and applied to a spill problem where surface tension forces oppose the late stage spreading. The new formulation admits both a closed form analytical solution and a numerical solution, representing, to our knowledge, the first joint analytical-numerical treatment of this extension. From these solutions, we derived new practical expressions for the slick extent and thickness distribution near termination, yielding an improved representation of the tail end profile. Comparisons with laboratory-scale spill experiments demonstrate improved agreement relative to the classical parabolic similarity solution, particularly for outer-radius growth and thinning behavior. The proposed approach provides a computationally efficient extension of existing spreading models, improving physical realism without the prohibitive cost of fully multiphase simulations.