Wave energy dissipation by a viscous surface layer

Abstract

Mineral oil spills at sea can have many negative consequences. For both preventive and responsive purposes, it is essential to accurately forecast oil spill evolution. Shear diffusion (in this context, i.e. the combined effect of vertical mixing and differentiated horizontal advection of mass) determines for a significant part the evolution of an oil spill. These processes are partially forced by waves. A viscous fluid layer attenuates the waves throughout the area the layer covers. In this thesis, surface oil slicks are modeled as a continuous viscous fluid layer. It is investigated to what extent the wave-forced shear diffusion of the oil is affected by the oil-induced attenuation of the waves. For this purpose, the spectral wave model SWAN is extended with a module for energy dissipation due to a viscous fluid layer. The stationary, 1D wave energy balance is solved for uniformly forced waves in deep water. A high cutoff frequency (5 Hz) is employed to include the wave frequencies at which the dissipation is active. Also, special attention is paid to the choice of the wind and whitecapping formulation. Simulations are performed in full factorial setup, varying wind speed, oil layer thickness and oil viscosity. The results are compared to a no-oil case. Based on the difference, functions are fitted for the reduction of two key wave properties: the whitecapping dissipation rate and the surface Stokes drift velocity. The reduction functions are included in the oil spill module of the particle tracking model OpenDrift, which is subsequently used to calculate oil spill evolution due to shear diffusion for 2DV cases. The results of oil spill simulations with and without the implemented reduction functions are compared. Idealized cases (only wave-forced) show that for sufficiently thick layers (h+ ≥ O{10^-3} m) of sufficiently viscous (ν+ ≥ O{10^-3} m^2/s) oil, the Stokes drift reduction can significantly affect the wave-driven evolution of an oil spill in two ways: the average forward transport is reduced and the skewness of the oil mass distribution is increased to ‘less negative’ or even positive values. If simple sheared wind drift and ambient vertical turbulence are added, however, the relative importance of these effects becomes smaller. In none of the cases, a difference is found for the distribution of the oil mass between surface and subsurface, which implies that the whitecapping reduction hardly affects the results. It is recommended that further effort is put into obtaining a detailed understanding of the (differentiated) forward transport of the surface and near-surface oil, so that wave and wind effects can be distinguished, and modeled independently, more accurately.