Oil spreading in instantaneous and continuous spills on rotating earth

Abstract

The effect of the Coriolis force on the oil spill spreading in the gravity-viscous regime is examined. A new shallow water model for the transport and spreading of oil slick of arbitrary shape is described in which the Coriolis force is included in the momentum equations and the oil-water friction is parameterized in a frame of the boundary layer theory including the Ekman friction. The numerical Lagrangian method based on smoothed particle dynamics is described. New similarity solutions of the model equations are obtained for unidirectional and axisymmetric spreading in gravity-viscous, gravity-turbulent and gravityviscous-rotational regimes for instantaneous as well as continuous releases. The numerical simulation extends these results for the case of continuous release in the presence of currents. It was shown that Coriolis term in the momentum equation can be omitted if slick thickness is much less of the laminar Ekman layer thickness. However, the Ekman friction should be retained for slicks of any thickness for larger times. The Ekman friction results in the essential slowdown of the spreading as well as in the deflection of the oil spreading velocity at 45 • from the direction of velocity in the non-rotation case. Numerical simulations of large-scale spills showed that after the 2 days the slick area with the Coriolis effect was approximately less than half of that without rotation. Therefore, the earth rotation can be also important in the oil weathering.

Viscous-Gravity Spreading of Oil on Water: Modeling and Challenges

“…The results obtained in [9] are compared with the experimental data and the theoretical work in [8] (using finite differences) in Table I, showing that the constant-volume case can be considered as well understood at least at the laboratory scale. The axisymmetric case results show consistency between the detailed boundary-layer treatment of the laminar boundary-layer flow in the water phase (η m =1.15) in [9] and the approximate analysis in [11] based on Blasius solution (η m =1.09).…”

“…On the other hand, the theoretical work in [11] shows significant deviation from the experimental value in [6] (see Table III). Both aspects are discussed in the next section.…”

“…The theoretical treatment of the variable oil discharge case was considered in [10]. Approximate treatments for the laminar boundary layer were used in [11] based on the well-known Blasius solution to solve for the dynamics of spreading in both cases of constant and variable oil-spill volumes. The present paper reviews the different findings and provides directions for future work based on the present challenges.…”

A Lagrangian oil spill transport model for the Red Sea

“…The spill model considers physical transport (advection due to water currents and mixing due to turbulence) plus some specific processes for oil, as buoyancy, evaporation and decomposition. The transport of the oil spill as a surface film and the effects of surface tension are not included in this model, although their theoretical description may be seen in Maderich et al (2012).…”

Lava spreading during volcanic eruptions on the condition of partial slip along the underlying surface

“…This approach to the boundary condition is similar to that used in [14,26,27]. Thus, the solution of problem (1.10) is reduced to the solution of the second-order ordinary differential equation (1.14) with condition (1.17).…”