Operational Oil Spill Modelling: From Science to Engineering Applications in the Presence of Uncertainty - Mathematical Modelling and Numerical Simulation of Oil Pollution Problems - page 105

5.5.3 Wind Forcing

The direct force of the wind on an oil spill is arguably negligible; however, few
operational hydrodynamic models are designed with the fine-resolution vertical grid
scales and algorithms that can accurately reproduce the surface and near-surface
water velocities. Thus, the hydrodynamic model surface water velocity field is not
the velocity field that an oil spill will actually see. Because the surface and near-
surface velocities are strongly affected by the local speed and direction of the wind,
oil spill models typically include a “wind drag” parameter that provides a correction
to the hydrodynamically-modelled water surface velocities for particle transport.

5.5.4 Wave Forcing

The transport cause by waves is typically added through a Stokes drift term that
requires empirical parameterization. Selection of the parameter depends on the type
of wave model.

5.5.5 Diffusivity

Diffusivity parameterization controls the overall spread of particles produced by an
oil spill model; i.e. this is not diffusion of oil molecules into solution with water, but
the dispersion or spreading of the oil on or near the water surface. This diffusivity is
not generally a direct representation of the dispersion physics acting on an oil slick,
but instead a stochastic parameterization of turbulence and the unresolved spatial
structure of the modelled water velocities. Thus, the appropriate oil spill diffusivity
is difficult to directly link to physically-based eddy diffusion coefficients (e.g. [ 34 ])
or turbulence models used in hydrodynamic simulations. Diffusivity for an oil spill
is often modelled as parameterized white noise.

5.5.6 Hydrodynamic Model Grid

Grid spacing affects the spatial and temporal velocity gradients that can be repre-
sented in the hydrodynamic model. Most models are limited by a CFL condition
such that u

ʔ t /ʔ x < C limit , where u is the water velocity, ʔ t is the model time step,

ʔ x is the local model grid scale in the same direction as u , and C limit is the CFL

limit that is typically O , with the exact value depending on the numerical algo-

rithm. Thus, the model grid spacing also controls the model time step. For coarser
model grids, both spatial and temporal gradients will be less accurate than with finer

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