Die Kuste, 81 (2014), 255-271 
260 
are given by the operational ocean model under consideration (e.g. BSHcmod), meaning 
that the particles move within die cell according to die given velocities resp. velocity gra 
dients. 
At die ocean surface the two-dimensional surface wind fields (e.g. LME) additionally 
move die particles, if desired. In each cell the bottom is flat and the location of die bot 
tom depends on die bathymetry of the circulation model. For example a sloping bottom 
is represented by a staircase shape meaning die bottom consist of horizontal and vertical 
faces of die grid cells. In the horizontal the staircase shaped model coastline is replaced 
by a realistic coastline in order to have a more realistic representation. 
Next to die purely advective displacement of die particles by a given wind and current 
field (as described above), horizontal as well as vertical spreading occurs as a result of 
water current or wind shear at various temporal and spatial scales (so called sub-grid pro 
cesses). In SeatrackWeb the small-scale isotropic turbulent mixing is included by adding 
turbulent velocities depending on the turbulent kinetic energy and its dissipation rate ran 
domly to die drift of the particles. 
In case of an oil slick die density differences between water and oil and die viscous as 
well gravitational forces lead to horizontal surface spreading of oil at the interface be 
tween water and air. To compute this process slick heights computed from die Fay for 
mulas (Fay 1971) give - by assuming cylindrical particles witii individual particle volumes 
— particle radiuses. The spreading is then a result of an iterative procedure calculating 
non-overlapping discs. 
The vertical dispersion of particles from the surface down into die water column de 
pends on the kind of substance simulated. For dissolved substances die turbulent mixing 
is a major player, but for oil slicks breaking waves have to be included to simulate the 
breaking up of cohesive slicks and die dispersion of tiiese droplets into die water column. 
For this purpose a dissipative energy due to breaking waves is computed from die signifi 
cant wave height leading to a mass of oil to be dispersed for each droplet size. Then die 
new depth values are assigned randomly by adding extra negative vertical velocities to die 
movement of die particles. 
Density differences between die particle and die surrounding water leads to sinking or 
rising. A formula primarily developed for oil (SOARES DOS SANTOS and DANIEL 2000) 
gives a buoyancy velocity depending on the reduced gravity, viscosity, diameter of die 
particle and a critical diameter. The critical diameter divides the particles into two re 
gimes: die large, spherical-cap bubble and die small spherical droplet (Stokes’s) regime. 
Otiier substances than oil also have a buoyancy velocity, which is simply die reduced 
gravity multiplied by an adjustable coefficient. 
If die particles simulate die drift of oil, oil weathering processes like evaporation and 
emulsification influence its properties. Density depends on emulsification and evapora 
tion. Each particle’s viscosity changes due to temperature (die rate of evaporation) and 
the degree of emulsification. For details about the implementation of weatiiering process 
es we refer to AMBJORN et al. (2011) and die scientific documentation of SeatrackWeb 
(LlUNGMAN and MATTSSON 2011) accessible tiirough http://stw.bsh.de/seatrack or 
https://stw-helcom.smhi.se/. 
Stokes drift is a net drift caused by the orbital motion of deep-water waves, which is 
not exactly closed due to the decrease of orbital velocities witii deptii. In die considered 
hydrodynamic models this motion is neitiier resolved nor implicitly included in the