The oil spill model OILTRANS and its application to the Celtic Sea ...

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1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556575859606162636465OILTRANS formulations. The time to formation of the emulsions has previously been studied byFingas and Fieldhouse (2004), who related the time to formation of each emulsion type to theenergy required for formation (expressed as equivalent wave height) and expressed as:y = a + (b / x 1.5 ) (26)where y is the time to formation (min), a & b are coefficients depending on emulsion type afterFingas (2011), and x is the wave height (cm). The emulsification algorithms of Mackay et al.(1980a, 1980b) are also encoded in the OILTRANS system for use in sensitivity analyses and togive end users the options to choose an alternative algorithm for local implementations.2.2.5. DispersionNatural dispersion, or entrainment, of oil slicks at sea occurs when droplets of oil are mixed into thewater column by breaking waves. If the droplets are small enough natural turbulence in the waterwill prevent the oil from resurfacing whilst larger droplets tend to rise and will not stay in the watercolumn for more than a few minutes. The droplets that stay in the water column are considered tobe permanently dispersed. The natural dispersion process within the OILTRANS model is based onthe classic method of Delvigne and Sweeney (1988) who developed a relationship for entrainmentrate, Q d , as a function of droplet size and oil viscosity, as:* 0.57 0.7Qd C DdSFd d(27)where: Q d is the entrainment rate, (kg/m 2 s), for droplet diameter d, (m), C* is an empiricalentrainment constant which depends on oil type and weathering state. Using a series ofexperimental data by Delvigne and Hulsen (1994), the entrainment constant, C*, was fit to thefollowing equations by French-McCay (2004):C* = exp(-0.1023 ln(υ oil ) + 7.575) for υ oil < 132 (cSt)(28)C* = exp(-1.8927 ln(υ oil ) + 16.313) for υ oil ) ≥ 132 (cSt)where: υ oil is the viscosity of the oil, (cSt). D d is the dissipated breaking wave energy per unitsurface area, (J/m 2 ), and is given by:2D d = 0.0034 ρ w gH b (29)where H b is the breaking wave height, assumed to be equal to 1.5H sig using the simple estimate ofLiungman and Mattsson (2011) where H sig is the significant wave height (m), and assuming a fullydeveloped sea-state, can be calculated according to CERC (1984) as; 0.243U g2*H sig(30)21.23whereU* 0.71Uwind, is the wind stress factor associated with the 10m wind speed U wind (m/s). S isthe fraction of sea surface covered by oil (assumed as 0.75). F is the fraction of sea surface hit bybreaking waves and is parameterised as:
1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556575859606162636465F = 3.0x10 -6 3.5(U wind / T w ) for U wind U th ,where U th is the threshold 10m wind speed for onset of breaking waves assumed as 5m/s, T w is thesignificant wave period and assuming a fully developed sea-state can be calculated according toCERC (1984) as:T w Uwind 8 .13(32) g Δd is the oil droplet interval diameter, (m), equally spaced between d max and d min . After Reed et al.(1995) the maximum and minimum droplet size diameters are calculated as:d max = 3400E -0.4 (υ o ) 0.34(33)d min = 500E -0.4 (υ o ) 0.34where E is the wave energy dissipation rate per unit volume, (J/m 3 s) set as 5.0 x 10 3 after Delvigneand Sweeney (1988) as an intermediate value for breaking waves. The oil particle interval diameterwas then constructed by adopting ten size classes between d min and d max , equally spaced ondiameter, as:Δd = (d max - d min ) / 10.0 (34)The OILTRANS model randomly assigns a droplet diameter to each of the lagrangian particlesbased on the droplet distribution profile calculated from equations (33) and (34). The depth towhich the dispersed oil droplets mix, Z mix , is expressed as:DZ max(vmix , Zi)w(35)dwhere D v is the vertical diffusion coefficient (m 2 /s), equal to 0.0015U wind after Thorpe (1984), w d isthe rise velocity (m/s) for droplet diameter d, and Z i is the intrusion depth (m) of the breaking waveequal to 1.5H b after Delvigne and Sweeney (1988). The rise velocity, w d , of the droplets iscalculated based on the droplet Reynolds number with Stokes Law applied for small droplets andReynolds Law applied for larger droplets, after Tkalich and Chan (2002). The total entrainment rateof oil into the water column, Q total (kg/m 2 s), for all droplet size classes is:10Q (36)totalQ dd 1and the total mass entrained, M ent (kg), per time step is equal to:M ent = Q total A t Δt (37)The droplet sizes determine whether dispersed oil will re-surface and at what rate. Large dropletsizes will resurface faster than small droplets, which may remain permanently dispersed in thewater column. Droplets which do not re-surface within the model time-step are assumed to be
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