Environmental Engineering Reference
In-Depth Information
In this method, the particles will represent the mass of released oil which
transported under the influence of the environmental forcing, turbulent diffusion
and spreading processes. The Lagrangian particle-tracking trajectory algorithm is
according to the simple formula
d
x
i
d
t
=
U
a
(
x
i
,
t
)
+
U
d
(
x
i
,
t
),
(6.1)
where
x
i
is the i particle position,
U
a
is the advective velocity from hydrodynamic
model, and
U
d
is the random velocity fluctuations.
The advective velocity
U
a
of the oil particle is obtained by
U
a
=
U
cr
+
C
wind
D
wind
U
wind
+
U
wave
,
(6.2)
where
U
cr
is the water current velocity interpolated from hydrodynamic model;
U
wi nd
is the wind velocity at 10m above the water surface,
C
wind
is the wind drift
factor.
D
wind
is the transformation matrix used to account the wind deflection angle,
and this matrix is defined as follows:
cos
B
sin
B
sin
B
cos
B
D
wind
=
,
(6.3)
25
ⓦ
exp
10
−
8
U
wind
/ʽ
where
B
is the kinematic viscosity of the seawater.
U
wave
represents the wave Stokes drift calculated as
=
(
−
g
)
,
ʽ
H
s
k
˃
cosh
(
2
kz
0
)
U
wave
=
,
(6.4)
8sinh
2
(
)
kh
where
k
is the wave number,
is the angular frequency,
H
s
is the significant wave
weight,
z
0
is the vertical position of oil particles measured upwards from the still
water surface.
In addition to the determinate advective movements, oil droplets experience a
random diffusion due to the turbulent fluctuations. The turbulent diffusive transport
is calculated by a random walk procedure with a horizontal diffusion coefficient.
Based on the previous study, the diffusive distance can be expressed by:
˃
0
12
D
h
1
S
=[
R
]
t
,
(6.5)
1
[
]
where
0
is the random number in the interval [0,1],
D
h
is the horizontal diffusion
coefficient calculated from Smagorinsky formulation.
During the early stages of oil slick transformation, the mechanical spreading is a
dominant process, which is treated as a diffusion process and is also simulated using
the random walk method. The diffusion-like spreading coefficient is calculated from
the following formulation:
R
Search WWH ::
Custom Search