Geoscience Reference
In-Depth Information
Vistula Lagoon is primarily determined by the vertical shear stresses. The reason is
that this lagoon is shallow and the frictional boundary layer occupies the whole
lagoon volume.
6.3.3.4
Wind Surge
The local level inclination develops at all times when the wind acts on the water
surface. Its upper bound value may be estimated from
τ
ρ
d
dx
ς
=
w
(6.45)
g
⋅⋅
H
where
(
x
) is the water surface level,
x
is the horizontal coordinate in the direction
studied (not obligatory in the wind direction),
g
is the gravity acceleration (
ς
≈
9.81
m s
−2
),
ρ
is the water density (approximately 1.000-1.035 kg m
−3
),
H
(
x
) is the depth,
and
τ
w
is the projection of the wind stress vector along
x.
The wind stress vector along the wind direction may be estimated as
τ
=⋅
CWW
ρ
⋅
|
|
⋅
(6.46)
w
a
a
a
ρ
a
and
W
a
are the air density and wind velocity, respectively, and
C
is the
dimensionless wind drag coefficient. Several empirical values have been proposed
for
C
(as, for example, 0.0026
20
). More elaborate expressions can be found, where
C
increases with wind speed as
18,21
where
−
3
−
1
C
=⋅
11 10
.
,
for |
W
| < 6 m s
a
(6.46a)
3
−
1
−
1
10
⋅ = +
C
0 61
.
0 063
.
⋅
|
W
|
for 6 m s
< |
W
| < 22 m s
a
a
Considering the standard of hydrometeorological observation when wind speed
is measured at a height of 10 m (
W
10
), the value of the drag coefficient
C
10
may be
estimated according to the Garratt recommendation:
15
C
=
0 00075
.
+
0 000067
.
⋅
|
W
|
for 4 m s
−1
< |W
10
| < 21 m s
−1
(6.46b)
10
10
h
) can be
estimated by integration of Equation (6.45) from side to side along the length
L
in
the direction studied (
x
), considering the wind component along this direction and
depth variations, or by using a simple formula with an average depth (
H
avg
):
The wind-induced level set up on opposite sides of a lagoon (
∆
L
gH
⋅
⋅⋅
τ
ρ
∆
h
=
w
,
(6.47)
avg
It follows from Equation (6.45) and Equation (6.47) that the level set up is
proportional to the wind and inversely proportional to the lagoon depth, or to the
lagoon shallowness ratio (
HL
−1
).
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