Geoscience Reference
In-Depth Information
TABLE 6.8
Current Speed and Direction vs. Depth in the Ekman Layer
The Angle between the Ekman Surface Current
and the Current at Depth (
z
)
Depth (
z
)
Current Speed
0° (the surface current direction is 45° to the right of
the wind direction in the northern hemisphere)
0
U
E
0.25 ⋅
h
E
45° to the right
0.456 ⋅
U
E
0.5 ⋅
h
E
90° to the right
0.208 ⋅
U
E
0.75 ⋅
h
E
135° to the right
0.095 ⋅
U
E
h
E
180° (opposite to the surface current)
0.043 ⋅
U
E
An opposite situation develops in the
bottom boundary friction layer. Currents
above this layer are assumed to be in geostrophic equilibrium, that is, the pressure
gradient balances the Coriolis force. At a depth
h
E
above the bottom, currents start
feeling the effect of bottom friction and progressively veer to the left of the geo-
strophic current direction and vanish at the bottom. This forms the bottom Ekman
spiral of depth
h
E
. Table 6.9 presents the vertical distribution of currents in the
bottom boundary layer.
For typical turbulent vertical mixing coefficients between 10
−4
and 10
−3
m
2
/sec,
the thickness of the friction layer (
h
E
) has typical values between 4 and 13 m at middle
latitudes. The comparison of lagoon depths with
h
E
provides information on the extent
to which currents at various depths will be deflected by winds and surface currents.
This thickness is also important for the evaluation of the vertical grid step for 3D
models, which should not exceed 0.3-0.5 of
h
E
.
It should be noted once more that wind-induced Ekman currents (Equations
(6.39)-(6.40)), which are directed at 45
°
to the right of the wind direction, only
TABLE 6.9
Current Speed and Direction in the Bottom Boundary Friction
(or Ekman) Layer
Elevation over
the Bottom
The Angle between the Ekman Current and the
Geostrophic Deep Water Velocity V
0
Current Speed
45
(the limit of current rotation to the left
from the undisturbed velocity)
°
0
0
0.001
⋅
h
E
44.9
°
to the left
0.004
⋅
V
0
0.01
⋅
h
E
36.5
°
to the left
0.380
⋅
V
0
0.25
⋅
h
E
25.5
°
to the left
0.750
⋅
V
0
0.5
⋅
h
E
11.7
°
to the left
1.021
⋅
V
0
0.75
⋅
h
E
3.6
°
to the left
1.069
⋅
V
0
h
E
0.0
°
1.043
⋅
V
0
1.25
⋅
h
E
0.8
°
to the right
1.014
⋅
V
0
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