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new pressure gradient is t >> 1/ f . A good approximation is t ~ 3 to 5 inertial periods.
A minimal estimate for the time of current adjustment can be half of a one-node
seiche period (see Section 6.3.3.5) because level inclinations during a storm surge
that generates a pressure gradient do not develop faster than this seiche period.
When the depth of a lagoon is deeper than h E , a distinction must be made between
two time scales of current adjustment in the upper layer. These time scales correspond
to (1) Ekman adaptation due to the influence of the Coriolis force and internal
frictional stresses in the upper Ekman layer, and (2) inertial motion due to the
influence of the Coriolis force and pressure gradients. These two factors act indepen-
dently on the currents. Their combination may produce one of the following results:
A rapid formation (period less than the inertial period) of variable currents
subjected to inertial oscillations adjusting to a constant Ekman solution
over time scales t >> 1/ f
A rapid dampening of inertial oscillations leading to Ekman currents
within an Ekman adjustment time scale
A current adjustment time scale that combines the effects of both inertial accel-
eration and vertical turbulent diffusion (friction), and which gives a minimum esti-
mate of the time during which 75% of the current changes following a wind change,
is 19
05
.
4
105 05
.
h
2
10505
π
T
=
=⋅
τ
+
.
E
(6.44)
inert
H
4
f
+ ⋅
.
(.
h
/)
H
E
where h E (m) is the Ekman depth (Equation (6.40)) and H is the depth (m) where
the turbulence coefficient becomes zero, or the lagoon depth.
For example, the result of using both Equation (6.38) and Equation (6.44) for
the Vistula Lagoon (Table 6.11) shows the current adjustment time corresponds
closely to estimates in Table 6.10. Therefore, the current adjustment time in the
TABLE 6.11
Friction Layer Current Adjustment Times ( h ) for the Vistula Lagoon
Using Equations (6.40), (6.43), and (6.44)
Wind Velocity, m s 1
Depth of Turbulent Layer, m
5
10
15
2
3.02 h
1.54 h
1.02 h
3
4.4 h
2.28 h
1.54 h
5
6.81 h
3.72 h
2.53 h
 
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