Modeling Concepts - Coastal Lagoons: Ecosystem Processes and Modeling for Sustainable Use and Development - page 271

characterize the initial phase of current adaptation. Once the pressure gradient is
established, currents will adjust to a different equilibrium pattern under the influ-
ence of Coriolis acceleration, friction, and pressure gradients. In other words,
pressure gradient currents will be added to Ekman currents.

6.3.3.3 Time Scales of Current Adaptation

In the absence of tides at the entrance, wind stress is the main force that generates
or changes currents in a lagoon. Currents set up within a certain time interval after
the wind starts to act on the surface because of the water mass inertia. In order to
understand the time scale of the lagoon response to wind stress, it is necessary to
estimate the current adjustment time scales. This time scale may be useful in
determining the model simulation time step. For example, when studying currents
generated by constant winds, it is desirable to have some 20 to 30 computational
time steps during the adaptation time. For longer simulations under real wind
conditions, at least 5 to 10 time steps are required to resolve the adjustment time.

6.3.3.3.1 Wind-Driven Current
Once the wind stress starts acting on the surface of a lagoon, the upper layer currents
respond with some lag because the Coriolis force does not act instantaneously. Kundu 17
showed that the influence of the Coriolis force becomes significant after t > 0.25/ f .
For the Vistula Lagoon (55 latitude), this adjustment time is about 30-40 min. As

mentioned in Section 6.3.3.2, the current adjustment is a progressive process during
which momentum is transmitted in the vertical direction by turbulence in the upper
layer. The period of the current adjustment (the 63% development) under constant
wind influence can be estimated as follows 16

°

2
2

⋅
⋅⋅

H
fK z

T = (6.41)

where H is the depth (m) at which the vertical mixing turbulence coefficient K z may
be assumed to be zero or is the average depth of the lagoon, assuming it is completely
mixed.
Since the turbulent coefficient is not known a priori, it may be evaluated as
follows:

γ ⋅ ⋅

⋅⋅

Wh
k

K =

a

(6.42)

z

4 ρ

10 −3 kg m −3 , W a is wind speed (m s −1 ), h is the depth (m) at which
the turbulence coefficient may be assumed to be zero,

where γ = 3.25 ⋅

is water density (kg m −3 ),
k is the wind friction coefficient (~0.0125). When the mixing depth H is not known
a priori, it may be replaced by the lagoon depth.
The examples of current adjustment time for the Vistula Lagoon (

ρ

ϕ = 55 ° ,

H max = 2.75 m), calculated by Equation (6.41) and Equation (6.42), are

presented in Table 6.10.

5 m, H avg =