Modeling Concepts - Coastal Lagoons: Ecosystem Processes and Modeling for Sustainable Use and Development - page 277

the water surface relaxes from its previous wind-induced inclined position and starts
to oscillate freely.
Using Equation (6.47) and Equation (6.51) for the Vistula Lagoon, a 10 m/s wind
along the longitudinal axis will generate a corresponding level deviation of 25 cm in
amplitude. Assuming this wind stops suddenly, the maximum nodal current associated
with the pure seiche can be estimated to be 20 cm/s, according to Equation (6.51).
In contrast to a deep lake, it is rather difficult to observe clear seiches in shallow
lagoons. Bottom friction tends to quickly damp the seiche oscillation before some
periods of seiche oscillation are realized.

6.3.3.6 Wind Waves

Wind waves in lagoons are controlled by the barrier islands, the depth, and the limited
fetch. As they progress from the sea into the lagoon through its entrance, sea waves
are significantly deformed. High waves are damped due to bottom friction and wave
spectra adjust to local bathymetry in the lagoon area adjacent to the barrier islands.
This sudden constriction prevents sea waves from progressing deep inside the lagoon.
The destruction of oceanic waves at barrier island boundaries results in a wave-
pumping effect into the lagoon, which may be the main flushing mechanism in some
coral reef lagoons. 15a
Therefore, lagoon surface waves are generated mainly by local winds, and wave
parameters quickly reach their upper limits for increasing wind speeds, wind dura-
tion, and fetch. The shallowness of the lagoon also increases the wave sharpness,
and the ratio between the wave height and the wavelength can reach , as, for example,
in the Vistula Lagoon. 25 There are no residual long waves (or swell) in a lagoon after
the wind relaxation. Much like seiches, they are rapidly damped out by bottom friction.
There are many empirical, semiempirical, or spectral methods for wind wave
simulation in shallow waters. 15,26-29 These take into consideration all stages of wave
development, wave refraction with depth, coastal configurations, and transformation
into the surf zone. 28 A simple formula for the upper limits of the average wave height
( h avg [m]) and the average wave period (

1
7

τ avg [s]) for a depth H [m] and a wind speed

W a [m s −1 ] is 30

25 45

h = 0 062 . ⋅ W ⋅ H

(6.52)

avg a

12

τ avg =⋅ 146 . H

(6.53)

Although Equations (6.52) and (6.53) do not consider the wind fetch and only
provide the upper limit of the average wave parameters at the local depth, they can
be used in shallow waters where waves rapidly become depth limited. The relation
between average wave length ( λ avg ) and average wave period ( τ avg ) in shallow waters

can be extracted from the following implicit relationship: 30

2

g ⋅ ( τ )

2 π

λ

⋅ H

avg

λ = tanh (6.54)

avg

2 π

avg