Modeling Concepts - Coastal Lagoons: Ecosystem Processes and Modeling for Sustainable Use and Development - page 278

Results of field measurements show that the average wave length can exceed five
times the depth in shallow areas. The above relationship can then be further simpli-
fied for practical use, becoming similar to that for deep water:

2

g ( ⋅ τ )

avg

2

λ = =⋅ 156 . ( τ ) (6.55)

avg avg

2 π

2 π ⋅ H

avg

since 1/5.

The information about wind waves is important for estimating the depth of the
upper mixing layer, where high turbulence coefficients are expected in the presence
of waves. A reasonable estimation for the depth of this mixing is about one quarter
of wave length. Actually, a wave becomes a shallow water wave when the water
depth is less than half a wave length.
Suspension of bottom material by wind waves is another important parameter
that can affect the water quality in a lagoon. Those areas affected by wave suspension
under constant wind conditions can be delimited 31,32 on the basis of the simple
criterion that waves are able to suspend fine bottom material if the water depth is
less than one quarter of the wave length. 33
We emphasize that all the relations developed in this section apply only to regular
waves, using wave length as a key parameter. But, in reality, wave motion is highly
irregular and various waves can be present at the same time. In this case, one should
use instead the maximum wave heights and lengths, with low probability of occur-
rence (e.g., 1 or 0.1%). Relations for average waves can then be reformulated from
known relations between maximum waves and average waves. These can be found
in most wave calculation manuals. 29

(tanh ) is very close to 1 up to H / λ =

λ

6.3.3.7 Coriolis Force Action

The Coriolis force will affect currents in lagoons as in other water bodies. 4b The
Coriolis force results from the rotation of the Earth, causing currents in the northern
(southern) hemisphere to be deflected to the right (left). In stratified or estuarine
lagoons, the effect is to move less-dense water to the right (left) looking seaward in
the northern (southern) hemisphere. The interface between waters of different den-
sities tends to be sloped as the pressure gradient force reaches equilibrium with the
Coriolis force to achieve a geostrophic balance. 4c
The Coriolis force starts to become significant for the dynamics of a lagoon when
the width is greater than five , being the radius of inertial circle, and dominates
when the width is greater than 20 . 4c,34,35 In other words, the Coriolis force is con-
sidered important for a low Rossby number

r c r c

r c

R ϕ , < 0.1 4c,36 where

r

u
f

r = , and R =

c

(6.56)

c ϕ

L

width

and f is the Coriolis parameter (Equation (6.38)), u is the mean water velocity (m s −1 ),
and L width is the characteristic lagoon width scale. For example, for the Vistula Lagoon,