Modeling Concepts - Coastal Lagoons: Ecosystem Processes and Modeling for Sustainable Use and Development - page 275

For example, let us consider two different water basins, the Vistula Lagoon
(91 km long, 2.7 m average depth, and HL −1 10 −5 ) and Lake Constance

(Austria/Germany/Switzerland; 65 km long, 120 m average depth, and HL −1

= 2.96 ⋅

=

184 10 −5 Pa corresponding to a wind speed of 15 m s −1 .

The maximum wind-induced water level set-up (

⋅ 10 −5 ), and a wind stress of 3.5 ⋅

h ) will be about 1.2 m for the Vistula
Lagoon (which actually does occur during extreme wind surges) and only 0.02 m for
Lake Constance.
Away from shore, the geostrophic current solution may be used for estimation
of maximum currents or flows perpendicular to the line of wind-induced level set-up:

∆

d
dx

ς

Ugf = (/ ) ⋅ (6.48)

G

/ dx is the surface inclination
set up by the wind. The equation, however, leads to overestimation of speed due to
the absence of bottom friction in the geostrophic solution. For example, the geo-
strophic current estimated for the Vistula Lagoon is about 1 m s −1 , whereas for Lake
Constance, which is deep, it gives a more realistic value of 0.03 m s −1 .
The duration of wind action is of specific importance for the lagoon water
dynamics as the wind stress (1) directly generates currents when the wind starts to
blow and (2) establishes a level set-up that sustains a compensation near bottom
flow within the time scale of long gravity wave propagation. For example, for the
Vistula Lagoon (91 km

where g ≈ 9.81 m/s −2 , f is the Coriolis parameter, and d ς

9 km), this time scale is on the order of 5 h for alongshore
winds and 0.5 to 1 h for transversal winds. In the Darss-Zingst Bodden Chain Lagoon
(55 km

×

3 km), and it will have a
shorter alongshore length scale. The time for appearance of recurrent bottom flows
in this case will be shorter: 0.5-1 h for alongshore winds and 12 to 30 min for
transversal winds.

× 3.6 km), there are several subbasins (3 to 10 ×

6.3.3.5 Seiches or Natural Oscillations of a Lagoon Basin

One more time scale that can be estimated for a lagoon is its natural (or eigen or
fundamental) period of oscillation. It is the period of the free oscillation, which
develops in the lagoon basin when, for example, the wind suddenly stops blowing.
In the open ocean, inertial oscillations waves will develop. However, in confined
areas such as a lagoon basin, these free waves, or inertial oscillations, combine to
form standing waves whose characteristics depend on the size of the lagoon. These
waves are called “seiches” and represent the eigenmodes of the particular basin
under consideration. The only difference between these waves and their free open
ocean counterparts is that their frequencies are determined by the size and the
geometry of the basin. 22 Once the wind stops blowing, and in the absence of other
forcing functions, these waves will control the currents in the lagoon.
Generally, this eigenvalue problem must be solved numerically for real lagoon
basins. However, a preliminary estimate of the natural period of oscillation can be
obtained for a constant-depth rectangular basin. 23 Equation (6.49) provides an