Modeling Concepts - Coastal Lagoons: Ecosystem Processes and Modeling for Sustainable Use and Development - page 272

TABLE 6.10
Friction Layer Current Adjustment Times (h) for the Vistula Lagoon
Using Equations (6.41) and (6.42)

Wind Velocity [m s − 1 ]

Depth of Turbulent Layer, m

5 10 15

2 2.8 h 2.0 h 1.6 h

3 3.5 h 2.5 h 2.0 h

5 4.5 h 3.2 h 2.6 h

6.3.3.3.2 Equilibrium Current Structure
Currents in a lagoon will adjust to winds in a time given by Equation (6.41) if the
size of the lagoon is unlimited. In real cases, compensatory currents are set up
through the continuity equation because of the enclosed nature of the lagoon.
In lagoons, as in any other closed water reservoirs, water levels under the influence
of wind stress will rise at the downwind side of the lagoon and decrease at the upwind
side. This hydraulic head sets up a longitudinal pressure gradient that modifies the current
structure in the lagoon. Furthermore, when the depths near the sides of the lagoon are
shallower, wind-driven coastal currents are set up in the direction of the wind, and an
upwind return flow must be expected in the deeper central parts through continuity.
This return flow can occur at a depth when the lagoon is slightly stratified in the vertical
(e.g., in the presence of a thermocline and/or a halocline). See Chapter 9, Case
Study 9.2, for an example of equilibrium current structure.
As a result, a rather complicated current pattern arises, which is not always possible
to describe without a numerical model that takes into account the morphological
characteristics, wind conditions, density stratification, and other parameters in the
lagoon.

6.3.3.3.3 Gradient Flow Development
When the wind or the pressure gradient changes suddenly, the adjustment process
of water fluxes under the influence of the Earth's rotation to its new equilibrium is
accompanied by oscillations about this new equilibrium state. These oscillations,
which are eventually damped out, are called inertial oscillations. They have a char-
acteristic period called the inertial period, which depends on latitude as 18

2 π 2 π

τ == ⋅ ⋅ (6.43)

inert

f 2 Ω sin () ϕ

For example, for the Vistula Lagoon (55 ° latitude), the inertial period is exactly

14.7 h, whereas for latitudes near 30 , this period is around 24 h. In the latter case,

provisions must be made during the data analysis to distinguish between inertial
oscillations and diurnal tidal oscillations when present. The rate at which inertial
oscillations are damped depends on their period. For example, 18 it can be shown
that, for a liquid on a rotating Earth, the time scale of the current adjustment to a

°