94
3 Basics of Nonhydrostatic Modelling
flushing times based on an e-folding timescale and to compare the results with the
predicted age distribution.
3.25 Exercise 15: Inverse Estuaries
3.25.1 Aim
The aim of this exercise is to explore the circulation of inverse estuaries being caused
by a net evaporative loss of water. Since this loss of water creates a pressure gradient
directed into the estuary, the question is: What drives the outflow (see Fig. 3.50, right
panel)?
3.25.2 Task Description
The model configuration is identical to that of the previous exercise with a few
modifications outlined in the following. The estuary is closed on the left side and,
for simplicity, tidal forcing is not included. An evaporation rate of 5 cm per day
(which is fairly high) is prescribed along the estuary up to x = 110 km. This rate
is decreased linearly to zero value over the the adjacent 20 km across the mouth of
the estuary. Evaporation over the ambient sea is set to zero. This design is purely
academic and its sole purpose is to create a salinity distribution along the estuary
that resembles that observed in real inverse estuaries.
Evaporative water loss appears in the vertically integrated continuity equation as:
∂η
∂t
= −
1
b
∂(b h u)
∂ x
− E
(3.90)
where E is the evaporation rate. Owing to a loss of freshwater, the salt concentration
(i.e. salinity) in the water column increases. On the basis of conservation of volume
and salt mass, this salinity change can be calculated from:
∂ S
∂t
= S
E
h
(3.91)
where h is the depth over which this salinity increase becomes distributed. We use
a linearised equation of state expressed in terms of density anomaly ρ
:
ρ
= ρ o β(S − S o )
(3.92)
where temperature effects are ignored, the salinity coefficient β is taken as 8×10
−4 ,
and S o is a reference salinity, taken as 35 g/kg. Accordingly, Eq. (3.91) can be converted into a density change according to:
3 Basics of Nonhydrostatic Modelling
flushing times based on an e-folding timescale and to compare the results with the
predicted age distribution.
3.25 Exercise 15: Inverse Estuaries
3.25.1 Aim
The aim of this exercise is to explore the circulation of inverse estuaries being caused
by a net evaporative loss of water. Since this loss of water creates a pressure gradient
directed into the estuary, the question is: What drives the outflow (see Fig. 3.50, right
panel)?
3.25.2 Task Description
The model configuration is identical to that of the previous exercise with a few
modifications outlined in the following. The estuary is closed on the left side and,
for simplicity, tidal forcing is not included. An evaporation rate of 5 cm per day
(which is fairly high) is prescribed along the estuary up to x = 110 km. This rate
is decreased linearly to zero value over the the adjacent 20 km across the mouth of
the estuary. Evaporation over the ambient sea is set to zero. This design is purely
academic and its sole purpose is to create a salinity distribution along the estuary
that resembles that observed in real inverse estuaries.
Evaporative water loss appears in the vertically integrated continuity equation as:
∂η
∂t
= −
1
b
∂(b h u)
∂ x
− E
(3.90)
where E is the evaporation rate. Owing to a loss of freshwater, the salt concentration
(i.e. salinity) in the water column increases. On the basis of conservation of volume
and salt mass, this salinity change can be calculated from:
∂ S
∂t
= S
E
h
(3.91)
where h is the depth over which this salinity increase becomes distributed. We use
a linearised equation of state expressed in terms of density anomaly ρ
:
ρ
= ρ o β(S − S o )
(3.92)
where temperature effects are ignored, the salinity coefficient β is taken as 8×10
−4 ,
and S o is a reference salinity, taken as 35 g/kg. Accordingly, Eq. (3.91) can be converted into a density change according to: