92
3 Basics of Nonhydrostatic Modelling
A z =
ν 1
(1 + 5 Ri) 2 + ν o
(3.87)
with ν 1 = 5 × 10
−3 m
2
/s and ν o = 5 × 10
−4 m
2
/s. Eddy diffusivity is parameterised
as:
K z =
A z
(1 + 5 Ri)
+ k o
(3.88)
where k o is set to 1 × 10
−5 m
2
/s. For the calculation of the Richardson number it
is useful to recall that, with use of the Arakawa C-grid, eddy viscosity/diffusivity
values are determined at scalar grid points which are centred between velocity grid
points. To this end, the Richardson number is derived from:
Ri
n
i,k = −2Δz
g
ρ o
(ρ
n
i−1,k − ρ
n
i+1,k )
(u t − u b ) 2
(3.89)
where
u t = 0.5(u
n
i−1,k + u
n
i−1,k−1 ) and u b = 0.5(u
n
i+1,k + u
n
i+1,k−1 )
There is no need to account for convective mixing in this exercise.
3.24.5 Results
The tidal volume flux is about 1.4 m
3 /s per unit width of the estuary for all forcing cases. The choice of η river = 1 cm leads to an R/V ratio of 0.01 and therefore
corresponds to a vertically-mixed estuary (Fig. 3.54, top panel). The brackish water
zone does not reach far into the estuary and the transition zone between freshwater
and seawater occupies only a width of 10–15 km. The lack of density stratification
provides a means of oxygen supply (also called ventilation) via surface fluxes over
the entire length of the estuary.
In contrast, an increased value of η river = 30 cm, corresponding to an R/V ratio of
1.9, creates a salt-wedge estuary characterised by a freshwater surface layer extending the entire length of the estuary and spilling into the ambient sea (Fig. 3.54,
bottom panel). In this situation, the brackish water zone is located closer to the estuary mouth, which enables relatively rapid ventilation of the bottom layer through
the baroclinic return flow despite the existence of strong density stratification.
Forcing with η river = 5 cm gives an R/V ratio of 0.16 and leads to the establishment of a highly stratified estuary (Fig. 3.55, top panel). Saltier bottom water
is entrained into the surface outflow. Owing to turbulence reduction via density
stratification, bottom layers attain an age of 13–14 days (Fig. 3.55, bottom panel),
which is an indication that oxygen depletion might occur in this zone. Discharge of
pollutants should be avoided in such regions of little ventilation.
3 Basics of Nonhydrostatic Modelling
A z =
ν 1
(1 + 5 Ri) 2 + ν o
(3.87)
with ν 1 = 5 × 10
−3 m
2
/s and ν o = 5 × 10
−4 m
2
/s. Eddy diffusivity is parameterised
as:
K z =
A z
(1 + 5 Ri)
+ k o
(3.88)
where k o is set to 1 × 10
−5 m
2
/s. For the calculation of the Richardson number it
is useful to recall that, with use of the Arakawa C-grid, eddy viscosity/diffusivity
values are determined at scalar grid points which are centred between velocity grid
points. To this end, the Richardson number is derived from:
Ri
n
i,k = −2Δz
g
ρ o
(ρ
n
i−1,k − ρ
n
i+1,k )
(u t − u b ) 2
(3.89)
where
u t = 0.5(u
n
i−1,k + u
n
i−1,k−1 ) and u b = 0.5(u
n
i+1,k + u
n
i+1,k−1 )
There is no need to account for convective mixing in this exercise.
3.24.5 Results
The tidal volume flux is about 1.4 m
3 /s per unit width of the estuary for all forcing cases. The choice of η river = 1 cm leads to an R/V ratio of 0.01 and therefore
corresponds to a vertically-mixed estuary (Fig. 3.54, top panel). The brackish water
zone does not reach far into the estuary and the transition zone between freshwater
and seawater occupies only a width of 10–15 km. The lack of density stratification
provides a means of oxygen supply (also called ventilation) via surface fluxes over
the entire length of the estuary.
In contrast, an increased value of η river = 30 cm, corresponding to an R/V ratio of
1.9, creates a salt-wedge estuary characterised by a freshwater surface layer extending the entire length of the estuary and spilling into the ambient sea (Fig. 3.54,
bottom panel). In this situation, the brackish water zone is located closer to the estuary mouth, which enables relatively rapid ventilation of the bottom layer through
the baroclinic return flow despite the existence of strong density stratification.
Forcing with η river = 5 cm gives an R/V ratio of 0.16 and leads to the establishment of a highly stratified estuary (Fig. 3.55, top panel). Saltier bottom water
is entrained into the surface outflow. Owing to turbulence reduction via density
stratification, bottom layers attain an age of 13–14 days (Fig. 3.55, bottom panel),
which is an indication that oxygen depletion might occur in this zone. Discharge of
pollutants should be avoided in such regions of little ventilation.