4 Studying the Baltic Sea Circulation with Eulerian Tracers
111
with
P = ν t
∂u
∂z
2
+
∂v
∂z
2
,
G= −
ν t
σ t
N
2 ,
(4.31)
N
2
= −
g
ρ 0
∂ρ
∂z
,
ν t = c μ
k 2
ε
.
(4.32)
Here, N denotes the Brunt–Väisälä frequency. The constants c μ , c ε1 , c ε2 , c ε3 , σ k and
σ ε are given in Table 4.1 according to Rodi (1980). The turbulence model gives no
information about the turbulent Prandtl number σ t . We used an empirical formula
following (Blanke and Delecluse 1993). Both, the turbulent friction coefficient ν t
and σ t close in (4.9)–(4.12) the system of partial differential equations for temperature, salinity, density, pressure and current velocity (4.1)–(4.13).
4.2.1.7 Bottom Friction
Unresolved bottom roughness is parameterized according to Cox (1984) using a
second order law for bottom friction (4.18):
τ
B
= ρ 0 c B
u 2
b + v 2
b ·
− −−−→
(u b , v b )
(4.33)
with u b = u z=−H , v b = v z=−H . As during some major inflows, like the one in January 1993, the accumulated transport through the Danish Straits into the Baltic Sea
is known from observations (e.g., Matthäus et al. 1993; Jakobsen 1995), the bottom friction coefficient c B can be determined comparing modelled and observed
transports. Provided that the critical strait cross sections are correct the bottom drag
coefficient is estimated to be c B = 0.5 × 10 −3 .
4.2.2 Model Setup
4.2.2.1 Introduction
Ocean circulation models like the RCO model integrate the primitive equations forward in time (cf. Chap. 3). Output fields are water temperature, salinity, currents,
sea level, and sea ice parameters like sea ice concentration and sea ice thickness
(Mårtensson et al. 2012). In the applications presented below, the RCO model was
used with a horizontal resolution of 3.7 km (2 nautical miles) and with equally thick,
vertical levels with layer thicknesses of 3 m (Höglund and Meier 2012). For the integration of the primitive equations the following information is needed:
1. water depth at all model grid points,
2. initial conditions of 3D fields of water temperature and salinity,
3. water temperature and salinity profiles at the lateral boundary that are prescribed
here in the case of inflow into the model domain,
4. records of sea level elevations at the lateral boundary,
111
with
P = ν t
∂u
∂z
2
+
∂v
∂z
2
,
G= −
ν t
σ t
N
2 ,
(4.31)
N
2
= −
g
ρ 0
∂ρ
∂z
,
ν t = c μ
k 2
ε
.
(4.32)
Here, N denotes the Brunt–Väisälä frequency. The constants c μ , c ε1 , c ε2 , c ε3 , σ k and
σ ε are given in Table 4.1 according to Rodi (1980). The turbulence model gives no
information about the turbulent Prandtl number σ t . We used an empirical formula
following (Blanke and Delecluse 1993). Both, the turbulent friction coefficient ν t
and σ t close in (4.9)–(4.12) the system of partial differential equations for temperature, salinity, density, pressure and current velocity (4.1)–(4.13).
4.2.1.7 Bottom Friction
Unresolved bottom roughness is parameterized according to Cox (1984) using a
second order law for bottom friction (4.18):
τ
B
= ρ 0 c B
u 2
b + v 2
b ·
− −−−→
(u b , v b )
(4.33)
with u b = u z=−H , v b = v z=−H . As during some major inflows, like the one in January 1993, the accumulated transport through the Danish Straits into the Baltic Sea
is known from observations (e.g., Matthäus et al. 1993; Jakobsen 1995), the bottom friction coefficient c B can be determined comparing modelled and observed
transports. Provided that the critical strait cross sections are correct the bottom drag
coefficient is estimated to be c B = 0.5 × 10 −3 .
4.2.2 Model Setup
4.2.2.1 Introduction
Ocean circulation models like the RCO model integrate the primitive equations forward in time (cf. Chap. 3). Output fields are water temperature, salinity, currents,
sea level, and sea ice parameters like sea ice concentration and sea ice thickness
(Mårtensson et al. 2012). In the applications presented below, the RCO model was
used with a horizontal resolution of 3.7 km (2 nautical miles) and with equally thick,
vertical levels with layer thicknesses of 3 m (Höglund and Meier 2012). For the integration of the primitive equations the following information is needed:
1. water depth at all model grid points,
2. initial conditions of 3D fields of water temperature and salinity,
3. water temperature and salinity profiles at the lateral boundary that are prescribed
here in the case of inflow into the model domain,
4. records of sea level elevations at the lateral boundary,