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E.V. Stanev and X. Lu
lower layer flow was associated with tides. These results were used to remove the
tidal currents from the individual measurements and to calculate the mean flow.
The magnitude of the transport was estimated to be 0.81 Sv for the upper layer
and 0.76 Sv for the lower layer (given in Table 5.1 in km 3 /yr). Another important
outcome of this work is that it resulted in a reconstruction of transport patterns along
meridional vertical sections. Three-dimensional (3D) model simulations of Skliris
and Beckers (2009) suggested that the water exchange through the Strait of Gibraltar
was sub-maximal with a mean value of about 1.1 Sv.
5.2.5 Modelling Strait Processes and Outflows
Numerical modelling and observations of exchange flows in straits have recently
shown numerous promising results. Winters and Seim (2000) investigated the effects of interfacial and bottom friction on an exchange flow through a contraction. They used a Smagorinsky-type parameterization based on a local balance
of turbulent kinetic energy, in which dissipation and the buoyancy flux balance
the production of shear. Adding interfacial friction produced shear instabilities
and larger mixing. Using the same numerical model, Hogg et al. (2001) confirmed the results of analytical theories in the sense that fluxes and volume fluxes
depend on three dimensionless parameters: the aspect ratio D/L, the turbulent
Grashof number Gr T = g D 3 /K 2
ν , which compares the effect of buoyancy forces
to the turbulent viscous forces, and the turbulent Prandtl number σ t = K ν /K ρ ,
where K ν and K ρ are the eddy diffusivity coefficients for momentum and mass.
They demonstrated that for geophysical flows Gr T varies in a wide range between 10 7 for the hydraulic limit to 10 2 for the viscous-advective-diffusive limit.
While the flow in the Strait of Gibraltar lies close to the hydraulic limit, the flow
in the Bosporus lies within the transitional region, therefore the exchange flow is
damped by internal mixing, which supports the earlier analytical estimates of Pratt
(1986).
Simulations in the transition zone between the North Sea and the Baltic Sea
have reached a quite good level of realism. The two-way strait exchange with the
Baltic Sea has been addressed with the help of numerical modelling since the 1990s
(Krauss and Brügge 1991; Kleine 1994; Lehmann 1994, 1995; Sayin and Krauss
1996; Andrejev et al. 2002; Meier 2007). From the very beginning the roles of wind
and barotropic pressure differences across the straits have been identified as the major mechanisms controlling the transport in the straits (Krauss and Brügge 1991).
The next important step was the parallel analysis of idealistic and realistic models (Sayin and Krauss 1996) aiming to check the dominating controls (hydraulic or
geostrophic). They proved that cyclonic circulation in the Arkona Basin plays an
important role in controlling the outflow of water to the Bornholm Basin and further to the Baltic Proper. Numerical modelling made clear that the ratio between
transports in the two straits is extremely variable. It can strongly differ for inflow
and outflow, and is very sensitive to large disturbances in the forcing during extreme
events.
E.V. Stanev and X. Lu
lower layer flow was associated with tides. These results were used to remove the
tidal currents from the individual measurements and to calculate the mean flow.
The magnitude of the transport was estimated to be 0.81 Sv for the upper layer
and 0.76 Sv for the lower layer (given in Table 5.1 in km 3 /yr). Another important
outcome of this work is that it resulted in a reconstruction of transport patterns along
meridional vertical sections. Three-dimensional (3D) model simulations of Skliris
and Beckers (2009) suggested that the water exchange through the Strait of Gibraltar
was sub-maximal with a mean value of about 1.1 Sv.
5.2.5 Modelling Strait Processes and Outflows
Numerical modelling and observations of exchange flows in straits have recently
shown numerous promising results. Winters and Seim (2000) investigated the effects of interfacial and bottom friction on an exchange flow through a contraction. They used a Smagorinsky-type parameterization based on a local balance
of turbulent kinetic energy, in which dissipation and the buoyancy flux balance
the production of shear. Adding interfacial friction produced shear instabilities
and larger mixing. Using the same numerical model, Hogg et al. (2001) confirmed the results of analytical theories in the sense that fluxes and volume fluxes
depend on three dimensionless parameters: the aspect ratio D/L, the turbulent
Grashof number Gr T = g D 3 /K 2
ν , which compares the effect of buoyancy forces
to the turbulent viscous forces, and the turbulent Prandtl number σ t = K ν /K ρ ,
where K ν and K ρ are the eddy diffusivity coefficients for momentum and mass.
They demonstrated that for geophysical flows Gr T varies in a wide range between 10 7 for the hydraulic limit to 10 2 for the viscous-advective-diffusive limit.
While the flow in the Strait of Gibraltar lies close to the hydraulic limit, the flow
in the Bosporus lies within the transitional region, therefore the exchange flow is
damped by internal mixing, which supports the earlier analytical estimates of Pratt
(1986).
Simulations in the transition zone between the North Sea and the Baltic Sea
have reached a quite good level of realism. The two-way strait exchange with the
Baltic Sea has been addressed with the help of numerical modelling since the 1990s
(Krauss and Brügge 1991; Kleine 1994; Lehmann 1994, 1995; Sayin and Krauss
1996; Andrejev et al. 2002; Meier 2007). From the very beginning the roles of wind
and barotropic pressure differences across the straits have been identified as the major mechanisms controlling the transport in the straits (Krauss and Brügge 1991).
The next important step was the parallel analysis of idealistic and realistic models (Sayin and Krauss 1996) aiming to check the dominating controls (hydraulic or
geostrophic). They proved that cyclonic circulation in the Arkona Basin plays an
important role in controlling the outflow of water to the Bornholm Basin and further to the Baltic Proper. Numerical modelling made clear that the ratio between
transports in the two straits is extremely variable. It can strongly differ for inflow
and outflow, and is very sensitive to large disturbances in the forcing during extreme
events.