2 Topography, Hydrography, Circulation and Modelling of the Baltic Sea
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fast processes with the time scale T of only some hours and in so-called inertial
oscillations.
Given the small size of the Baltic Sea, it is acceptable to assume the Coriolis
parameter to be constant. Its frequently used value for the particular geographical
location is f = 1.26 × 10 −4 1/s and corresponds to φ = 60 ◦ N. The use of this value
is particularly suitable for the description of the dynamics in the Gulf of Finland
(Chap. 6). A further simplification is to consider motions on a local plane projection, which rotates around the local vertical axis (so-called f -plane approximation).
The beta-plane approximation, in which the Coriolis parameter varies in the north–
south direction, is infrequently used in the Baltic Sea context because of its small
size. The equations would be much more complicated in spherical coordinates. The
boundary conditions are rather simple in the Baltic Sea. Nearly everywhere there is
a passive solid boundary. Inflow of fresh water takes place in the river mouths, and
a dynamic inflow-outflow system exists in the Danish Straits. The water exchange
in the Danish Straits has a dominant role for the circulation of deep water and indirectly for the general circulation of the Baltic Sea through regulating the general
sea level elevation.
2.3.2 Barotropic and Baroclinic Flows and Rossby Radii
The main dimensionless numbers in the Baltic Sea dynamics are the (external
or barotropic) Rossby number Ro = U/f L, the Froude number Fr = U/(Lg) 1/2
and the (vertical and horizontal) Ekman numbers Ek v = A v /(U H ) and Ek H =
A H /(U L). They describe the significance of, respectively, the Coriolis acceleration,
gravity acceleration, vertical friction and horizontal friction (see, e.g., Leppäranta
and Myrberg 2009, for details).
There are two basic types of large-scale flow fields in the marine environment:
barotropic and baroclinic circulation. The motions are barotropic, for example,
when the density of sea water is constant. More generally, in the barotropic motions isopycnals (isolines of density) are parallel to isobars. In the baroclinic case
isopycnals and isobars are inclined with respect to each other (the inclination angle
usually varies with depth). Consequently, the pressure gradient and the resulting currents vary also in depth. The baroclinic and barotropic components of motions can
be formally separated in a linear framework and are usually called baroclinic and
barotropic modes. In practice, in homogeneous waters the circulation is barotropic
and in stratified waters the baroclinic circulation needs to be considered.
A number of case studies based on current measurements have shown that the
response of the Baltic Sea is baroclinic to wind events with a duration of more than
50 hours, whereas in short-term wind events, of duration 10–40 hours, the response
is barotropic. The response to wind events shorter than 10 hours quickly vanishes.
Differently from the open ocean, where the energy of the two modes is comparable,
the energy in the baroclinic mode exceeds that of the barotropic mode by one order
of magnitude in the Baltic Sea. Therefore, the Baltic Sea cannot be treated as a
homogeneous water body.
43
fast processes with the time scale T of only some hours and in so-called inertial
oscillations.
Given the small size of the Baltic Sea, it is acceptable to assume the Coriolis
parameter to be constant. Its frequently used value for the particular geographical
location is f = 1.26 × 10 −4 1/s and corresponds to φ = 60 ◦ N. The use of this value
is particularly suitable for the description of the dynamics in the Gulf of Finland
(Chap. 6). A further simplification is to consider motions on a local plane projection, which rotates around the local vertical axis (so-called f -plane approximation).
The beta-plane approximation, in which the Coriolis parameter varies in the north–
south direction, is infrequently used in the Baltic Sea context because of its small
size. The equations would be much more complicated in spherical coordinates. The
boundary conditions are rather simple in the Baltic Sea. Nearly everywhere there is
a passive solid boundary. Inflow of fresh water takes place in the river mouths, and
a dynamic inflow-outflow system exists in the Danish Straits. The water exchange
in the Danish Straits has a dominant role for the circulation of deep water and indirectly for the general circulation of the Baltic Sea through regulating the general
sea level elevation.
2.3.2 Barotropic and Baroclinic Flows and Rossby Radii
The main dimensionless numbers in the Baltic Sea dynamics are the (external
or barotropic) Rossby number Ro = U/f L, the Froude number Fr = U/(Lg) 1/2
and the (vertical and horizontal) Ekman numbers Ek v = A v /(U H ) and Ek H =
A H /(U L). They describe the significance of, respectively, the Coriolis acceleration,
gravity acceleration, vertical friction and horizontal friction (see, e.g., Leppäranta
and Myrberg 2009, for details).
There are two basic types of large-scale flow fields in the marine environment:
barotropic and baroclinic circulation. The motions are barotropic, for example,
when the density of sea water is constant. More generally, in the barotropic motions isopycnals (isolines of density) are parallel to isobars. In the baroclinic case
isopycnals and isobars are inclined with respect to each other (the inclination angle
usually varies with depth). Consequently, the pressure gradient and the resulting currents vary also in depth. The baroclinic and barotropic components of motions can
be formally separated in a linear framework and are usually called baroclinic and
barotropic modes. In practice, in homogeneous waters the circulation is barotropic
and in stratified waters the baroclinic circulation needs to be considered.
A number of case studies based on current measurements have shown that the
response of the Baltic Sea is baroclinic to wind events with a duration of more than
50 hours, whereas in short-term wind events, of duration 10–40 hours, the response
is barotropic. The response to wind events shorter than 10 hours quickly vanishes.
Differently from the open ocean, where the energy of the two modes is comparable,
the energy in the baroclinic mode exceeds that of the barotropic mode by one order
of magnitude in the Baltic Sea. Therefore, the Baltic Sea cannot be treated as a
homogeneous water body.