44
K. Myrberg and A. Lehmann
Many properties of geophysical flows are governed by the Rossby radius (of
deformation). This fundamental length scale of planetary-scale flows for a particular
mode of motion is, in essence, the ratio of the phase speed of the waves associated
with this mode to the Coriolis parameter. As the barotropic mode is associated with
long shallow-water 5 waves (which propagate very fast) and the baroclinic mode(s)
with internal wave(s) (that are much slower, see Sect. 3.3.1.1 in Chap. 3 for more
detailed information), the relevant wave speeds and the resulting Rossby radii are
drastically different.
The baroclinic (also called internal) Rossby radius R 1 of deformation (understood here as the first eigenvalue of the baroclinic Rossby radius) is one of the
fundamental length scales in geophysical fluid dynamics that inter alia defines to
a large extent the typical scale of mesoscale dynamic features such as (synoptic)
eddies, fronts and local jets. The above-discussed specific features of the Baltic Sea,
especially the strong stratification, have substantial implications on its dynamics already at the level of this fundamental scale. Owing to strong gradients, R 1 is very
small in the Baltic. Its typical values are between 3 and 10 km in the open Baltic
(Fennel et al. 1991). Differently from the barotropic Rossby radius, the baroclinic
Rossby radius depends not only on changes in local stratification conditions but also
on changes in longer time scales. Osi´ nski et al. (2010) found that the major inflow
in the winter 2002/2003 increased the value of R 1 in the southern Baltic from about
4 km (during the pre-inflow period) to more than 9 km.
Such spatial scales given by the Rossby radius for the open Baltic Sea can easily
be resolved by contemporary numerical models. Namely, to properly describe the
small-scale eddies, fronts and jets, it has been suggested that in numerical modelling
the grid size should be 1/2–1/3 of R 1 (Drijfhout 1989; Lindow 1997). The situation is more complicated in shallow and strongly stratified sub-basins of the Baltic
Sea such as the Gulf of Finland (see Chap. 6) or the south-western Baltic Sea, at
which most of the efforts of the developed technology for the preventive management of pollution have been targeted. In these basins the requirements for numerical
modelling are even higher than for the open Baltic Sea. Based on a dataset of about
1800 observations, the baroclinic Rossby radius was estimated to be on average in
the range of only 2–4 km in the Gulf of Finland (Alenius et al. 2003) whereas it
has also extensive spatial and temporal variability. Similar and even smaller values, down to 1 km, have been recently obtained for the south-western part of the
Baltic Sea (Osi´ nski et al. 2010). In shallow coastal regions and in the eastern Gulf
of Finland R 1 is sometimes as small as about 500 m (Nekrasov 1999; Nekrasov and
Lebedeva 2002). In such a case the numerical models need very high resolution,
down to about 0.25 nautical miles (Andrejev et al. 2010).
The meteorological conditions govern to a large extent the changes in the flow
field, and, not surprisingly, there are similarities in the spectra of wind and current
velocities. Especially in the surface layer the variability of the currents is strongly
5 The term ‘shallow water’ is used here and on some occasions below to distinguish the situation
where the typical length of waves of a particular class (Rossby waves, internal waves, surface
waves, etc.) considerably exceeds the water depth.
K. Myrberg and A. Lehmann
Many properties of geophysical flows are governed by the Rossby radius (of
deformation). This fundamental length scale of planetary-scale flows for a particular
mode of motion is, in essence, the ratio of the phase speed of the waves associated
with this mode to the Coriolis parameter. As the barotropic mode is associated with
long shallow-water 5 waves (which propagate very fast) and the baroclinic mode(s)
with internal wave(s) (that are much slower, see Sect. 3.3.1.1 in Chap. 3 for more
detailed information), the relevant wave speeds and the resulting Rossby radii are
drastically different.
The baroclinic (also called internal) Rossby radius R 1 of deformation (understood here as the first eigenvalue of the baroclinic Rossby radius) is one of the
fundamental length scales in geophysical fluid dynamics that inter alia defines to
a large extent the typical scale of mesoscale dynamic features such as (synoptic)
eddies, fronts and local jets. The above-discussed specific features of the Baltic Sea,
especially the strong stratification, have substantial implications on its dynamics already at the level of this fundamental scale. Owing to strong gradients, R 1 is very
small in the Baltic. Its typical values are between 3 and 10 km in the open Baltic
(Fennel et al. 1991). Differently from the barotropic Rossby radius, the baroclinic
Rossby radius depends not only on changes in local stratification conditions but also
on changes in longer time scales. Osi´ nski et al. (2010) found that the major inflow
in the winter 2002/2003 increased the value of R 1 in the southern Baltic from about
4 km (during the pre-inflow period) to more than 9 km.
Such spatial scales given by the Rossby radius for the open Baltic Sea can easily
be resolved by contemporary numerical models. Namely, to properly describe the
small-scale eddies, fronts and jets, it has been suggested that in numerical modelling
the grid size should be 1/2–1/3 of R 1 (Drijfhout 1989; Lindow 1997). The situation is more complicated in shallow and strongly stratified sub-basins of the Baltic
Sea such as the Gulf of Finland (see Chap. 6) or the south-western Baltic Sea, at
which most of the efforts of the developed technology for the preventive management of pollution have been targeted. In these basins the requirements for numerical
modelling are even higher than for the open Baltic Sea. Based on a dataset of about
1800 observations, the baroclinic Rossby radius was estimated to be on average in
the range of only 2–4 km in the Gulf of Finland (Alenius et al. 2003) whereas it
has also extensive spatial and temporal variability. Similar and even smaller values, down to 1 km, have been recently obtained for the south-western part of the
Baltic Sea (Osi´ nski et al. 2010). In shallow coastal regions and in the eastern Gulf
of Finland R 1 is sometimes as small as about 500 m (Nekrasov 1999; Nekrasov and
Lebedeva 2002). In such a case the numerical models need very high resolution,
down to about 0.25 nautical miles (Andrejev et al. 2010).
The meteorological conditions govern to a large extent the changes in the flow
field, and, not surprisingly, there are similarities in the spectra of wind and current
velocities. Especially in the surface layer the variability of the currents is strongly
5 The term ‘shallow water’ is used here and on some occasions below to distinguish the situation
where the typical length of waves of a particular class (Rossby waves, internal waves, surface
waves, etc.) considerably exceeds the water depth.