6 The Gulf of Finland
203
The magnitudes of different terms in these equations can be radically different
for different classes of motions as described in Chaps. 2–4. There is an essentially
never-ending discussion about which choice of scaling at best represents the motions in a particular basin. A sensible choice obviously depends on the guesses of
the scientist but is still to some extent predefined by the class of motions under consideration. The task of calculating the statistics of transport of pollutants in surface
currents intrinsically requires accounting for the scales from the basin dimensions
down to, at least, typical parameters of mesoscale motions. Then a few parameters
such as the typical horizontal extension L = 50 km, vertical extension (basically
equivalent to the mean depth here) H = 25 m, the basin-scale inclination of the
sea surface β ∼ 1 mm/(1 km) and the horizontal pressure gradient in the surface
layer ρ −1 ∇p = −gβ ∼ 10 −5 m/s 2 are externally defined and mostly coincide with
similar values for the open Baltic Sea (Chap. 2).
The limited north–south extension of the Gulf of Finland favours using the constant value of the Coriolis parameter f = 1.26 × 10 −4 1/s at φ = 60° N and a local
plane projection, which rotates around the local vertical axis (the so-called f -plane
approximation). The beta-plane approximation, in which the Coriolis parameter
varies in the north–south direction, is used infrequently in applications involving the
dynamics of the gulf. The typical scales of horizontal velocity U = |U| = 10 cm/s
and (eddy turnover) time T = 5 days are more site-specific although they coincide
here with those for the entire Baltic Sea. Similarly, representative turbulent (eddy)
viscosities A H = 10 5 m 2 /s and A v = 0.05 m 2 /s apparently are the same in the Gulf
of Finland and for the entire Baltic Sea.
The corresponding characteristic magnitudes of the terms of Eq. (6.1) of horizontal motions also coincide with their typical values for the whole Baltic Sea (in units
of 10 −6 m/s 2 , see Table 2.3 in Chap. 2): inertia U/T ∼ 0.2, advection U 2 /L ∼ 2,
Coriolis term f U and pressure gradient ρ −1 H p/L both ∼10, and internal friction terms A H U/L 2 ∼ 10 and A v U/H 2 ∼ 4. As the characteristic value of the term
representing vertical velocity is also U 2 /L, all the advection terms have an equal
weight. As for the entire Baltic Sea, they are by almost one order of magnitude
smaller than the dominating terms (the Coriolis acceleration, pressure gradient and
vertical friction) for the motions with a chosen scale. Note that the friction term includes the transfer of wind stress to the sea surface and the damping of motions by
bottom friction. Differently from the deep ocean, the pressure gradient is not necessarily large in the Gulf of Finland and in many cases the Coriolis acceleration and
vertical friction are approximately balanced.
Although in this greatly simplified scale analysis the role of advection and horizontal friction terms is smaller than that of the Coriolis term, advection does play
an important role in intensive mesoscale dynamics (when U becomes large for relatively small values of L). Horizontal friction becomes important near the coasts
where L decreases. The inertia term is significant in relatively fast processes with
a time scale T of some hours and in so-called inertial oscillations (see Sect. 2.3.4
in Chap. 2). The boundary conditions are rather simple for the Gulf of Finland. The
gulf is largely surrounded by mainland (which is a passive solid boundary) except
for point sources of fresh water in the river mouths and a dynamic inflow-outflow
system at the open boundary towards to the Northern Gotland Basin.
203
The magnitudes of different terms in these equations can be radically different
for different classes of motions as described in Chaps. 2–4. There is an essentially
never-ending discussion about which choice of scaling at best represents the motions in a particular basin. A sensible choice obviously depends on the guesses of
the scientist but is still to some extent predefined by the class of motions under consideration. The task of calculating the statistics of transport of pollutants in surface
currents intrinsically requires accounting for the scales from the basin dimensions
down to, at least, typical parameters of mesoscale motions. Then a few parameters
such as the typical horizontal extension L = 50 km, vertical extension (basically
equivalent to the mean depth here) H = 25 m, the basin-scale inclination of the
sea surface β ∼ 1 mm/(1 km) and the horizontal pressure gradient in the surface
layer ρ −1 ∇p = −gβ ∼ 10 −5 m/s 2 are externally defined and mostly coincide with
similar values for the open Baltic Sea (Chap. 2).
The limited north–south extension of the Gulf of Finland favours using the constant value of the Coriolis parameter f = 1.26 × 10 −4 1/s at φ = 60° N and a local
plane projection, which rotates around the local vertical axis (the so-called f -plane
approximation). The beta-plane approximation, in which the Coriolis parameter
varies in the north–south direction, is used infrequently in applications involving the
dynamics of the gulf. The typical scales of horizontal velocity U = |U| = 10 cm/s
and (eddy turnover) time T = 5 days are more site-specific although they coincide
here with those for the entire Baltic Sea. Similarly, representative turbulent (eddy)
viscosities A H = 10 5 m 2 /s and A v = 0.05 m 2 /s apparently are the same in the Gulf
of Finland and for the entire Baltic Sea.
The corresponding characteristic magnitudes of the terms of Eq. (6.1) of horizontal motions also coincide with their typical values for the whole Baltic Sea (in units
of 10 −6 m/s 2 , see Table 2.3 in Chap. 2): inertia U/T ∼ 0.2, advection U 2 /L ∼ 2,
Coriolis term f U and pressure gradient ρ −1 H p/L both ∼10, and internal friction terms A H U/L 2 ∼ 10 and A v U/H 2 ∼ 4. As the characteristic value of the term
representing vertical velocity is also U 2 /L, all the advection terms have an equal
weight. As for the entire Baltic Sea, they are by almost one order of magnitude
smaller than the dominating terms (the Coriolis acceleration, pressure gradient and
vertical friction) for the motions with a chosen scale. Note that the friction term includes the transfer of wind stress to the sea surface and the damping of motions by
bottom friction. Differently from the deep ocean, the pressure gradient is not necessarily large in the Gulf of Finland and in many cases the Coriolis acceleration and
vertical friction are approximately balanced.
Although in this greatly simplified scale analysis the role of advection and horizontal friction terms is smaller than that of the Coriolis term, advection does play
an important role in intensive mesoscale dynamics (when U becomes large for relatively small values of L). Horizontal friction becomes important near the coasts
where L decreases. The inertia term is significant in relatively fast processes with
a time scale T of some hours and in so-called inertial oscillations (see Sect. 2.3.4
in Chap. 2). The boundary conditions are rather simple for the Gulf of Finland. The
gulf is largely surrounded by mainland (which is a passive solid boundary) except
for point sources of fresh water in the river mouths and a dynamic inflow-outflow
system at the open boundary towards to the Northern Gotland Basin.