2 Topography, Hydrography, Circulation and Modelling of the Baltic Sea
41
usually at the halocline. But due to the effect of horizontal advection the water temperature beneath the winter thermocline can be much higher than the temperature of
maximum density. Ice forms in the Baltic Sea annually for 5–7 months. Landfast ice
occurs in coastal and archipelago areas; significant salinity stratification may form
even in shallow waters in the neighbourhood of river mouths. Further offshore drift
ice fields exist. Mechanically forced mixing continues due to the motion of the ice
with similar strength as in the ice-free winter season.
2.3 Circulation Dynamics
2.3.1 Basic Principles
The system of ocean currents is three-dimensional (3D). Their dynamics is governed by the Navier–Stokes equations and the continuity equation. These equations
express the fundamental laws for the conservation of momentum and mass in differential form for a continuous medium. In ocean dynamics the water is assumed to
be incompressible and the Boussinesq approximation 4 is used, stating that density
differences are sufficiently small to be neglected, except where they appear in terms
multiplied by the acceleration due to gravity. The basic equations of ocean dynamics
are (see, e.g., Cushman-Roisin and Beckers 2011):
∂u
∂t
+ u · ∇u + 2 × u = −
1
ρ
∇p + ∇·τ + ν∇
2 u,
(2.1)
∇ · u = 0,
(2.2)
where u = (u, v, w) is the current velocity, is the Earth’s rotation rate (Ω =
0.7292 × 10 −4 1/s), ρ is density, p is pressure, τ is the Reynolds stress tensor and ν
is the molecular viscosity. Traditionally, the x-axis is directed to the east, the y-axis
to the north and the z-axis upwards. Equations (2.1), (2.2) are purely dynamical. For
the complete circulation system the equation of state for sea water and equations
describing the budget of heat and salt must be added. A more detailed treatment
of the resulting system of equations in the rotating reference frame is presented in
Chap. 3, Sect. 3.3.2, and in Chap. 4.
The molecular viscosity is generally neglected in the circulation theory and the
horizontal part of the Coriolis acceleration is included. There is a strong distinction
between the horizontal and vertical directions due to the fact that gravity strongly
limits vertical motions. The horizontal currents in the Baltic Sea have a typical magnitude of 10 cm/s, whereas the vertical velocities are typically less than 0.1 mm/s.
This feature, a much more prominent property of the velocity field in the shallow
4 After Joseph Valentin Boussinesq (1842–1929).
41
usually at the halocline. But due to the effect of horizontal advection the water temperature beneath the winter thermocline can be much higher than the temperature of
maximum density. Ice forms in the Baltic Sea annually for 5–7 months. Landfast ice
occurs in coastal and archipelago areas; significant salinity stratification may form
even in shallow waters in the neighbourhood of river mouths. Further offshore drift
ice fields exist. Mechanically forced mixing continues due to the motion of the ice
with similar strength as in the ice-free winter season.
2.3 Circulation Dynamics
2.3.1 Basic Principles
The system of ocean currents is three-dimensional (3D). Their dynamics is governed by the Navier–Stokes equations and the continuity equation. These equations
express the fundamental laws for the conservation of momentum and mass in differential form for a continuous medium. In ocean dynamics the water is assumed to
be incompressible and the Boussinesq approximation 4 is used, stating that density
differences are sufficiently small to be neglected, except where they appear in terms
multiplied by the acceleration due to gravity. The basic equations of ocean dynamics
are (see, e.g., Cushman-Roisin and Beckers 2011):
∂u
∂t
+ u · ∇u + 2 × u = −
1
ρ
∇p + ∇·τ + ν∇
2 u,
(2.1)
∇ · u = 0,
(2.2)
where u = (u, v, w) is the current velocity, is the Earth’s rotation rate (Ω =
0.7292 × 10 −4 1/s), ρ is density, p is pressure, τ is the Reynolds stress tensor and ν
is the molecular viscosity. Traditionally, the x-axis is directed to the east, the y-axis
to the north and the z-axis upwards. Equations (2.1), (2.2) are purely dynamical. For
the complete circulation system the equation of state for sea water and equations
describing the budget of heat and salt must be added. A more detailed treatment
of the resulting system of equations in the rotating reference frame is presented in
Chap. 3, Sect. 3.3.2, and in Chap. 4.
The molecular viscosity is generally neglected in the circulation theory and the
horizontal part of the Coriolis acceleration is included. There is a strong distinction
between the horizontal and vertical directions due to the fact that gravity strongly
limits vertical motions. The horizontal currents in the Baltic Sea have a typical magnitude of 10 cm/s, whereas the vertical velocities are typically less than 0.1 mm/s.
This feature, a much more prominent property of the velocity field in the shallow
4 After Joseph Valentin Boussinesq (1842–1929).