3.12 The Coriolis Force
43
where reduced gravity is given by g
= ρ
/ρ o g. This simplificatio is known as the
Boussinesq approximation in appreciation of early work by Boussinesq (1903).
3.11.7 The Case of Uniform Density
In a flui of uniform density, the horizontal pressure-gradient force turns into:
−g
∂η
∂ x
and −g
∂η
∂ y
which is yielded when inserting (3.29) with ρ
= 0 into (3.30). In the absence of
density variations, this force is the same throughout the flui column. We can therefore expect that the resultant fl w is also depth-independent, a feature referred to as
barotropic flo . In contrast to this, pressure gradients associated with lateral density
difference in the ocean interior triggers horizontal fl w that changes with depth.
Such a f ow is called baroclinic flo . Figure 3.11 shows sketches of barotropic and
baroclinic fl ws.
Fig. 3.11 Examples of barotropic and baroclinic fl ws
3.12 The Coriolis Force
3.12.1 Apparent Forces
Newton’s laws of motion are valid in a f xed coordinate system, that is one that
doesn’t rotate or translate. These laws imply that in the absence of forces, objects
follow a straight path with unchanged speed. In a rotating coordinate system, however, straight paths appear as curved paths (Fig. 3.12). If we want to apply Newton’s
laws of motion in rotating coordinates, this implies the existence of apparent forces.
There are two different apparent forces involved in the observed curved path of
the object, namely the centrifugal force and the Coriolis force (Coriolis, 1835). In
order to understand the Coriolis force, we need to understand the centrifugal force
first
43
where reduced gravity is given by g
= ρ
/ρ o g. This simplificatio is known as the
Boussinesq approximation in appreciation of early work by Boussinesq (1903).
3.11.7 The Case of Uniform Density
In a flui of uniform density, the horizontal pressure-gradient force turns into:
−g
∂η
∂ x
and −g
∂η
∂ y
which is yielded when inserting (3.29) with ρ
= 0 into (3.30). In the absence of
density variations, this force is the same throughout the flui column. We can therefore expect that the resultant fl w is also depth-independent, a feature referred to as
barotropic flo . In contrast to this, pressure gradients associated with lateral density
difference in the ocean interior triggers horizontal fl w that changes with depth.
Such a f ow is called baroclinic flo . Figure 3.11 shows sketches of barotropic and
baroclinic fl ws.
Fig. 3.11 Examples of barotropic and baroclinic fl ws
3.12 The Coriolis Force
3.12.1 Apparent Forces
Newton’s laws of motion are valid in a f xed coordinate system, that is one that
doesn’t rotate or translate. These laws imply that in the absence of forces, objects
follow a straight path with unchanged speed. In a rotating coordinate system, however, straight paths appear as curved paths (Fig. 3.12). If we want to apply Newton’s
laws of motion in rotating coordinates, this implies the existence of apparent forces.
There are two different apparent forces involved in the observed curved path of
the object, namely the centrifugal force and the Coriolis force (Coriolis, 1835). In
order to understand the Coriolis force, we need to understand the centrifugal force
first