50
3 Basics of Geophysical Fluid Dynamics
Fig. 3.18 Pathway of an object that experiences the Coriolis force in a clockwise rotating f uid.
The SciLab script “Coriolis Force Revealed.sce” in the folder “Miscellaneous/Coriolis Force” of
the CD-ROM produces an animation
circle twice while the tank revolves only once about its centre. Accordingly, the
period of this so-called inertial oscillation is 0.5 T , known as inertial period, with
T being the rotation period of the flui tank.
Rather than working in a fi ed coordinate system, it is more convenient to formulate the Coriolis force from the viewpoint of an observer in the rotating frame of
reference. In the absence of other forces, it can be shown that inertial oscillations
are governed by the momentum equations:
∂u
∂t
= +2Ω v and
∂v
∂t
= −2Ω u
(3.47)
The Coriolis force acts perpendicular to the direction of motion and the factor
of 2 reflect the fact that inertial oscillations have a period half that of the rotating
frame of reference. If a parcel is pushed with an initial speed of u o into a certain
direction, it can also be shown that its resultant path is a circle of radius u o /(2 |Ω)|).
With an initial speed of about 0.7 m/s and |Ω| = 0.727×10
−5
s
−1
, as in the above
example, this inertial radius is about 4.8 km.
3.13 The Coriolis Force on Earth
3.13.1 The Local Vertical
In rotating fluid at rest, the centrifugal force is compensated by pressure-gradient
forces associated with slight modificatio of the shape of the flui surface. On the
rotating Earth, this leads to a minor variation of the gravity force by less than 0.4%.
The local vertical at any geographical location is now define as the coordinate
axis aligned at right angle to the equilibrium sea surface. This implies that, for a
3 Basics of Geophysical Fluid Dynamics
Fig. 3.18 Pathway of an object that experiences the Coriolis force in a clockwise rotating f uid.
The SciLab script “Coriolis Force Revealed.sce” in the folder “Miscellaneous/Coriolis Force” of
the CD-ROM produces an animation
circle twice while the tank revolves only once about its centre. Accordingly, the
period of this so-called inertial oscillation is 0.5 T , known as inertial period, with
T being the rotation period of the flui tank.
Rather than working in a fi ed coordinate system, it is more convenient to formulate the Coriolis force from the viewpoint of an observer in the rotating frame of
reference. In the absence of other forces, it can be shown that inertial oscillations
are governed by the momentum equations:
∂u
∂t
= +2Ω v and
∂v
∂t
= −2Ω u
(3.47)
The Coriolis force acts perpendicular to the direction of motion and the factor
of 2 reflect the fact that inertial oscillations have a period half that of the rotating
frame of reference. If a parcel is pushed with an initial speed of u o into a certain
direction, it can also be shown that its resultant path is a circle of radius u o /(2 |Ω)|).
With an initial speed of about 0.7 m/s and |Ω| = 0.727×10
−5
s
−1
, as in the above
example, this inertial radius is about 4.8 km.
3.13 The Coriolis Force on Earth
3.13.1 The Local Vertical
In rotating fluid at rest, the centrifugal force is compensated by pressure-gradient
forces associated with slight modificatio of the shape of the flui surface. On the
rotating Earth, this leads to a minor variation of the gravity force by less than 0.4%.
The local vertical at any geographical location is now define as the coordinate
axis aligned at right angle to the equilibrium sea surface. This implies that, for a