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3 Basics of Geophysical Fluid Dynamics
Fig. 3.20 The centripetal force for a variation of the orientation of local vertical
3.13.3 The f -Plane Approximation
The curvature of the Earth’s surface can be ignored on spatial scales of 100 km, to
first-orde approximation. Hence, on this scale, we can place our Cartesian coordinate system somewhere at the sea surface with the z-axis pointing into the direction
of the local vertical and use a constant Coriolis parameter (Fig. 3.21). The constant
value of f is define with respect to the point-of-origin of our coordinate system.
This configuratio is called the f-plane approximation.
3.13.4 The Beta-Plane Approximation
The curved nature of the sea surface can still be ignored on spatial scales of up to
a 1000 km (spans about 10
◦
in latitude), if the Coriolis parameter is described by a
constant value plus a linear change according to:
f = f o + β y
(3.49)
Fig. 3.21 The sketch gives an example of a f-plane. The Coriolis parameter is given by
f = 2Ω sin(ϕ), where ϕ is geographical latitude of the centre of the plane