Geography Reference
In-Depth Information
deflection character of the Coriolis force. The Coriolis force can only change the
direction of motion, not the speed of motion.
1.5.4
Constant Angular Momentum Oscillations
Suppose an object initially at rest on the earth at the point (x
0
, y
0
) is impulsively
propelled along the
x
axis with a speed
V
at time t
0. Then from (1.12a)
and (1.12b), the time evolution of the velocity is given by u
=
=
V cos ft and
v
Dy/Dt , integration with
respect to time gives the position of the object at time
t
as
=−
V sin ft. However, because u
=
Dx/Dt and v
=
V
f
V
f
x
−
x
0
=
sin ft
and
y
−
y
0
=
(cos ft
−
1)
(1.15a,b)
where the variation of
f
with latitude is here neglected. Equations (1.15a) and
(1.15b) show that in the Northern Hemisphere, where
f
is positive, the object
orbits clockwise (anticyclonically) in a circle of radius R
=
V/f about the point
(x
0
,y
0
−
V/f) with a period given by
τ
=
2πR/V
=
2π/f
=
π/( sin φ)
(1.16)
Thus, an object displaced horizontally from its equilibrium position on the sur-
face of the earth under the influence of the force of gravity will oscillate about
its equilibrium position with a period that depends on latitude and is equal to
one sidereal day at 30˚ latitude and 1/2 sidereal day at the pole. Constant angular
momentum oscillations (often referred to misleadingly as “inertial oscillations”)
are commonly observed in the oceans, but are apparently not of importance in the
atmosphere.
1.6
STRUCTURE OF THE STATIC ATMOSPHERE
The thermodynamic state of the atmosphere at any point is determined by the values
of pressure, temperature, and density (or specific volume) at that point. These field
variables are related to each other by the equation of state for an ideal gas. Letting
p, T
ρ, and α(
ρ
−
1
) denote pressure, temperature, density, and specific volume,
respectively, we can express the equation of state for dry air as
≡
=
=
pα
RT
or
p
ρRT
(1.17)
287 J kg
−
1
K
−
1
).
where
R
is the gas constant for dry air (R
=
