Geoscience Reference
In-Depth Information
and
/
F
z
dw
z
z
z
z
==++ +
F
F
F
F
,
(6.5)
m
COR
PGF
GRAV
F
dt
where the most important forces governing large-scale motion in the atmo-
sphere and oceans are included, namely, the Coriolis force per unit mass (
F
COR
),
the pressure gradient force per unit mass (
F
PGF
), gravitation (
F
GRAV
)and fric-
tion (
F
F
). Each of these is discussed below, where we refer to, for example, the
“Coriolis force per unit mass” simply as the “Coriolis force.”
6.1 THE CORIOLIS FORCE
The Coriolis force is an “apparent force” that arises because of the rotating
frame of reference from which we observe the atmosphere and oceans. The
laws of Newtonian physics apply in an
absolute,
or
inertial, frame of reference
,
but we observe the atmosphere and oceans within the
noninertial frame of
reference
rotating with the earth. With the Coriolis force included, the govern-
ing equations in the rotating frame of reference (seem to) conserve angular
momentum, and centrifugal accelerations are accounted for.
CONSERVATION OF ABSOLUTE ANGULAR MOMENTUM
A parcel of air or water with constant mass
m
moving with velocity
v
in a cir-
cular orbit must conserve absolute angular momentum (angular momentum in
the absolute frame of reference) in the absence of externally applied torques.
Angular momentum,
v
, is a vector quantity, defined as
v
v
v
Lrmv
/
#
,
(6.6)
where
m
v
is linear momentum, and
v
is the moment arm extending from the
mv
T
where
v
T
is the tangential velocity and the direction of
v
is given by the
right- hand
rule
. (Curl the fingers of your right hand in the direction of rotation and your
,
(a)
(b)
ν
T
L
r
ν
T
r
Figure 6.1. Definition of angular momentum.
