1
Momentum Equations in Spherical
Coordinates
•
For a variety of reasons, it is useful to express
the vector momentum equation for a rotating
earth as a set of scalar component equations.
•
The use of latitude-longitude coordinates to
describe positions on earth’s surface makes it
convenient to write the momentum equations in
spherical coordinates.
•
The coordinate axes are
(
λ
,
φ
,z)
where
λ
is
longitude,
φ
is latitude, and
z
is height.
Orientation of Coordinate Axes
λ
φ
d
cos
a
dx
=
The x- and y-axes are customarily defined to point east
and north, respectively, such that
and
φ
d
a
dy
=
Thus the horizontal velocity components are
dt
dy
v
,
dt
dx
u
=
=

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