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Elementary Application of the Basic Equations
For many applications it is preferable to work with the equations that
govern atmospheric motions using an isobaric coordinate system.
Basic Equations in Isobaric Coordinates
Horizontal Momentum Equation
We will neglect the curvature terms, friction force, and Coriolis force due to
vertical motion.
In height coordinates the horizontal momentum equation is then given by:
D
?
V
Dt
+ f
?
k ×
?
V = ?
1
?
?p,
where
?
V = u
?
i + v
?
j is the horizontal wind vector.
Replace the pressure gradient force term with:
?
1
?
?p = ??
p
? = ?
??
?x
?
??
?y
In an isobaric coordinate system:
D
Dt
=
?
?t
+ u
?
?x
+ v
?
?y
+?
?
?p
,
where
? ?
Dp
Dt
How does this differ from the expression for a total derivative in a height
based coordinate system?
What is the physical interpretation of ??
The horizontal momentum equation ...

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