1
Kinematics
•
The atmosphere is
characterized by horizontal
(and vertical) variations in
the wind field.
•
For example, look at the
horizontal variations of wind
speed and direction (and
hence
u
and
v
) on this
weather map depicting
surface streamlines.
•
These horizontal variations
can be expressed as partial
derivatives of
u
and
v
with
respect to
x
and
y
.
•
Consider the possible sums of derivatives that can be
constructed including a derivative of
u
with respect to
one direction and a derivative of
v
with respect to the
other direction:
y
u
x
v
y
u
x
v
y
v
x
u
y
v
x
u
∂
∂
−
∂
∂
∂
∂
+
∂
∂
∂
∂
−
∂
∂
∂
∂
+
∂
∂
•
What do these quantities tell us about the characteristics
of the fluid flow?
Let’s use a Taylor series expansion for
find out.

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