SO335
Chapters 1 and 2 example problems
1. The Rossby Number is often used to describe the response of a weather system to the Earth’s
rotation. I.e., if the Rossby Number of the weather system is small, then rotation (Coriolis)
becomes important, and if it is large, then the weather system will not ‘feel’ the effects of
rotation.
If the Rossby Number is given as
U
,
fL
where U is the speed of the fluid parcel, f is the Coriolis parameter, and L is the horizontal
length scale of the weather system (i.e., how “big” it is), what are the units of the Rossby
Number? (Hint: use your textbook, the Ch. 1 notes, and the internet to find appropriate units for U, f, and L).
2. If two vectors are given as:
A  3 xiˆ  3 y 2 ˆj  2 zkˆ
B  3 yiˆ  22 xz 2 ˆj  2 zkˆ
Find: A  B and A  B .
3. If A  3iˆ  3 ˆj  2kˆ , what is the magnitude of A ?
4. If two vectors are given as:
A  3iˆ  3 ˆj  2kˆ
B  3iˆ   ˆj  3kˆ
What value must  have if A is perpendicular to B ?