1. Holton 2.3 (vector identities)

2. Perform a scale analysis of a seabreeze on the long north-south coastline of California. Use the following scales (note that the two horizontal scales are different):

U ~ 10 m s^-1
V ~ ? (but not larger than U)
W ~ 1 cm s^-1
H ~ 1 km (height of seabreeze layer)
Dp ~ ? (horizontal variations in pressure)
f ~ 10^-4 s^-1
Ro ~ 1 kg m^-3
Lx ~ 100 km (onshore/offshore length scale)
Ly ~ 1,000 km (along shore length scale)
t ~ 10⁴ s

a. Perform a scale analysis on the x-momentum equation. What is the greatest magnitude of the horizontal variation in pressure (Dp) consistent with the scales given above?

b. Use your answer to a. for the scale of p, and perform a scale analysis on the y-momentum equation. Which terms are dominant in this equation? What magnitude of V is required for this equation to balance? Do you expect the seabreeze to have a significant along-shore component?

3. A laboratory tank consists of a cylindrical container 30 cm in diameter, filled at rest by 20 cm of fresh water and then spun at 30 rpm. After a state of solid-body rotation is achieved, what is the difference in water level between the rim and the center?

4. Print out two upper level maps of weather systems of your choice. The maps should show one extratropical and one tropical system (phi < 30 degrees). Identify the horizontal extent of the major atmospheric feature and find the associated typical wind speed. From these numbers, estimate the Rossby number of the weather feature. What do you conclude about the importance of the Coriolis force? (Hint: When converting latitudinal and longitudinal differences in kilometers, use the earth's mean radius of 6371 km).

5. For a characteristic velocity of 10 (100) m/s, at what horizontal scale does the earth's rotation become important?

Solutions