Midterm: UNIT THREE

Question 1

What are the first two assumptions of a shallow water system?

Answer 1

• Hydrostatic balance du/dz=0
• Constant density, barotropic fluid

Question 2

Why do we use shallow water system?

Answer 2

allow to model how the flow will evolve in space and time
-eg: geostrophic winds and some type of waves (gravity waves, billow clouds)

Question 3

What is potential vorticity in shallow water system? What does its conservation mean?

Answer 3

q = (ζ + 𝑓)/h
because it is conserved, predictive power: allows to find the intensity of the spin of the fluid at a future time and from the spin recover the flow field

Question 4

How do we identify waves ?

Answer 4

Linearization:
1-V + V’ (background + pertubation)
2- governing equation terms involving VV’ are negligible

–> can identify short vs long waves:
Ld = sqrt(g+H)/f