Chapter 3

Question 1

Surface gravity waves are

Answer 1

waves on the surface of a liquid, in which the restoring force of which is gravity (is a force that gives rise to an equilibrium in a physical system. If the system is perturbed away from the equilibrium, the restoring force will tend to bring the system back toward equilibrium.)

Question 2

These waves are familiar to all of us as

Answer 2

the waves on the ocean or a lake.

Question 3

surface gravity waves or surface waves

Answer 3

These waves are familiar to all of us as the waves on the ocean or a lake. Gravity waves on an air–sea interface of the ocean

Question 4

internal waves

Answer 4

gravity waves that are within the body of the water (such as between parts of different densities)

Question 5

examples of gravity waves

Answer 5

Wind-generated waves on the water surface as are tsunamis and ocean tides

mountain waves or frontal. The effect of gravity waves in clouds can look like altostratus undulatus clouds

Question 6

We will first limit our study to:

Answer 6

• Surface gravity waves on the free surface of a constant density fluid (ρ=constant).
• Waves in hydrostatic balance. This assumption implies that we are studying waves whose wavelength is much larger than the depth of the fluid (remember the condition from scale analysis for assuming hydrostatic balance is that the horizontal length scale be much larger than the vertical length scale). Thus we are limited to either very-long wavelengths, or very shallow water.

Question 7

This is alternately known as either

Answer 7

the long-wave approximation or the shallow-water approximation.

Question 8

We have to assume that the fluid is deep in order to assume that p0 is constant. This is because

Answer 8

a displacement of the interface upward results in either divergence or convergence in the fluid as it adjusts to the change in interface height.

Question 9

We have to assume that the fluid is deep in order to assume that p0 is constant. This is because a displacement of the interface upward results in either divergence or convergence in the fluid as it adjusts to the change in interface height. This means that there would be

Answer 9

horizontal flow in the upper fluid, which would require a horizontal pressure gradient in the upper fluid.

Question 10

If the lower fluid is in hydrostatic balance, then

Answer 10

the pressure at any point in the lower fluid is proportional to the weight of the fluid above it.

Question 11

why are they called shallow-water momentum equations

Answer 11

we’ve assumed that the lower fluid is in hydrostatic balance, we’ve constrained our analysis to motions whose horizontal scale is much greater than the vertical scale (the depth of the fluid).

Question 12

Note that the pressure gradient force at any point in the lower fluid is

Answer 12

independent of depth

Question 13

Note that the pressure gradient force at any point in the lower fluid is independent of depth! This means that the

Answer 13

fluid motion is also independent of depth. Therefore, the lower fluid is barotropic