Chapter 4

Question 1

Gravity eaves can exist on either:

Answer 1

• The interface at the top of the upper fluid or
• On the interface between the two fluids

Question 2

Assumes that the space above the uppermost fluid is filled with:

Answer 2

• A fluid of very low density
• Very large depth
• We can use g instead of g’
• P0 at upper interface is zero
• Referred to as free surface

Question 3

The gravity waves that form on the free surface and ……… are ……. of one another

Answer 3

• The interface
• Not independent

Question 4

In the upper fluid and lower fluid the PGF is solely due to:

Answer 4

• Upper fluid:
  
  • The slope of the free surface
• Lower fluid:
  
  • Due to the slope of the interface
  • Slope of the free surface

Question 5

To find the dispersion relation we could:

Answer 5

Proceed by assuming sinusoidal function

Question 6

The disturbance on the free surface is:

Answer 6

• Larger in amplitude than the disturbance on the interior interface
  
  • The total depth of the fluid and the depth of the lower layer, H is greater than the lower depth H1
• Much smaller in amplitude than the disturbance on the interior interface and is of opposite sign
  
  • So the two interfaces are 180 out of phase

Question 7

Two-layer, shallow-water fluid there are two distinct modes:

Answer 7

• Baroclinic mode
• Barotropic mode

Question 8

In a three layer fluid it turns out there are three modes:

Answer 8

• Barotropic mode
• Two baroclinic modes

Question 9

barotropic mode:

Answer 9

the u-components of velocity are also in phase and are nearly equal

Question 10

baroclinic mode:

Answer 10

the u-components of velocity are also 180 out of phase

Question 11

an n-layer fluid will have n modes:

Answer 11

barotropic mode

n-1 baroclinic modes

Question 12

Infinite number of baroclinic modes:

Answer 12

a fluid with continuous stratification can be expected to have an infinite number of baroclinic modes

Question 13

discussion of two layer fluid will be important later when discussing:

Answer 13

• (concept of equivalent depth) internal waves
  
  • multi-layered
  • continuously stratified fluid

Question 14

Equivalent depth:

Answer 14

depth that the fluid would have to have in order for an external gravity wave to have the same speed as the baroclinic mode

Question 15

For a fluid with multiple layers:

Answer 15

• there are multiple baroclinic modes.
  
  • Each mode will have an equivalent depth
    
    • We know the dispersion relation

Question 16

Fluid with continuous stratification:

Answer 16

• There would be an infinite number of baroclinic modes
• Not all modes will be important
  
  • Some will be very weak
  • If we can identify the most important baroclinic modes
    
    • Maybe as few as two or three
    • Can find equivalent depths for them
    • Can find dispersion relations for these modes
    • This is known as normal mode analysis

Question 17

Why do we study the shallow water gravity waves:

Answer 17

• Because of the concept of equivalent depth
• The atmosphere is a multilayer fluid
• Supports many baroclinic modes of oscillation
• Scales of motion studied in synoptic scale dynamics
  
  • The hydrostatic assumption is valud
• To study the linear gravity waves that are supported by the atmosphere