Chapter 1

Question 1

Circulation and vorticity are

Answer 1

the two primary measures of rotation in a fluid

Question 2

Circulation is a

Answer 2

• scalar integral quantity
• macroscopic measure of rotation for a finite area of the fluid

Question 3

Vorticity is a

Answer 3

• vector field
• microscopic measure of the rotation at any point in the fluid

Question 4

draw an example of circulation and vorticity

Answer 4

Question 5

What is the difference between macroscopic and microscopic

Answer 5

• Macroscopic:
  
  • Large scale
  • rotation of entire fluid –> circulation
• Microscopic:
  
  • Very Small
  • How individual particles rotate “any point within the fluid”

Question 6

barotropic fluid

Answer 6

characterised by the absence of horizontal temperature gradients completely.

No horizontal gradient –> temperature is constant “Isotherm”

Question 7

A barotropic fluid is one in which

Answer 7

the surfaces of constant pressure (p1, p2 …) and constant density (or specific volume) are parallel.

Question 8

Specific volume (a):

Answer 8

volume of a unit mass of air

Question 9

density (p):

Answer 9

mass/volume = 1/volume

specific volume = 1/p (when p constant volume is constant)

Question 10

In a barotropic fluid, …………………..is a function of ………………and……………………………………………………

Answer 10

density

pressure only

density is constant along a constant pressure surface.

Question 11

P₁ ​stands for

Answer 11

Isotere (specific volume)

Question 12

a₁​ stands for

Answer 12

Pressure uniform

Question 13

ideal gas law:

Answer 13

Question 14

From ideal gas law:

Answer 14

If P is constant p is constant –> constant ratio = constant

Question 15

The law implies that

Answer 15

for a barotropic atmosphere, temperature is constant on a constant pressure surface.

Question 16

for a barotropic atmosphere, temperature is constant on a constant pressure surface.

Therefore, in a barotropic fluid,

Answer 16

surfaces of constant pressure, constant density and constant temperature all are parallel.

Question 17

Summary of barotropic fluid

Answer 17

No change in temperature and pressure –> no circulation due to these factors but circulation may develop due to other factors

Question 18

baroclinic fluid

Answer 18

characterized by the presence of horizontal temperature variations.

Question 19

A baroclinic fluid is characterized by the presence of horizontal temperature variations.

In such a fluid,

Answer 19

density is not a function of pressure alone and density variations occur due to horizontal temperature variations. Ex: Land and sea breeze.

Question 20

Explain the figure

Answer 20

the isobars slope upwards towards the warm, while the isosteres slope upward over the cold.

Therefore, in a baroclinic fluid, the surfaces of constant pressure and constant specific volume intersect each other, forming quadrilaterals known as ‘solenoids’.

Question 21

Fig. also shows that the solenoids give

Answer 21

rise to direct circulation (warm air rises and cold air sinks).

Question 22

circulation is a

Answer 22

scalar quantity

Question 23

Circulation

Answer 23

expresses the macroscopic rotational tendency of a finite area of a fluid.

Question 24

The circulation, C, around a given closed curve in a fluid is

Answer 24

the integral around the curve of the components of the velocities along the curve

Question 25

Circulation equation:

Answer 25

Question 26

Draw a figure that better represent the circulation equation

Answer 26

Question 27

C, a measure of

Answer 27

the rotation of the fluid

Question 28

C, a measure of the rotation of the fluid is:

Answer 28

* positive (C \> 0) for cyclonic circulation and * negative (C \< 0) for anticyclonic circulation

Question 29

Circulation has dimensions

Answer 29

Question 30

If dx, dy, dz are components of ......, then

Answer 30

dl

Question 31

Circulation around a closed loop is, simply the

Answer 31

integral of the tangential velocities around the loop.

Question 32

* Circulation around a closed loop is, simply the integral of the tangential velocities around the loop. * Hence, the mean tangential velocity around

Answer 32

the loop can be obtained from circulation (C) as follows: where r is the radius of the circular loop

Question 33

The Circulation theorem It gives an

Answer 33

expression for the individual rate of change of the circulation, over a closed chain of fluid particles.

Question 34

what are the terms in the following circulation theorem

Answer 34

Question 35

What is the simplified version of the solenoidal term

Answer 35

Question 36

Coriolis term

Answer 36

Question 37

What does F represents in the Coriolis term

Answer 37

represents the area enclosed by the projection of the chosen closed circuit on the equatorial plane.

Question 38

The coriolis term states that if a material surface

Answer 38

expands in time or displaced polewards its projection onto the equatorial plane increases (dF/dt \>0)

Question 39

What is the simplified version of the circulation theorem

Answer 39

Question 40

In a barotropic fluid, since density is a function of pressure only, we can write the solenoidal term as:

Answer 40

Question 41

Therefore, for a barotropic fluid, the circulation theorem becomes:

Answer 41

Question 42

When a material surface ............................... or .................................

Answer 42

expands in time or displaced polewards c decreases --\> cyclonic circulation decreases. anticyclonic circulation increases

Question 43

Since in a baroclinic fluid, density is not a function of pressure alone, \_\_\_\_\_\_\_\_\_\_\_\_Therefore, for a baroclinic fluid, the circulation theorem can be written as:

Answer 43

/o (a)(dp)not equal to 0

Question 44

Sea breeze

Answer 44

* During the day the land is heated while the water surface remains relatively cool. * The isosteric surfaces slope downwards towards the warmer land as depicted, causing the wind to blow from the sea toward the land.

Question 45

land breeze

Answer 45

* During night, the opposite situation occurs. * The land surface cools off and the water remains relatively warm so that the wind blows from the land toward the sea.

Question 46

On the small spatial scales of land–sea breezes the rotational (coriolis) effect of the earth

Answer 46

may be disregarded.

Question 47

On the small spatial scales of land–sea breezes the rotational (coriolis) effect of the earth may be disregarded. The observed circulation pattern is then due to

Answer 47

the solenoidal effect

Question 48

The observed circulation pattern is then solely due to the solenoidal effect and the circulation theorem can be written as:

Answer 48

Question 49

a counter clockwise (cyclonic) circulation will be developed with

Answer 49

rising motion over warmer land and sinking motion over colder ocean.

Question 50

the two primary measures of rotation in a fluid

Answer 50

Circulation and vorticity

Question 51

* scalar integral quantity * macroscopic measure of rotation for a finite area of the fluid

Answer 51

Circulation

Question 52

* vector field * microscopic measure of the rotation at any point in the fluid

Answer 52

Vorticity

Question 53

A resembles

Answer 53

Circulation

Question 54

B resembles

Answer 54

Vorticity

Question 55

characterised by the absence of horizontal temperature gradients completely

Answer 55

barotropic fluid

Question 56

the surfaces of constant pressure (p1, p2 ...) and constant density (or specific volume) are parallel in

Answer 56

A barotropic fluid

Question 57

volume of a unit mass of air

Answer 57

Specific volume (a)

Question 58

characterized by the presence of horizontal temperature variations.

Answer 58

baroclinic fluid

Question 59

expresses the macroscopic rotational tendency of a finite area of a fluid.

Answer 59

Circulation

Question 60

the integral around the curve of the components of the velocities along the curve

Answer 60

The circulation, C,

Question 61

integral of the tangential velocities around the loop.

Answer 61

Circulation around a closed loop

Question 62

expression for the individual rate of change of the circulation, over a closed chain of fluid particles.

Answer 62

The circulation theorem

Question 63

represents the area enclosed by the projection of the chosen closed circuit on the equatorial plane

Answer 63

What does F represents in the Coriolis term

Question 64

* During the day the land is heated while the water surface remains relatively cool. * The isosteric surfaces slope downwards towards the warmer land as depicted, causing the wind to blow from the sea toward the land.

Answer 64

Sea breeze

Question 65

* During night, the opposite situation occurs. * The land surface cools off and the water remains relatively warm so that the wind blows from the land toward the sea.

Answer 65

land breeze