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1
Q

Circulation and vorticity are

A

the two primary measures of rotation in a fluid

2
Q

Circulation is a

A
  • scalar integral quantity
  • macroscopic measure of rotation for a finite area of the fluid
3
Q

Vorticity is a

A
  • vector field
  • microscopic measure of the rotation at any point in the fluid
4
Q

draw an example of circulation and vorticity

A
5
Q

What is the difference between macroscopic and microscopic

A
  • Macroscopic:
    • Large scale
    • rotation of entire fluid –> circulation
  • Microscopic:
    • Very Small
    • How individual particles rotate “any point within the fluid”
6
Q

barotropic fluid

A

characterised by the absence of horizontal temperature gradients completely.

No horizontal gradient –> temperature is constant “Isotherm”

7
Q

A barotropic fluid is one in which

A

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

8
Q

Specific volume (a):

A

volume of a unit mass of air

9
Q

density (p):

A

mass/volume = 1/volume

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

10
Q

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

A

density

pressure only

density is constant along a constant pressure surface.

11
Q

P1 ​stands for

A

Isotere (specific volume)

12
Q

a1​ stands for

A

Pressure uniform

13
Q

ideal gas law:

A
14
Q

From ideal gas law:

A

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

15
Q

The law implies that

A

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

16
Q

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

Therefore, in a barotropic fluid,

A

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

17
Q

Summary of barotropic fluid

A

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

18
Q

baroclinic fluid

A

characterized by the presence of horizontal temperature variations.

19
Q

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

In such a fluid,

A

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

20
Q

Explain the figure

A

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’.

21
Q

Fig. also shows that the solenoids give

A

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

22
Q

circulation is a

A

scalar quantity

23
Q

Circulation

A

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

24
Q

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

A

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

25
Q

Circulation equation:

A
26
Q

Draw a figure that better represent the circulation equation

A
27
Q

C, a measure of

A

the rotation of the fluid

28
Q

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

A
  • positive (C > 0) for cyclonic circulation and
  • negative (C < 0) for anticyclonic circulation
29
Q

Circulation has dimensions

A
30
Q

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

A

dl

31
Q

Circulation around a closed loop is, simply the

A

integral of the tangential velocities around the loop.

32
Q
  • Circulation around a closed loop is, simply the integral of the tangential velocities around the loop.
    • Hence, the mean tangential velocity <v> around</v>
A

the loop can be obtained from circulation (C) as follows:

where r is the radius of the circular loop

33
Q

The Circulation theorem

It gives an

A

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

34
Q

what are the terms in the following circulation theorem

A
35
Q

What is the simplified version of the solenoidal term

A
36
Q

Coriolis term

A
37
Q

What does F represents in the Coriolis term

A

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

38
Q

The coriolis term states that if a material surface

A

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

39
Q

What is the simplified version of the circulation theorem

A
40
Q

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

A
41
Q

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

A
42
Q

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

A

expands in time or displaced polewards

c decreases –> cyclonic circulation decreases. anticyclonic circulation increases

43
Q

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:

A

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

44
Q

Sea breeze

A
  • 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.
45
Q

land breeze

A
  • 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.
46
Q

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

A

may be disregarded.

47
Q

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

A

the solenoidal effect

48
Q

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

A
49
Q

a counter clockwise (cyclonic) circulation will be developed with

A

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

50
Q

the two primary measures of rotation in a fluid

A

Circulation and vorticity

51
Q
  • scalar integral quantity
  • macroscopic measure of rotation for a finite area of the fluid
A

Circulation

52
Q
  • vector field
  • microscopic measure of the rotation at any point in the fluid
A

Vorticity

53
Q

A resembles

A

Circulation

54
Q

B resembles

A

Vorticity

55
Q

characterised by the absence of horizontal temperature gradients completely

A

barotropic fluid

56
Q

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

A

A barotropic fluid

57
Q

volume of a unit mass of air

A

Specific volume (a)

58
Q

characterized by the presence of horizontal temperature variations.

A

baroclinic fluid

59
Q

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

A

Circulation

60
Q

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

A

The circulation, C,

61
Q

integral of the tangential velocities around the loop.

A

Circulation around a closed loop

62
Q

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

A

The circulation theorem

63
Q

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

A

What does F represents in the Coriolis term

64
Q
  • 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.
A

Sea breeze

65
Q
  • 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.
A

land breeze