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Atmospheric Waves > Chapter 1 > Flashcards

Chapter 1 Flashcards

1
Q

…………………. support many wavelike motions

A

The governing equations

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2
Q

waves are broadly defined as

A

oscillations of the dependent variables

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3
Q

Some of the waves supported by the equations are:

A
  • External (surface) gravity waves
  • Internal gravity waves
  • Inertia-gravity waves
  • Acoustic waves (including Lamb waves)
  • Rossby waves
  • Kelvin waves
  • Kelvin-Helmholtz waves
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4
Q

Some of these waves are important for the

A

dynamics of synoptic scale systems

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5
Q

Some of these waves are important for the dynamics of synoptic scale systems, while others are merely

A

noise

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6
Q

In order to understand dynamic meteorology, we must understand

A

the waves that can occur in the atmosphere.

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7
Q

what are the governing equations?

A

set of equations that controls processes in the atmosphere

ex: momentum

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8
Q

what does a wave mean? (particles)

A

particles are not moving (stationary)

  • long wave (look like oscillation)
  • wide wave (ring)
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9
Q

what is the difference between oscillations and waves?

A

oscillations

  • No wavelength
  • can be part of the wave

sin and cosine can be applied to both

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10
Q

whenever you see sin and cosine think of

A

waves

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11
Q

define amplitude

A

half of the difference in height between a crest and a trough

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12
Q

define wavelength

A

(,) – the distance between crests (or troughs)

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13
Q

define wavenumber

A

K= 2pi/lamda

the number of radians in a unit distance in the direction of wave propagation. (sometimes the wave number is just defined as 1/lamda, in which case it is the number of wavelengths per unit distance.)

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14
Q

A higher wave number means

A

a shorter wavelength.

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15
Q

units of wavenumber

A

Units are radians m-1, or sometimes written as just m-1

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16
Q

We can also define wave numbers along each of the axes.

A
  • k is the wave number in the x-direction (k = 2pi/,<sub>x</sub>).
  • l is the wave number in the y-direction (l = 2pi/,\y).
  • m is the wave number in the z-direction. (m = 2pi/,\z).
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17
Q

The wave number vector is given by

A
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18
Q

define angular frequency

A

(w) 2 pi times the number of crests passing a point in a unit of time.

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19
Q

angular frequency units

A

radians s-1, sometimes just written as s-1.

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20
Q

define phase speed

A

(c) the speed of an individual crest or trough.

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21
Q

phase speed for a wave traveling solely in the x-direction

A

c = w/k.

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22
Q

phase speed for a wave traveling solely in the y-direction

A

c = w/l.

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23
Q

phase speed for a wave traveling solely in the z-direction

A

c = w /m

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24
Q

phase speed for wave traveling in an arbitrary direction

A

c = w /K, where K is the

total wave number given by K2= k2+ l2+ m2

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25
Q

For a wave traveling in an arbitrary direction, there is a

A

phase speed along each axis, given by cx = w/k, cy = w/l, and cz = w/m. Note that these are not the components of a vector!

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26
Q

The phase velocity vector is actually given by

A
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27
Q

The magnitude of the phase velocity (the phase speed) is given by

A
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28
Q

group velocity

A

(cg) the velocity at which the wave energy moves

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29
Q

group velocity components are given by

A
30
Q

The magnitude of the group velocity (……………….) is given by

A

the group speed

31
Q

define frequency

A

number of waves passing through a unit time

f=1/T

unit s-1 or HZ

32
Q

define period

A

he time needed for one complete cycle of vibration to pass a given point.

33
Q

As the frequency of a wave increases, the time period of the wave

A

decreases.

34
Q

define dispersion relation

A

an equation that gives the angular frequency of the wave as a function of wave number and physical parameters,

w=F(k, l, m, physical parameters)

35
Q

Each wave type has a

A

dispersion relation

36
Q

One of our main goals when studying waves is to determine

A

the dispersion relation.

37
Q

Wave dispersion

1.

2.

A
  1. Dispersion wave
  2. non dispersive wave
38
Q

when are the waves non dispersive

A

if the group velocity is the same as the phase speed of the individual waves making up the packet

39
Q

if waves are non-dispersive then

A

the shape of the wave packet never changes in time

40
Q

when are the waves dispersive

A

if the group velocity is different than the phase speed on the waves making up the packet

41
Q

if the waves are dispersive then

A

the shape of the wave packet will change with time

42
Q

waves are dispersive if

A

the phase velocity is not equal to the group velocity

43
Q

waves are non dispersive

A

if the phase velocity is equal to the group velocity

44
Q

expression of wave by wave number and angular frequency in x- direction with time

A
45
Q

expression of wave by wave number and phase speed in x- direction with time

A
46
Q

Eulerian formula

A
47
Q

what is the difference between even function and odd function

A
48
Q

apply the even and odd function in the eulerian formula

A
49
Q

express sin (t) and cos(t)

A
50
Q

Using Euler’s formula a wave traveling in the positive x-direction can be written as

A
51
Q

a wave traveling in the negative x-direction can be written as

A
52
Q

where the amplitude A

A
53
Q

and gives information about

A

the phase of the wave

54
Q

We will frequently use this complex notation for waves because it

A

makes differentiation more straightforward because you don’t have to remember whether or not to change the sign (as you do when differentiating sine and cosine functions).

55
Q

Spectral analysis is

A

working with wave in the frequency domain instead of the time domain

56
Q

It is rare to find a wave of a single wavelength in the atmosphere. Instead, there are

A

many waves of different wavelengths superimposed on one another.

57
Q

t is rare to find a wave of a single wavelength in the atmosphere. Instead, there are many waves of different wavelengths superimposed on one another. However, we can use the concept of spectral analysis to

A

isolate and study individual waves, recognizing that we can later sum them up if need be

58
Q

So, keep in mind that real atmospheric disturbances are

A

a collection of many individual waves of differing wavelengths.

59
Q

A fourier series is

A

a way to represent a function as the sum of simple sine waves.

60
Q

A fourier series is a way to represent a function as the sum of simple sine waves. more formally, it (what does it do?)

A

decomposes any periodic function or periodic signal into the sum of a (possibly infinte) set of simple oscillating functions, namely sine and cosine (or equivalently, complex exponentials)

61
Q

Most continuous periodic functions (period = L) can be represented by

A

an infinite sum of sine and cosine functions as

62
Q

the Fourier coefficients are given by

A
63
Q

The Fourier coefficients give

A

the amplitudes of the various sine and cosine waves needed to replicate the original function.

64
Q

The coefficient a0 is

A

just the average of the function

65
Q

The coefficients an are the

A

coefficients of the cosine waves (the even part of the function).

66
Q

The coefficients bn are

A

the coefficients of the sine waves (the odd part of the function).

67
Q

Smoother functions require

A

fewer waves to recreate, and have fewer higher frequency components.

68
Q

Sharper functions require

A

more waves to recreate, and have more higher frequency components.

69
Q

Broad functions require

A

fewer waves to recreate, and have fewer higher frequency components.

70
Q

Narrow functions require

A

more waves to recreate, and have more higher frequency components.

71
Q

In general, the narrower the function, the

A

broader the spectrum, and vice versa.

Atmospheric Waves (11 decks)

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