Lecture 4: Atmospheric Turbulence

Question 1

layers of the atmosphere

Answer 1

earth
troposphere
stratosphere
mesosphere
ionosphere

Question 2

at 50km, pressure has fallen to around 1 mbar so

Answer 2

little turbulence above this altitude

Question 3

temperature variations giving rise to optical effects of turbulence only significant in

Answer 3

the troposhere

Question 4

where is turbulence usually greatest

Answer 4

nearest the ground

Question 5

turbulence falls of exponentially with increasing altitude except

Answer 5

for peak that occurs at the tropopause

Question 6

Peak that occurs at the tropopause is due to

Answer 6

wind shear

Question 7

wind shear gives rise to

Answer 7

kelvin-helmholtz instabilities

Question 8

kolmogorov model - energy added to fluid in the form of

Answer 8

large scale disturbances

Question 9

kolmogorov model - eddies or vortices generated on

Answer 9

outer scale
L0

spawns cascade on smaller eddies

Question 10

kolmogorov model - turbulence dies away at

Answer 10

inner scale
l0

Question 11

kolmogorov model - kinetic energy dissipated by

Answer 11

viscosity

Question 12

kolmogorov model - outer scale L0 is typically

Answer 12

10m

Question 13

kolmogorov model - inner scale l0 is typically

Answer 13

few mm

Question 14

kolmogorov model - stable state…

Answer 14

rate of input of turbulent energy =
rate of viscous dissipation

Question 15

kolmogorov model - fluctuations in velocity are governed only by

Answer 15

scale, l , and the rate of energy input/dissipation per unit mass, epsilon

Question 16

kolmogorov model - epsilon

Answer 16

rate of energy per unit mass

(units of J/s/kg)

Question 17

kolmogorov model - scale

Answer 17

l
units m

Question 18

structure functions were introduced by Kolmogorv to describe

Answer 18

non-stationary random functions encountered in turbulence

Question 19

structure functions - temporal - use

Answer 19

difference function
F(τ)=f(t+τ)-f(t)

Question 20

structure function

Answer 20

average of square difference

F(τ)= <[T(τ)]^2> = <[f(t+τ)-f(t)]^2>

Question 21

spatial difference and structure functions

Answer 21

same as temporal but replace t with x and τ with r

Question 22

Structure function of velocity at locations separated by
distance r along a coordinate x

Answer 22

D(r)=<[V(x+r)-V(x)]^2> = C_v^2 r^2/3

Question 23

C_v^2

Answer 23

structure parameter for velocity

characterises mechanical turbulence

Question 24

temperature varies with

Answer 24

altitude

Question 25

mechanical turbulence mixes air at

Answer 25

the tropopause

Question 26

temperature cells

Answer 26

cells or pockets of air with different temperatures

Question 27

Structure function of temperature has same spatial dependence as

Answer 27

structure function of velocity

Question 28

C_T

Answer 28

structure parameter for temperature variations

Question 29

temperature fluctuations affect the

Answer 29

density of air and therefore change its refractive index

Question 30

optical effects produced by

Answer 30

variations in refractive index

Question 31

dependence of refractive index on

Answer 31

temperature and pressure

Question 32

local pressure fluctuations smoothed out at

Answer 32

speed of sound negligible effect compared with temperature fluctuations

Question 33

autocorrelation of pupil

Answer 33

area of overlap / total area

Question 34

wavefront distortions - phase shift

Answer 34

thi(x) = 2pi (Delta (nl) / lambda) =2pi (optical path length/lambda)

Question 35

including the effect of wavefront distortion over the pupil, P(X)=

Answer 35

Ψ(x)=e^iphi(x) over aperture 0 elsewhere (before we were just using Ψ=1 over aperture)

Question 36

bold font indicates that this represents

Answer 36

a generalised 2D spatial coordinate

Question 37

coherence function

Answer 37

optical transfer functions of the atmosphere as a result of turbulence at height h

Question 38

given that phi(x) obeys gaussian statistics and has a mean of zero, we can say

Answer 38

coherence func Bh(r)=e^-1/2 phase structure func

Question 39

steps to derive the phase structure function in terms of the strength of refractive index fluctuations

Answer 39

1. D(r) in terms of B(r), the covariance of phase 2. B(r) in terms of B_N(r,z) 3. D(r) in terms of D_N(r,z) via B_N(r,z) and B_phi(r) 4. D(r) in terms of C_N^2

Question 40

delta h much larger than the scale of fluctuation so can

Answer 40

extend integration to -inf to inf

Question 41

atmospheric transfer function

Answer 41

coherence function or optical transfer function of the atmosphere

Question 42

for observations at an angle from the zenith, the thickness of each layer is

Answer 42

increased by the factor sec(angle from zenith)

Question 43

for large telescopes, image filtering/point spread dominated by

Answer 43

atmospheric effects

Question 44

point spread function of the atmosphere

Answer 44

inverse FT of the atmospheric transfer function

Question 45

image intensity

Answer 45

convolution of geometric image with point spread of the atmosphere

Question 46

phase variation across the wavefront is described by

Answer 46

the phase structure function

Question 46

planar wavefronts from the distant source are distorted by

Answer 46

the turbulent layers of the atmosphere

Question 47

by applying the Kolomogorov model, one can

Answer 47

derive the dependence of structure function on atmospheric parameters, specifically the structure parameter

Question 48

structure parameter characterises the

Answer 48

strength of fluctuations in refractive index

Question 49

knowing the phase structure function, one can

Answer 49

derive the optical transfer function of the atmosphere

Question 50

taking the inverse fourier transform of the optical transfer function, one derives the

Answer 50

point spread function due to the atmosphere

Question 51

the observed image is the convolution of

Answer 51

the point spread function with the geometrical image of the star

Question 52

can rewrite the atmospheric transfer function as

Answer 52

B=exp[-3.44(r/r0)^5/3] ro is the fried parameter

Question 53

fried parameter is an indication of

Answer 53

the strength of the phase fluctuations

Question 54

beta

Answer 54

parameter is an angle in radians and is referred to as the seeing of the atmosphere

Question 55

beta is found by

Answer 55

finding FWHM of |h_atm|^2 gives beta = 0.98 lambda / ro

Question 56

seeing is the equivalent resolution one would get by

Answer 56

viewing through a diffraction limited telescope of diameter ro

Question 57

ro is typically about

Answer 57

10-20cm in the visible region of the spectrum

Question 58

regardless of the diameter of the primary mirror, resolution still

Answer 58

corresponds to that of a telescope with a 10cm aperture

Question 59

Wind Shear leads to turbulence and the generation of

Answer 59

turbulence cells

Question 60

the kolomogorov model describes the

Answer 60

variation of temperature and refractive index over a wide range of scales

Question 61

wavefront distortions occure due to

Answer 61

changes in the optical path length