Chapter 3 (notebook)

Question 1

Turbulent statistics differ case by case because of

Answer 1

• surface forcing (surface temprature)
• geostrophic wind (impotant for wind shear)
• sounding (profile)

Question 2

employing typical characteristic length, time and velocity scale enable us to

Answer 2

derive governing equations in non-dimentional form

Question 3

scaling variables

Answer 3

• variables in combination to form new variable (ex: richardsons number Ri)
• variables having simple dimensional units (velocity, length, time)
  
  • related to important scales of motion in eddies

Question 4

length scales

Answer 4

• Zi: altitude of the capping inversion (length of BL for UNSTABLE and NEUTRAL)
• Zo (aerodynamic roughness length): indicates the roughness of the surface
  
  • in the SL within 5% of the BL
• L (Obukhau lenght): NON NEUTRAL at SL
  
  • the absolute value of L indicates the height bellow which mechanically generated turbulences dominate

Question 5

L equation

Answer 5

u³_*: friction velocity

k: von kum. constant = 0.4

Tv: virtual temperature

w’g’: vertical turbulent heat flux at the surface

Question 6

velocity scales:

Answer 6

• Deardorff velocity scale (w^*): for charactarising the turbulent mixing due to free convection in an unstable boundary layer
  
  • typical magnitude (w^*)= 1 m/s (average updraft velocity of thermals)
    
    • thermals are small eddies that form during daytime
• friction velocitu (u^*): applicable to NEUTRAL conditions in the SL

Question 7

w^* equation

Answer 7

Zi : PBL height

Tv: virtual temperature (depend on temperaure and moisture)

w’ O-‘: vertical heat flux

Question 8

u^* equation

Answer 8

u’w’ + v’w’: kinamatic momentum fluxes (vertical fluxes of u and v momentums (covarience))

Question 9

time scale for CBL

Answer 9

zi: PBL height

w^*: PBL velocity

Question 10

time scale for NEUTRAL SL

Answer 10

z: SL height

u^*: friction velocity (velocity of surface layer)

Question 11

summerize the scales

Answer 11

• length
  
  • BL: Zi
  • SL:
    
    • Z0 (aerodynamic/ describe roughness)
    • L (the height bellow which mechanical turbulences dominate)
• velocity
  
  • BL: w^*
  • SL: u^*
• Time
  
  • BL: t*
  • SL:t*SL

Question 12

the scaling laws describe

Answer 12

the functional relationship between scaling variables

example: wind profile law for BL

Question 13

wind profile law

(AND EQUATION)

Answer 13

wind speed varies near logarithmically with height in the SL

• Wind speed becomes zero near the ground due to FRICTIONAL DRAG
• wind increase with height due to PGF

Question 14

Wind profile law when plotted on semilog paper

Answer 14

• concave up for UNSTABLE BL
• straight line in neutral
• concave down for stable BL

IT increases non linearly

rate of change is different in different conditions (of stability)

Question 15

Air stability

Answer 15

Tendancy (veritcal mixing tendancy) in responce to a small disturbance

• unstable: atm applifies and produce turbulances by BUOYANCY
• neutral: (wind shear) neutral conditions amplify due to:
  
  • wind shear and
  • viscous force
    to produce turbulences (Shear turbulences/mechanical turb)
• stable: Richardson numbe <0.25 to produce mechanical turb

Question 16

buoyance and turbulent production

Answer 16

• positive: UNSTABLE warm air rise
  
  • generate turbulences
• Negative:
  
  • destroy turbulences

Question 17

stability criteria based on potential temperature

Answer 17

• positive: stable
• negative: unstable
• =0: neutral

Question 18

to quantify the stability effects of the atmosphere two scaling variables:

Answer 18

• The richardon no
• the monin obukhov stability parameter

Question 19

according to richardson number turbulent production depends on

Answer 19

• temperature stratification
• strength of winds

Question 20

flux richardson number (Rf):

Answer 20

express the comined effect

• buoyancy can produce or destroy
• shear production of turbulence

Question 21

flux richardson number equation:

Answer 21

term ignored because its small magnitude in the surface layer compared to u’w’….

Question 22

stability criteria based on Rf

Answer 22

• Positive: STABLE
  
  • shear prod > buoyancy prod
    
    • buoyancy distroys turb
• =0: neutral
• negative: unstable
  
  • shear prod < buoyancy prod
    
    • both contribute to turbulences

Question 23

how does buoyance and shear production change in convective boundary layer?

Answer 23

• Bouyancy term decreases linearly with ht
• Shear production term is highest near the surface and decrease more rapidly with ht (non linear)
  
  • highest near the surface due to friction

Question 24

Monin Obukhav stability parameter

Answer 24

donated by ع

is based on the fact that the vertical variation of

• mean flow and
• turbulent charactaristics

in SL depend on the surface momentum fluxes, measured by

• friction velocity u*
• buoyancy flux
• height z

A combination of these three gives (ع)

Question 25

equation of ع varies between

Answer 25

عvaries between: * +5: STABLE * -5: unstable L vaires between: * positibe: STABLE * negative: unstable