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Planetary Boundary Layer > Chapter 3 (notebook) > Flashcards

Chapter 3 (notebook) Flashcards

1
Q

Turbulent statistics differ case by case because of

A
  • surface forcing (surface temprature)
  • geostrophic wind (impotant for wind shear)
  • sounding (profile)
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2
Q

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

A

derive governing equations in non-dimentional form

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3
Q

scaling variables

A
  • 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
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4
Q

length scales

A
  • 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
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5
Q

L equation

A

u3*: friction velocity

k: von kum. constant = 0.4

Tv: virtual temperature

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

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6
Q

velocity scales:

A
  • 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
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7
Q

w* equation

A

Zi : PBL height

Tv: virtual temperature (depend on temperaure and moisture)

w’ O-‘: vertical heat flux

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8
Q

u* equation

A

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

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9
Q

time scale for CBL

A

zi: PBL height

w*: PBL velocity

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10
Q

time scale for NEUTRAL SL

A

z: SL height

u*: friction velocity (velocity of surface layer)

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11
Q

summerize the scales

A
  • 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
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12
Q

the scaling laws describe

A

the functional relationship between scaling variables

example: wind profile law for BL

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13
Q

wind profile law

(AND EQUATION)

A

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
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14
Q

Wind profile law when plotted on semilog paper

A
  • 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)

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15
Q

Air stability

A

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
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16
Q

buoyance and turbulent production

A
  • positive: UNSTABLE warm air rise
    • generate turbulences
  • Negative:
    • destroy turbulences
17
Q

stability criteria based on potential temperature

A
  • positive: stable
  • negative: unstable
  • =0: neutral
18
Q

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

A
  • The richardon no
  • the monin obukhov stability parameter
19
Q

according to richardson number turbulent production depends on

A
  • temperature stratification
  • strength of winds
20
Q

flux richardson number (Rf):

A

express the comined effect

  • buoyancy can produce or destroy
  • shear production of turbulence
21
Q

flux richardson number equation:

A

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

22
Q

stability criteria based on Rf

A
  • Positive: STABLE
    • shear prod > buoyancy prod
      • buoyancy distroys turb
  • =0: neutral
  • negative: unstable
    • shear prod < buoyancy prod
      • both contribute to turbulences
23
Q

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

A
  • 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
24
Q

Monin Obukhav stability parameter

A

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)

25
Q

equation of ع

varies between

A

عvaries between:

  • +5: STABLE
  • -5: unstable

L vaires between:

  • positibe: STABLE
  • negative: unstable

Planetary Boundary Layer (10 decks)

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