chapter 5 - pbl mt 454 material based on chapter 5 the planetary boundary layer
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Chapter 5 - PBL MT 454
Material Based on Chapter 5
The Planetary Boundary Layer
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The Planetary Boundary Layer
Chapter 5 - PBL
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Chapter 5 - PBL
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Chapter 5 - PBL
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Chapter 5 - PBL
5.1 Turbulence - 1
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5.1 Turbulence - 2
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5.1 Turbulence - 3
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Red = w’(t)Blue = ’(t)
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is the radiative heating rate.Note:
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5.1 Turbulence - 11
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5.1 Turbulence - 13
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5.2 TKE - 1
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5.2 TKE - 2
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5.2 TKE - 3
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Derive TKE EquationDerive TKE Equation
Similarly for vSimilarly for v’’ and w and w’’Similarly for vSimilarly for v’’ and w and w’’5.2 TKE - 5
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= Frictional dissipation (molecular diffusion) > 0
TR = Redistribution by transport & pressure forces(no new TKE created)
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Analogue in large-scale flow:
How does this circulation lower center of mass?
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BPL - TKE increase for unstable PBLBPL - TKE increase for unstable PBL
w’ < 0
’ < 0
w’ > 0
’ > 0
z
If PBL heated from below, then (z):
BPL > 0
Primary energy source for unstable PBL
(In stable PBL, BPL term gives energy loss)5.2 TKE - 11
BPL - Side NoteBPL - Side Note
z
More precise (z) when well-mixed PBL is fully developed.
Homogeneous, well-mixed layer
Unstable layer maintained near surface by surface heating
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5.3 PBL momentum
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5.3 PBL momentum
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5.3 PBL momentum
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5.3 PBL momentum
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(See figures)
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5.3 PBL momentum
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5.3 PBL momentum
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5.3 PBL momentum
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5.3 PBL momentum
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5.3 PBL momentum
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5.3 PBL momentum
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5.3 PBL momentum
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(Add friction? See Figure 5.3 in Holton.)
5.3 PBL momentum
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5.3 PBL momentum
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5.3 PBL momentum
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5.3 PBL momentum
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5.3 PBL momentum
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5.3 PBL momentum
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5.3 PBL momentum
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5.3 PBL momentum
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5.3 PBL momentum
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5.3 PBL momentum
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5.3 PBL momentum
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5.3 PBL momentum
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5.3 PBL momentum
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5.3 PBL momentum
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5.3 PBL momentum
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5.3 PBL momentum
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(See Figures 5.4 and 5.5 in Holton.)
5.3 PBL momentum
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5.3 PBL momentum
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5.3 PBL momentum
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5.3 PBL momentum
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5.3 PBL momentum
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5.3 PBL momentum
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5.3 PBL momentum
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5.3 PBL momentum
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5.3 PBL momentum
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5.3 PBL momentum
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(See Fig. 5.5 in Holton + additional figures.)
5.3 PBL momentum
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5.4 Spin Down
Horizontal Wind in PBLHorizontal Wind in PBL
In PBL, wind component toward lower pressure …
LL
v g
v
… giving horizontal convergence around low center
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Vertical Wind in PBLVertical Wind in PBL
Mass convergence around low pressure …
LL
… gives upward motion over low. Effect on vortex?
PBL top
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5.4 Spin Down
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5.4 Spin Down
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5.4 Spin Down
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5.4 Spin Down
Slowing Vortex: Vortex CompressionSlowing Vortex: Vortex Compression
Ekman pumping reduces vorticity in free troposphere by vortex compression:
LLPBL top
Tropopause(w ≈ 0)
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Slowing Vortex: Conservation of Angular MomentumSlowing Vortex: Conservation of Angular Momentum
Alternatively, outward secondary circulation in free troposphere slows vortex by conservation of angular momentum
LLPBL top
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5.4 Spin Down
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5.4 Spin Down
Spin-Down TimeSpin-Down Time
Use H = 10 km
and previous values for other constants:
Then, e ~ 7 days
• Longer than synoptic time scale
• A reason why PBL was ignored when introducing quasi-geostrophic motion
e = H | 2/(fKm) |1/2
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5.4 Spin Down
Ekman-Pumping: TorqueEkman-Pumping: Torque
Outward (secondary ) flow gives torque against primary flow by Coriolis force.
LL
v 1
v 2
fˆ k v 2
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Ekman-Pumping EffectivenessEkman-Pumping Effectiveness
Ekman pumping more effective than diffusion:
• Works not by mixing high/low vorticity air
• Rather by forcing mass divergence in free troposphere
Angular momentum = (moment of intertia) x (rotation rate)
Outward mass movement
=> increased moment of inertia
=> reduced rotation to conserve angular mom.
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Baroclinic Atmosphere?Baroclinic Atmosphere?
If atmosphere baroclinic (not barotropic):
• Circulation confined closer to surface
• Shear created in vortex => more damping closer to surface
• Shear balanced by induced T: uplifted air at center cooler than air at vortex edge
Final note: all rests on Ekman PBL
• Qualitatively OK
• Gives correct approximate physics (cross isobar flow)
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Chapter 5 – Planetary Boundary Layer MT 454
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