Chapter 5 - PBL MT 454 Material Based on Chapter 5 The Planetary Boundary Layer

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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5.1 Turbulence - 4

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Red = w’(t)Blue = ’(t)

5.1 Turbulence - 5

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5.1 Turbulence - 6

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5.1 Turbulence - 7

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5.1 Turbulence - 8

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5.1 Turbulence - 9

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5.1 Turbulence - 10

is the radiative heating rate.Note:

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5.1 Turbulence - 11

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5.1 Turbulence - 12

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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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5.2 TKE - 4

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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5.2 TKE - 6

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5.2 TKE - 7

= Frictional dissipation (molecular diffusion) > 0

TR = Redistribution by transport & pressure forces(no new TKE created)

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5.2 TKE - 8

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5.2 TKE - 9

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Analogue in large-scale flow:

How does this circulation lower center of mass?

5.2 TKE - 10

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

5.2 TKE - 12

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5.2 TKE - 13

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5.2 TKE - 14

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5.2 TKE - 15

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5.2 TKE - 16

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5.2 TKE - 17

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5.2 TKE - 18

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5.2 TKE - 19

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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)

5.3 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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(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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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

Slowing Vortex: Vortex CompressionSlowing Vortex: Vortex Compression

Ekman pumping reduces vorticity in free troposphere by vortex compression:

LLPBL top

Tropopause(w ≈ 0)


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

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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


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.


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)


Chapter 5 – Planetary Boundary Layer MT 454

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Documents

Chapter 5 - PBL MT 454 Material Based on Chapter 5 The Planetary Boundary Layer