material based on chapter 5

Chapter 5 - PBLMT 454Material Based on Chapter 5The Planetary Boundary Layer

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MT 454Class SlideThe Planetary Boundary LayerChapter 5 - PBL

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MT 454Class SlideChapter 5 - PBL

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5.1 Turbulence - 1MT 454Class Slide

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5.1 Turbulence - 2

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MT 454Class Slide5.1 Turbulence - 3

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MT 454Class SlideRed = w(t)Blue = q(t)5.1 Turbulence - 5

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is the radiative heating rate.Note:

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MT 454Class Slide5.2 TKE - 1

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Derive TKE EquationSimilarly for v and w5.2 TKE - 5


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= Frictional dissipation (molecular diffusion) > 0TR = Redistribution by transport & pressure forces(no new TKE created)

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MT 454Class SlideAnalogue in large-scale flow:How does this circulation lower center of mass?5.2 TKE - 10

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BPL - TKE increase for unstable PBLw < 0 < 0w > 0 > 0zIf PBL heated from below, then (z):BPL > 0Primary energy source for unstable PBL(In stable PBL, BPL term gives energy loss)5.2 TKE - 11

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BPL - Side NotezMore precise (z) when well-mixed PBL is fully developed.Homogeneous, well-mixed layer

Unstable layer maintained near surface by surface heating5.2 TKE - 12

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MT 454Class Slide5.3 PBL momentum

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MT 454Class Slide(See figures)5.3 PBL momentum

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MT 454Class Slide(Add friction? See Figure 5.3 in Holton.)5.3 PBL momentum

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MT 454Class Slide(See Figures 5.4 and 5.5 in Holton.)5.3 PBL momentum

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MT 454Class Slide(See Fig. 5.5 in Holton + additional figures.)5.3 PBL momentum

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MT 454Class Slide5.4 Spin Down

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Horizontal Wind in PBLIn PBL, wind component toward lower pressure L giving horizontal convergence around low center5.4 Spin Down

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Vertical Wind in PBLMass convergence around low pressure L gives upward motion over low. Effect on vortex?PBL top5.4 Spin Down

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Slowing Vortex: Vortex CompressionEkman pumping reduces vorticity in free troposphere by vortex compression:LPBL topTropopause(w 0)5.4 Spin Down

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Slowing Vortex: Conservation of Angular MomentumAlternatively, outward secondary circulation in free troposphere slows vortex by conservation of angular momentumLPBL top5.4 Spin Down

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Spin-Down TimeUse H = 10 km and previous values for other constants:Then, e ~ 7 days

Longer than synoptic time scaleA reason why PBL was ignored when introducing quasi-geostrophic motionte = H | 2/(fKm) |1/2 5.4 Spin Down

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Ekman-Pumping: TorqueOutward (secondary ) flow gives torque against primary flow by Coriolis force.L5.4 Spin Down

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Ekman-Pumping EffectivenessEkman pumping more effective than diffusion:Works not by mixing high/low vorticity airRather by forcing mass divergence in free troposphereAngular momentum = (moment of intertia) x (rotation rate) Outward mass movement => increased moment of inertia=> reduced rotation to conserve angular mom.5.4 Spin Down

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Baroclinic Atmosphere?If atmosphere baroclinic (not barotropic):Circulation confined closer to surfaceShear created in vortex => more damping closer to surfaceShear balanced by induced T: uplifted air at center cooler than air at vortex edgeFinal note: all rests on Ekman PBL Qualitatively OK Gives correct approximate physics (cross isobar flow)5.4 Spin Down

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Chapter 5 Planetary Boundary LayerMT 454END

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material based on chapter 5

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