dry boundary layer dynamics
DESCRIPTION
Dry Boundary Layer Dynamics. Idealized theory Shamelessly ripped from Emanuel Mike Pritchard. Outline. Highlights of Rayleigh-Bernard convection Similarity theory review (2.1) Application to semi-infinite idealized dry boundary Uniformly thermally (buoyancy) driven only - PowerPoint PPT PresentationTRANSCRIPT
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Dry Boundary Layer Dynamics
Idealized theoryShamelessly ripped from Emanuel
Mike Pritchard
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Outline Highlights of Rayleigh-Bernard convection Similarity theory review (2.1) Application to semi-infinite idealized dry boundary
Uniformly thermally (buoyancy) driven only Mechanically (momentum) driven only Thermally + Mechanically driven
The “Monin-Obunkov” length scale Characteristics of a more realistic typical dry
atmospheric boundary layer
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Rayleigh vs. Reynolds number Laminar case
Re = Ra / Turbulent case
Re2 = (Fr)(Ra) /
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The Rayleigh-Bernard problem Parallel-plate convection in the lab
Governing non-dimensional parameter is
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Linear stability analysis Critical Rayleigh number yields convection onset Steady rolls/polygons Horizontal scale ~ distance between plates
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The Rayleigh-Bernard problem Linear theory
succeeds near onset regime
Predicts aspect ratio and critical Rayleigh number
Further analysis requires lab-work or nonlinear techniques
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Laboratory explorations… up to Ra = 1011
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Lessons & Limitations Potential for convective
regime shifts & nonlinear transitions.
Atmosphere is Ra ~ 1017-1020 Lab results only go so far
Appropriate surface BC for idealized ABL theory is constant flux (not constant temperature)
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Similarity theory Applicable to steady flows only, can’t know in advance if
it will work.
Posit n governing dimensional parameters on physical grounds
Flow can be described by n-k nondimensional parameters made out of the dimensional ones
Allows powerful conclusions to be drawn (for some idealized cases)
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Thermally driven setup
T = T0
QStatistical steady state…
w’B’
Buoyancy flux
Volume-integrated buoyancy sink
What can dimensionalanalysis tell us?
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Mechanically driven setup
T = T0
MStatistical steady state…
w’u’
Convective momentum flux (J/s/m2)
Volume-integrated momentum sink
What can dimensionalanalysis tell us?
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Joint setup
T = T0
M
w’u’
Momentum flux
Volume-integrated momentum sink
Q
w’B’
Buoyancy flux
Volume-integrated buoyancy sink
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Whiteboard interlude…
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Hybrid idealized model resultsafter asymptotic matching…
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Theory:
Obs:
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Summary of theoretical results Thermally driven
Convective velocity scales as z1/3
Mechanically driven Convective velocity independent of height
Hybrid Mechanical regime overlying convective regime Separated at Monin-Obunkov length-scale Matched solution is close but not a perfect match to the
real world
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Things that were left out of this model Mean wind Depth-limitation of convecting layer
Due to static stability of free atmosphere Height-dependent sources and sinks of
buoyancy and momentum Rotation Non-equilibrium
E.g. coastal areas
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Typical observed properties of a dry convecting boundary layer
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The Entrainment Zone Temperature inversion; boundary between
convective layer and “free atmosphere” Monin-Obukov similarity relations break
down Buoyancy flux changes sign
Forced entrainment of free-atmosphere air I.e. boundary layer deepens unless balanced by
large-scale subsidence
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Next week….? Adding moisture to equilibrium BL theory
Ch. 13.2 Adding phase changes
Stratocumulus-topped mixed layer models Ch 13.3