# Dry Boundary Layer Dynamics Outline Rayleigh vs. Reynolds number The Rayleigh-Bernard problem The Rayleigh-Bernard problem

## Dry Boundary Layer Dynamics Outline Rayleigh vs. Reynolds number The Rayleigh-Bernard problem The Rayleigh-Bernard problem

Maas, Ton, Contributing Editor has reference to this Academic Journal, PHwiki organized this Journal 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 Uni as long as mly 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 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 Linear stability analysis Critical Rayleigh number yields convection onset Steady rolls/polygons Horizontal scale ~ distance between plates The Rayleigh-Bernard problem Linear theory succeeds near onset regime Predicts aspect ratio in addition to critical Rayleigh number Further analysis requires lab-work or nonlinear techniques Laboratory explorations up to Ra = 1011

Lessons & Limitations Potential as long as convective regime shifts & nonlinear transitions. Atmosphere is Ra ~ 1017-1020 Lab results only go so far Appropriate surface BC as long as idealized ABL theory is constant flux (not constant temperature) 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 ( as long as some idealized cases) Thermally driven setup T = T0 Q Statistical steady state wB Buoyancy flux Volume-integrated buoyancy sink What can dimensional analysis tell us

Mechanically driven setup T = T0 M Statistical steady state wu Convective momentum flux (J/s/m2) Volume-integrated momentum sink What can dimensional analysis tell us Joint setup T = T0 M wu Momentum flux Volume-integrated momentum sink Q wB Buoyancy flux Volume-integrated buoyancy sink Whiteboard interlude

Hybrid idealized model results after asymptotic matching Theory: Obs: 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 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 in addition to sinks of buoyancy in addition to momentum Rotation Non-equilibrium E.g. coastal areas

Typical observed properties of a dry convecting boundary layer The Entrainment Zone Temperature inversion; boundary between convective layer in addition to 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 Next week . Adding moisture to equilibrium BL theory Ch. 13.2 Adding phase changes Stratocumulus-topped mixed layer models Ch 13.3

## Maas, Ton Contributing Editor

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