Lecture 3: Nocturnal (Stably Stratified) Boundary Layer

; Stable Stratification – Ri > 0

Stable flows Richardson Number

Thermally Driven Slope Flows Reproduced from Mountain Meteorology (2000). Courtesy of Dr. Whiteman, PNNL.

Thermally Driven Valley flows Reproduced from Mountain Meteorology (2000). Courtesy of Dr. Whiteman, PNNL.

Salt Lake City

A Typical Urban Experiment

VTMX ASU Equipment

Theta profile in the valley

VTMX Measurements

Downslope – Field Data

Flow Analysis

Idealized Slope Flow Analysis Entrainment Coefficient, Ri =  bh/U 2 X X X X XXXXXX

Downslope flow - Pulsation Linearized governing equations with neglected flux divergence and the entrainment-rate, have oscillatory solution with the frequency or period

Downslope flow - Pulsation T=55 min ACS  = 4.7 deg: T=20 – 50 min SS  = 1.8 deg: T=50 – 130 min

Other Observations –the Riviera valley (Gorsel et al., ICAM/MAP proceedings, 2003) –Cobb Mountain (Doran and Horst, JAM, 20(4), , 1981) –Phoenix valley (Keon, Master Thesis, ASU, 1982) –Slope and ACS sites of the VTMX campaign in Salt Lake City (Doran et al., BAMS, 83(4), ). American Scientist 2004

Manin and Sawford’s (1978) Solutions (Combining with Briggs formula) For (  is the slope angle, the stabilizing buoyancy flux driving the flow and s the along-slope distance measured downward, h I integral scales of katabatic layer depth, U I velocity and Db I buoyancy )

Flow Velocity High Ri Entrainment is Unimportant Low Ri Entrainment is dominant

High Ri Entrainment is Unimportant

Low Ri Entrainment is dominant

Parameterization of Vertical Mixing PB D Flux Richardson Number Gradient Richardson Number Diffusion Coefficientse.g..

Flux versus Gradient Richardson Numbers J. Fluid Mech. 2002

Eddy Coefficients for the entire range of Rig; for Rig < 1 and for Rig > 1

Normalization of the eddy coefficients in the VTMX J. Atmospheric Sci., 2003

Eddy Diffusivity (Semi Empirical) for Rig < 1 and for Rig > 1

Eddy Diffusivity Ratio Inverse Prandtl Number J. Physical Oceanography 2001 Boundary layer Meteor. 2005

CROSS SECTION SW-NE 45 deg.

Temperature & Wind comparison

(averaged over 1- h, at 10 km inland versus simulations) RAMS uses Therry and Lacarrere’s (1983) parameterization (200x200 km domain, including Rome)

Entrainment -- Encroachment of nearby fluid across a boundary Boundary entrainment velocity (rate of propagation of a bounding surface due to turbulence). Entrainment Coefficient U Characteristic velocity Due to a normal mean flow Flux entrainment velocity (characteristic velocity the scales cross across an interface – boundary stationary).

Downslope flow - Entrainment Entrainment coefficientRichardson number

Entrainment Velocity Ellison and Turner, JFM, 1959

Ellison & Turner Results

Oquirrh Mountain

ASU Doppler Lidar

ENTRAINMENT

Entrainment Coefficient J. Fluid Mech. 2005, Mixing Transition -- above a certain critical Reynolds number, entrainment increases

Re vs. E

Hydraulic Adjustment

Steady state, small angle Ri < 1 Hydraulic Equation Ri > 1

a) α= (10˚, 20˚)b) α= (0˚, 26˚)

Applications Power plant emissions

Phoenix Terrain

Dispersion of Air Pollutants