Richard Rotunno National Center for Atmospheric Research, USA Dynamic Mesoscale Mountain Meteorology Lecture 2: Thermally Driven Circulations.

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Richard Rotunno National Center for Atmospheric Research, USA Dynamic Mesoscale Mountain Meteorology Lecture 2: Thermally Driven Circulations

Topics Lecture 1 : Introduction, Concepts, Equations Lecture 2: Thermally Driven Circulations Lecture 3: Mountain Waves Lecture 4: Mountain Lee Vortices Lecture 5: Orographic Precipitation

Thermally Driven Circulations Whiteman (2000)

Summary of Simplified Governing Equations Conservation of momentum energy mass

Vorticity Batchelor (1967, Chapters 2 and 5)

Baroclinicity

Relation of vorticity and velocity in 2D by definition mass conservation heavier lighter Example: Localized Vorticity

Slope Flow Heat Input

Whiteman (2000) Slope Flow Feels Good

Bernhard Muehr photos, Karlsruher Wolkenatlas © 2000 Clouds Make Slope Flow Visible

Whiteman (2000) Slope Flow Theory

Modify Simplified Governing Equations Conservation of momentum energy mass

Prandtl’s Model Inifinitely long slope/Constant Stratification Heat Flows to the Cool Ground

Governing Equations momentum energy mass

Governing equations in slope coordinates momentum energy mass

Look for solutions with momentum energy combine 1 st and 3 rd equations  / boundary conditions

Solution

Example 1km

VTMX, Salt Lake Valley, UT Whiteman photos

Topographic map Thomas Haiden Sharon Zhong Eric Skyllingstad

Potential temperature soundings, 2 Oct K temp deficit in m temp deficit strengthens with downslope distance coldest air at lowest elevations

Compare / Prandtl Theory 200m

Downslope wind comp soundings, 2 Oct 2000 jet profile at all sites max velocity approx 15m above slope max velocity increases with downslope distance max velocity reaches 7 m/s downslope flow layer extends to ~150 m above slope volume(mass) flux increase with downslope distance Mass flux = 300 kg/s/m * 20 km = 6000 t/s (22 km 3 /h)

Compare / Prandtl Theory 200m

Further Complications

Downslope flows leave the slope… Whiteman (2000)

Multi-Scale Topography Whiteman (2000)

Along-valley flows Valley winds are closed circulations that attempt to equalize horizontal pressure gradients that are built up hydrostatically between the valley and plain caused by the greater temperature range of a column of air within the valley compared to a similar column of air over the plain at the same elevation. Whiteman (2000)

Summary -Baroclinity (Buoyancy Gradient) Produces Motion -Ambient Stratification and Turbulent Mixing Modulates Motion Warning Label: Prediction for slope/valley winds for any real valley requires knowledge of insolation, heat absorption, surface characteristics (e.g. vegetation), large-scale weather conditions. (Whiteman 2000)