1. Richard Rotunno National Center for Atmospheric Research, USA Dynamical Mesoscale Mountain Meteorology

2. Dynamic Of or pertaining to force producing motion Meso-(intermediate)scale Length ~ 1-100km Time ~1h – 1day Mountain Meteorology Science of atmospheric phenomena caused by mountains

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

4. Thermally Driven Circulations Whiteman (2000)

5. Jane English Mt. Shasta Mountain Waves

6. Hawaii Mountain Lee Vortices East Space Shuttle

7. Orographic Precipitation

8. What do all these phenomena have in common? Buoyancy Displacement = density “env” = environment “par” = parcel

9. Buoyancy is acceleration To a good approximation... = pressure = vertical coordinate

10. Stability = “static stability” = “Brunt-Väisälä Frequency” = 0 for incompressible density-stratifed fluid

11. Air is a compressible fluid… Gas Law  1 st Law of Thermo (adiabatic)  in terms of Temperature = specific heat at constant pressure, R = gas constant for dry air

12. Air Parcel Behavior in a Stable Atmosphere Temperature z

13. Air Parcel Behavior in an Unstable Atmosphere Temperature z

14. in terms of potential temperature

15. Air Parcel Behavior in Stable or Unstable Atmosphere Potential Temperature z

16. Dynamic Mesoscale Mountain Meteorology Governing Equations

17. In terms of and ….. 1 st Law of Thermodynamics With previous definitions  Common form…

18. Newtons 2 nd Law With previous definitions  = frictional force/unit mass

19. Mass Conservation With previous definitions 

20. Summary of Governing Equations Conservation of momentum energy mass

21. Simplify Governing Equations I Conservation of momentum energy mass Neglect molecular diffusion 

22. Simplify Governing Equations II Conservation of momentum Boussinesq Approximation

23. Simplify Governing Equations III Conservation of energy With

24. Simplify Governing Equations IV Conservation of mass By definition  3 conditions for effective incompressibility (Batchelor 1967 pp. 167-169) = speed of sound = velocity, length, frequency scales

25. Summary of Simplified Governing Equations Conservation of momentum energy mass Still nonlinear (advection) Filtering  equations for mean / turbulent fluxes of B and u (see Sullivan lectures)

26. Summary -Buoyancy is a fundamental concept for dynamical mountain meteorology -Boussinesq approximation simplifies momentum equation -For most mountain meteorological applications, velocity field approximately solenoidal ( )