1. Chapter 13.1: flow over isolated peaks

2. 13.1: 3D perspective: What controls whether the flow goes around or over a mountain obstacle?

3. Flow over isolated peaks wind ridge across wind ridge along wind Fr>1 Fr<1 ND mountain height stagnation limit Fig. 13.2 linear mountain waves

4. First, below the stagnation limit: linear mountains waves forced by isolated peaks (12.2) Fig. on right shows the non-dimensional vertical displacement at 4 ND levels [0,  /8,  /4,  /2] for Fr=10 (linear theory, analytical solution) Smith (1980) Fig. above shows the vertical velocity (blue up, red down) at the non-dimensional level  /2, for Fr >> 1. (numerical solution) wind l=vertical wave number solid: mtn outline compare to 3D Fig in upper left down up down up down up down up

5. 3D trapped waves triggered by a local obstacle are of 2 types: ship

6. Second, above the stagnation limit: 3D lee vortices wind (arrows), isentropic vorticity (color), and vortex tubes (purple) on an isentropic surface

7. 3D lee vortices Three mechanisms have been proposed: a.boundary-layer separation (friction) (e.g. Hunt and Snyder 1980) b.potential vorticity generation by friction (Smith 1989, Schär and Smith 1993) c.tilting of baroclinically-generated vorticity (Smolarkiewicz & Rotunno 1989) (can be inviscid)

8. lee vortices generation: (a) boundary-layer separation side view plan view N = node (no flow) S = saddle point (deformation center) a= BL attachment s = BL separation detached BL air

9. lee vortices around isolated peaks: (b) PV generation Schematic depiction of PV generation on an isentropic surface in quasi-steady flow past an isolated mountain for (a) flow over obstacle with wave breaking and (b) flow around obstacle with flow splitting. The thin lines are streamlines, and the gray shading highlights region of Bernouilli (energy) deficit in the wake. White arrows indicate fluxes of PV. The wave-breaking region in (a) is hatched. The terrain intersecting the isentropic surface in (b) is shaded dark gray. Schär and Durran (1997) Potential Vorticity generated by friction along terrain’s side slopes wind friction F curl of friction mountain outline B is the total energy (potential & kinetic) Some of this energy is lost in the wake of the obstacle due to friction & wave breaking shaded: region of Bernouilli deficit PV flux vector blocking mtn mountain outline

10. steady splitting flow, with a pair of PV anomalies in the lee ND mountain height = 3  Fr=1/3 constant high stability (N= 0.01 s -1 ) half-domain simulation (symmetric other half is copied for completeness) Schär and Durran (1997) flow around isolated peaks: sensitivity to small perturbations well-mixed such flow may produce a banner cloud plan view vertical transect

11. steady splitting flow, with a pair of PV anomalies in the lee ND mountain height = 3  Fr=1/3 constant high stability (N= 0.01 s -1 ) half-domain simulation (symmetric other half is copied for completeness) Schär and Durran (1997) exactly the same, but full-domain simulation: Note the instability of the wake vortices to small, asymmetric perturbations. flow around isolated peaks: sensitivity to small perturbations well-mixed oscillating vortex street

12. unstable wake vortices being shed off Jan Mayen Island, Greenland Sea von Kármán vortex street

13. von Kármán vortex streets

14. bell-shaped mtn, plan view over near- surface flow Fr > 1: flow over Fr < 1: flow around, increasingly blocked Fr < 1/3: symmetric lee vortices wind (c) tilting of baroclinically- generated vorticity Smolarkiewicz & Rotunno (1989) Fr=2.2 Fr=0.06Fr=0.22 Fr=0.7 wind

15. plan view vertical transect wind (c) tilting of baroclinically- generated vorticity Smolarkiewicz & Rotunno (1989) Fr=2.2 Fr=0.22 wind

16. vertical displacement (solid: up, dashed: down) (c) tilting of baroclinically- generated vorticity Smolarkiewicz & Rotunno (1989) Fr=2.2 Fr=0.06Fr=0.22 Fr=0.7 height: z/h=0.2 updown wind updown

17. E-W vertical transect thru central plane (c) tilting of baroclinically- generated vorticity Smolarkiewicz & Rotunno (1989) Fr=2.2 Fr=0.06Fr=0.22 Fr=0.7 wind

18. (c) tilting of baroclinically- generated vorticity Smolarkiewicz & Rotunno (1989) upward (downward) view from upwind side close-up view of lee vortices, for Fr=0.22 isentropic surface intersecting terrain purple lines: vortex lines blue: uplift (cold) red: depression (warm) wind

19. isentropic surface, colored by buoyancy (ie. vertical displacement). The red and purple lines are select vortex tubes on the isentropic surface. Black vectors are surface winds. Epifanio & Rotunno (2005) Baroclinically generated vorticity check solenoidal vorticity generation along mountain sides