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Richard Rotunno

Dynamic Mesoscale Mountain Meteorology Lecture 4: Mountain Lee Vortices. Richard Rotunno. National Center for Atmospheric Research , USA . Topics. Lecture 1 : Introduction, Concepts, Equations Lecture 2: Thermally Driven Circulations Lecture 3: Mountain Waves

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Richard Rotunno

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  1. Dynamic Mesoscale Mountain Meteorology Lecture 4: Mountain Lee Vortices Richard Rotunno National Center for Atmospheric Research , USA

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

  3. Mountain Lee Vortices momentum

  4. Hawaii H=3km East

  5. Smith and Grubišić(1993)

  6. Numerical Simulations Smolarkiewicz, Rasmussen & Clark (1988)

  7. Laboratory Simulations Hunt and Snyder (1980)

  8. Idealized Numerical Simulations Smolarkiewicz and Rotunno (1989a)

  9. Source of Vorticity? momentum energy continuity vorticity Assume Newtonian fluid with constant viscosity

  10. Frictional Contact with Mountain

  11. Baroclinicity produces horizontal vorticity tilting produces vortex pair Smolarkiewicz and Rotunno (1989a)

  12. Vortex Lines on B surface Smolarkiewicz and Rotunno (1989a)

  13. A different interpretation: Creation of potential vorticity q defines lee vortex (Smith 1989) upstream downstream

  14. Initial Value Problem: Vortex formation precedes mixing time Smolarkiewicz and Rotunno (1989b)

  15. Recent Work Epifanio and Rotunno (2005,JAS) • New high–resolution simulations • Zero stress on surface rigorously enforced • Contribution to total flow from 3D vorticity deduced

  16. Two types of wake formation Wave Breaking N,U constant wake Upstream blocking 2-layer N with U constant wake 0 -2 2 2D Obstacle / 3D y-periodic domain

  17. Case with Upstream Blocking • Following graphs shows evolution of a • surface of B=constant • Flow induced by 3D vorticity field

  18. All the vortical flow originates with baroclinicty • For low aspect ratio obstacles H / L << 1 • almost all of the rotational flow induced by the horizontal • vorticity components small H/L inversion full vorticity inversion

  19. Summary • Baroclinicity is a fundamental source of lee-vortex vorticity in stratified flow • Numerical simulations of an initial-value problem show vortex formation as an adjustment under gravity of constant density surfaces displaced by the motion of the obstacle relative to the fluid.

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