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Coherent vortices in rotating geophysical flows Provenzale, ISAC-CNR and CIMA, Italy

Coherent vortices in rotating geophysical flows Provenzale, ISAC-CNR and CIMA, Italy Work done with: Annalisa Bracco, Jost von Hardenberg, Claudia Pasquero Babiano, E. Chassignet, Z. Garraffo, J. Lacasce, A. Martin, K. Richards J.C. Mc Williams, J.B. Weiss.

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Coherent vortices in rotating geophysical flows Provenzale, ISAC-CNR and CIMA, Italy

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  1. Coherent vortices • in rotating geophysical flows • Provenzale, ISAC-CNR and CIMA, Italy • Work done with: • Annalisa Bracco, • Jost von Hardenberg, • Claudia Pasquero • Babiano, E. Chassignet, Z. Garraffo, • J. Lacasce, A. Martin, K. Richards • J.C. Mc Williams, J.B. Weiss

  2. Rapidly rotating geophysical flows are characterized by the presence of coherent vortices: Mesoscale eddies, Gulf Stream Rings, Meddies Rotating convective plumes Hurricanes, the polar vortex, mid-latitude cyclones Spots on giant gaseous planets

  3. Vortices form spontaneously in rapidly rotating flows: Laboratory experiments Numerical simulations Mechanisms of formation: Barotropic instability Baroclinic instability Self-organization of a random field

  4. Rotating tank at the “Coriolis” laboratory, Grenoble • diameter 13 m, min rotation period 50 sec • rectangular tank with size 8 x 4 m • water depth 0.9 m • PIV plus dye • Experiment done by • Longhetto, L. Montabone, A. Provenzale, • C. Giraud, A. Didelle, R. Forza, D. Bertoni

  5. Characteristics of large-scale geophysical flows: Thin layer of fluid: H << L Stable stratification Importance of the Earth rotation

  6. Navier-Stokes equations in a rotating frame

  7. Incompressible fluid: Dr/Dt = 0

  8. Thin layer, strable stratification: hydrostatic approximation

  9. Homogeneous fluid with no vertical velocity and no vertical dependence of the horizontal velocity

  10. The 2D vorticity equation

  11. The 2D vorticity equation

  12. In the absence of dissipation and forcing, quasigeostrophic flows conserve two quadratic invariants: energy and enstrophy As a result, one has a direct enstrophy cascade and an inverse energy cascade

  13. Two-dimensional turbulence: the transfer mechanism As a result, one has a direct enstrophy cascade and an inverse energy cascade

  14. Two-dimensional turbulence: inertial ranges As a result, one has a direct enstrophy cascade and an inverse energy cascade

  15. Two-dimensional turbulence: inertial ranges As a result, one has a direct enstrophy cascade and an inverse energy cascade

  16. With small dissipation:

  17. Is this all ?

  18. Vortices form, and dominate the dynamics Vortices are localized, long-lived concentrations of energy and enstrophy: Coherent structures

  19. Vortex dynamics: Processes of vortex formation Vortex motion and interactions Vortex merging: Evolution of the vortex population

  20. Vortex dynamics: Vortex motion and interactions: The point-vortex model

  21. Vortex dynamics: Vortex merging and scaling theories

  22. Vortex dynamics: Introducing forcing to get a statistically-stationary turbulent flow

  23. Particle motion in a sea of vortices Formally, a non-autonomous Hamiltonian system with one degree of freedom

  24. Effect of individual vortices: Strong impermeability of the vortex edges to inward and outward particle exchanges

  25. Example: the stratospheric polar vortex

  26. Global effects of the vortex velocity field: Properties of the velocity distribution

  27. Velocity pdf in 2D turbulence (Bracco, Lacasce, Pasquero, AP, Phys Fluids 2001) Low Re High Re

  28. Velocity pdf in 2D turbulence Low Re High Re

  29. Velocity pdf in 2D turbulence Vortices Background

  30. Velocity pdfs in numerical simulations of the North Atlantic (Bracco, Chassignet, Garraffo, AP, JAOT 2003) Surface floats 1500 m floats

  31. Velocity pdfs in numerical simulations of the North Atlantic

  32. A deeper look into the background: Where does non-Gaussianity come from Vorticity is local but velocity is not: Effect of the far field of the vortices

  33. Effect of the far field of the vortices Background-induced Vortex-induced

  34. Vortices play a crucial role on Particle dispersion processes: Particle trapping in individual vortices Far-field effects of the ensemble of vortices Better parameterization of particle dispersion in vortex-dominated flows

  35. How coherent vortices affect • primary productivity in the open ocean • Martin, Richards, Bracco, AP, Global Biogeochem. Cycles, 2002

  36. Oschlies and Garcon, Nature, 1999

  37. Equivalent barotropic turbulenceNumerical simulation with a pseudo-spectral code

  38. Three cases with fixed A (12%) and I=100: “Control”: NO velocity field (u=v=0) (no mixing) Case A: horizontal mixing by turbulence, upwelling in a single region Case B: horizontal mixing by turbulence, upwelling in mesoscale eddies

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