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Plumes in turbulent convection

Plumes in turbulent convection. A short summary of convection Clustering of convective plumes The Prandtl problem. A. Provenzale, ISAC-CNR Torino and CIMA, Savona. Rayleigh-Benard convection:. Rayleigh-Benard convection:. Important parameters: R = g a D 3 D T / nk s = n / k

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Plumes in turbulent convection

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  1. Plumes in turbulent convection A short summary of convection Clustering of convective plumes The Prandtl problem A. Provenzale, ISAC-CNR Torino and CIMA, Savona

  2. Rayleigh-Benard convection:

  3. Rayleigh-Benard convection: Important parameters: R = ga D3DT / nk s = n / k a = L / D

  4. Rayleigh-Benard convection: If R < Rcritconduction T(x,y,z,t)=Tcond(z) (u,v,w)=(0,0,0) If R > Rcritconvection T= Tcond + q (u,v,w) non zero

  5. Rayleigh-Benard convection:

  6. Rayleigh-Benard convection:

  7. Rayleigh-Benard convection: Linear stability analysis Weakly nonlinear expansions “Turbulent” convection

  8. Convective patterns: Photo by Hezi Yizhaq, Sede Boker, Negev desert

  9. Turbulent convection (s=0.71, a=2p, R=107)

  10. Turbulent convection (R=106):

  11. Turbulent convection (s=0.71, a=2p, R=107)

  12. Turbulent convection (s=0.71, a=2p, R=107)

  13. Turbulent convection (s=0.71, a=2p, R=107)

  14. Turbulent convection: Statistical properties and transition from soft to hard turbulence Scaling of the heat transport: Nu vs R Nu = 1 + < wq >

  15. Turbulent convection: Dynamics of convective plumes

  16. Turbulent convection: Formation of large-scale structure and clustering of convective plumes

  17. Turbulent convection: Formation of large-scale structure and mean shear (wind) Krishnamurti and Howard (1981) Massaguer, Spiegel and Zahn (1992) Elperin, Kleeorin, Rogachevskii and Zilitinkevish (2003) Hartlep, Tilgner and Busse (2003) Parodi, von Hardenberg, Passoni, Spiegel, Provenzale (2003)

  18. Clustering of convective plumes:

  19. Clustering of convective plumes:

  20. Clustering of convective plumes:

  21. Clustering of convective plumes:

  22. Clustering of convective plumes:

  23. Clustering of convective plumes:

  24. Turbulent RB convection undergoesa process of inverse energy cascadefrom the scales of the linear instabilityto the largest scales (box size)Once reached an approximate k-5/3 spectrum,the system becomes statistically stationary(is there an upper scales where the cascade stops?)

  25. It is not a mean shear ( k = 0 )but rather a circulation at the largest scalesTurbulent convection is either non-stationaryor dominated by finite-domain effectsThe large-scale structures areclusters of individual plumes

  26. What causes the clustering ?

  27. Option 1: attraction of same-sign plumes

  28. Option 2: the interplay of the lower and upper boundary layersby the agency of plumes

  29. Other view:The fixed-flux instabilityof a coarse-grained field( with Reff << R )

  30. Is RB convection a good model fornatural convective processes ?Yes, as a first step (e.g. plumes)No, for proper understanding

  31. Most natural convective flowshave no up-down symmetryReasons:non-Boussinesqnon symmetric boundary conditions

  32. Penetrative convection

  33. Penetrative convection

  34. Solar granulation

  35. Tropical convective precipitation GATE 1 data set. D= 4 km, L=256 km, Dt=15 min

  36. “True” dynamics:turbulent, moist, non-Boussinesq precipitating convectionCan we find a simplified dynamical model ?

  37. The Prandtl problem Prandtl (1925)

  38. The Prandtl problem A Parodi, KA Emanuel, A Provenzale (2003)

  39. The Prandtl problem

  40. The Prandtl problem Heat flux

  41. The Prandtl problem Average temperature profile

  42. The Prandtl problem

  43. The Prandtl problem

  44. The Prandtl problem

  45. The Prandtl problem

  46. The Prandtl problem P(x,y,t) is taken as a proxy for convective rainfall

  47. The Prandtl problem

  48. The Prandtl problemstill a long way to go,but the results are intriguing.Linear stability, weakly nonlinear analysis,properties of the turbulent plumes,particle transport.And, then, addition of moisture.

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