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Turbulent Convection in the Laboratory

Turbulent Convection in the Laboratory. K.R. Sreenivasan New York University September 5, 2014. Gänseliesel. Interior convection is an important ingredient of solar physics I have been working on laboratory convection for many years

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Turbulent Convection in the Laboratory

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  1. Turbulent Convection in the Laboratory K.R. Sreenivasan New York University September 5, 2014 Gänseliesel

  2. Interior convection is an important ingredient of solar physics • I have been working on laboratory convection for many years • And have always thought controlled laboratory experiments might shed some light particularly on interior convection • Although you are all experts on the subject,I will explain some laboratory experiments and computer simulations which may have some bearing on your expertise.

  3. Basic Notation Nu depends on… Rayleigh number: Prandtl number: Aspect ratio: S ~ detailed shape ?? Nusselt number Nu = Q/(k DT/H) Q = vertical heat flux k = thermal conductivity of the fluid

  4. (exponent close to 1/3) Niemela, Skrbek, KRS & Donnelly, Nature404, 837 (2000) Slightly revised: Niemela & KRS, J. Low Temp. Phys.143, 163 (2006) [Pioneers: Threlfall (Cambridge); Libchaber, Kadanoff and coworkers (Chicago)]

  5. Nu ≈ 2.61010 Plasting & Kerswell (2003) “upperbound” 1010 Nu ≈ 2.9109 Kraichnan (1962) “ultimate state” 108 Nu = Q/(k DT/H) Nu ≈ 5106 (almost the same as the extrapolated value) 106 Seems consistent with Hanasoge, Duvall and KRS (2012) Convective processes are far from being optimally efficient. Ra=1024

  6. Urban et al. (2014) It is disappointing that we still don’t know with confidence the heat transport law at high Rayleigh numbers even in the simple case of Rayleigh-Bènard convection See also: Roche et al. (2010) Chillá & Schumacher (2012)

  7. Data on Rotating Convection our data

  8. (from Cheng et al. (2014), modified by me) Sun

  9. Nu/Nu0 exponent: 0.024 Rossby number W Rotating Convection Heat transport decreases only modestly with rotation, and this appears true for the conditions of the Sun

  10. “Giant Convection Cells Found on the Sun”---title of a Science paper “Large-scale toroidal cells a challenge to theories of the Sun”---a website declares

  11. The “mean wind” breaks symmetry, with its own consequences The mean wind large-scale circulation (“mean wind”) Large scale circulation (wind) the container For convection in a round cylinder, the mean wind precesses freely. For convection in a cubic box, the mean wind is constrained along a diagonal.

  12. The mean wind…with occasional reversals (KRS, Bershadskii & Niemela, PRE 65, 056306, 2000; Niemela et al. JFM, 2001) Segment of continuous 120-hour record; G = 1 Geomagnetic polarity reversals Glatzmaier, Coe, Hongre & Roberts, Nature 401, 885-890 (1999) The reversals become more frequent with increasing Ra.

  13. J.J. Niemela and KRS J. Fluid Mech.557, 411-422 (2006). 12.5 50 cm Ra = 1.9 x 109 G= 4 , H = 12.5 cm Aspect ratio effect

  14. Summary remarks High-Rayleigh-number convection experiments tantalize us with quantitative connections to the convection processes in the Sun: heat transport law, large-scale convection cells, rotation, etc. Alas, the connections seem to become weaker upon scrutiny, but there are reasons to be optimistic.

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