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

4. Niemela, Skrbek, KRS & Donnelly, Nature 404, 837 (2000) Slightly revised: Niemela & KRS, J. Low Temp. Phys. 143, 163 (2006) [Pioneers: Threlfall (Cambridge); Libchaber, Kadanoff and coworkers (Chicago)] (exponent close to 1/3)

5. 10 24 Ra=10 24 10 6 10 8 Nu ≈ 5  10 6 Nu ≈ 2.9  10 9 Nu ≈ 2.6  10 10 (almost the same as the extrapolated value) Kraichnan (1962) “ultimate state” Plasting & Kerswell (2003) “upperbound” Seems consistent with Hanasoge, Duvall and KRS (2012) Convective processes are far from being optimally efficient. Nu = Q/(k  T/H)

6. Urban et al. (2014) See also: Roche et al. (2010) Chillá & Schumacher (2012) 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

7. Data on Rotating Convection our data

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

9. Heat transport decreases only modestly with rotation, and this appears true for the conditions of the Sun exponent: 0.024 Rotating Convection  Nu/Nu 0 Rossby number

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. Large scale circulation (wind) the container large- scale circulation (“mean wind”) The “mean wind” breaks symmetry, with its own consequences The mean wind 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. Glatzmaier, Coe, Hongre & Roberts, Nature 401, 885-890 (1999) Geomagnetic polarity reversals The mean wind…with occasional reversals (KRS, Bershadskii & Niemela, PRE 65, 056306, 2000; Niemela et al. JFM, 2001) Segment of continuous 120-hour record;  The reversals become more frequent with increasing Ra.

13. 50 cm J.J. Niemela and KRS J. Fluid Mech. 557, 411-422 (2006). Ra = 1.9 x 10 9  cm 12.5 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.