Tuesday, August 22, 2006

F. Cattaneo: Challenges to the theory of solar convection (Review, Mon, Aug. 21)

The second talk of Symposium 239 was a historical introduction to numerical simulation of convection: During three decades of numerical simulation the simulations have proceeded from 1D to 3D. Here, one distinguishes between global (whole star) and local (small box) simulations (note that this is a different definition than in Canuto's talk). The punchline is that we have become very good at local ones and have much to do for global ones.

But first a detailed account of the evolution of computing power: From the IBM 370 mainframe (Megaflops) on to machines dedicated to number crunching (CDC 7600, Cray 1 in the 70s and early 80s), which were vector machines instead of scalar machines, to the Cray 2, etc. Machines became more and more compact, but at the end of the eighties the limit of compactness was encountered (problems with cooling, 265 MB memory). A principle change became necessary, and message passing was invented (the new idea of parallel programming) leading to cluster machines (early nineties). This architecture has basically prevailed until today (now with 100s of Gigaflops and 10000s of processors) and seems to be the way of the future. Algorithms have changed as well in parallel.

The talk continued with convection simulations - moving from Boussinesq to compressible. The effects of strong stratification (departures from Boussinesq) on stability and flow were structure covered: The center of action moves down, whereas upper and lower layer velocities are comparable.

The next topic was "buoyancy breaking". The role of pressure fluctuations is to enhance downflows and retard upflows, and downflows and upflows have different filling factors (see Hurlburt, Toomre & Massaguer 84; Massaguer & Zahn 80).

Several possible explanations to the unanswered question "Why does MLT work?" were proposed.

A discussion of the interaction between convection and other dynamical ingredients included interfacial motions between the radiative interior and the convection zone, concluding that "Whether we understand overshooting and penetration is an open question, but we can certainly model it." (Hurlburt et al., Roxburgh & Simmons, Malagoli & Cattaneo, Brummell et al.). Effects of rotation and magnetic fields were covered as well.

The last few minutes were about global simulations.
Early observations included surface differential rotation and the activity cycle of the Sun. Simulations (e.g. Gilman, Glatzmaier, Miller) were Boussinesq and could reproduce the equatorial acceleration. Later, we had helioseismology and simulations had higher resolution and included dynamo action.

Conclusions:
  • Local models are in a good state
  • Global models are not in a good state - cannot reproduce features of the Sun
  • What do we need?
    • More resolution? How much more?
    • Better physical understanding?
Another well-structured talk which gave a good overview of the topic.

V.M. Canuto: Theoretical Modelling of Convection (Review, Mon, Aug. 21)

Canuto started the symposium (239, Convection in Astrophysics) by giving a brief history of the theoretical modelling of convection. It starts in 1890 with Reynolds introducing the Reynolds stresses and continues with Boussinesq and the "down-gradient" approximation with diffusivity, which is the beginning of the Mixing Length Saga.

In 1929, Friedmann (the same as the one known from the Friedmann equations) wrote that the Navier-Stokes equations (NSE) should also yield an equation for the correleations of fluctuations, not only a dynamical equation for the mean components, which lead to the Reynolds stress model (RSM). But he was ignored - nobody continued in that direction.

Only in 1940, Chou published the first dynamical equation for the momentum Reynolds stresses. He treated only shear flows (no buoyancy) and the engineering community has since then used the RSM as a working tool. There was a nice story of how Chou was led to publish this equation, which I cannot reproduce here. The engineering community was followed by the geophysical community (early seventies) which used the RSM for global warming calculations.

Eventually, we get to stellar convection - its fortunes and misfortunes. Fortune: most of the convection zone is unstably stratified - the gradient is equal to the adiabatic one. Misfortune: the layers below the convection zone are stable but are affected by overshooting. The advantage of the convection zone is that it contains large eddies with long lifetime which carry most of the energy. One can use a mixing length invented by Prandtl (engineer, not astrophysicist!) to describe one large eddy or the Canuto & Mazzitelli model with many eddies. The disadvantage is that convection is non-local, but all models use the local approximation (which is bad because it is false). The overshooting zone is stable, contains small eddies and is therefore local, but difficult to model because of short life-times, vorticity, etc.

A very good paper was mentioned (even though it contains no equations at all), by J.D. Woods (1969, Radio Science vol. 4).

Now followed a detailed account of the Peclet number debate with lots of equations, as well as a discussion on the modifications that should be included in the equation for mixing and transport: Both shear and vorticity tensors should appear, and buoyancy and gravity waves should be included in the Reynolds stress tensor. Check out MNRAS 328, 829 (2001), which contains the complete algebraic espressions.

Further topics: "salt-fingers" (in oceans, correspond to molecular weight gradient in stars) and semi-convection and their influence on overshooting: salt-fingers cause larger overshooting, semi-convection causes smaller overshooting. Shear distroys salt-fingers (in models and experiments) showing that instabilities can act against each other.

After a few more equations, the non-local, so-called plume model by Morton, Taylor, Turner (1956) was mentioned but found to be unsuitable for astrophysics (because of assumption of small area of down plumes).

Some final words on turbulence:
It's not a source of anything! It is a very efficient distribution mechanism at zero cost (like superconductivity). Without an energy source it dies out. We need a formalism resilient enough to accommodate different processes without changing the rules of the game every time. The only formalism that can do that is the one derived directly from the NSE - the Reynolds stress model.

All this made for an exciting and at times entertaining first 40 minutes of the Symposium.

New kid on the blog

My name is Ulrike Heiter and I'm a senior postdoc at Uppsala Astronomical Observatory, working in the Stellar Atmospheres Group. I will continue this blog by summarizing some talks from the second week of the general assembly.
We will move on to something completely different - mainly "Convection in Astrophysics" (IAU Symposium 239) and probably also "Binary stars as critical tools and tests in contemporary astrophysics" (IAU Symposium 240).
Just as for the previous bloggers, please accept in advance my apologies for errors or omissions. Enjoy reading and don't hesitate to write comments!