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.
- 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?