R.F. Stein: Applications of Convection Simulations to Oscillation Excitation and Local Helioseismology (Review, Wed, Aug. 23)
This was the review talk of session E in the Convection Symposium: "Oscillations, mass loss, and convection".
One application of numerical simulations is to understand the excitation process for p-mode oscillations. The excitation equation contains an integral, in which the terms for pressure fluctuations and mode compression are multiplied (don't take mode compression out of the integral!). Excitation decreases at low and high frequencies, which results in typical oscillation periods, e.g. 5 minutes for the Sun.
In the power spectrum for the turbulence, spatial and temporal factors cannot be separated. Therefore, a generalized Lorentzian is fit (where the width and power depend on wavenumber). This is another improvement needed for analytical work.
In a discussion on turbulent (Pt) and gas pressure (Pg), an analysis of local heating and cooling shows that excitation is due to entropy fluctuations. Pt and non-adiabatic Pg work comparably near the surface, Pt extends deeper. p-mode driving is primarily by turbulent pressure. There is some cancellation between Pt and non-adiabatic Pg.
Next, some work by Günther Houdek was shown, and his analytical model compared to simulations by Stein & Nordlund (2001). Excitation rates for p modes for the Sun, Procyon, and alf Cen A where shown - models and simulations agree.
Another application is helioseismology, i.e. to test and refine local helioseismic models. One needs a large size and a long time sequence (so far, the simulation is 48 Mm wide by 20 Mm deep, the intention is to double the size next month). As a bonus, the simulations lead to an understanding of supergranulation. The simulations run for 48 hours (1 turnover time), include f-plane rotation (surface shear layer), but no magnetic field yet. The resolution is 100 km horizontal, 12-70 km vertical.
After a presentation of the numerical method, some results were shown. The mean atmosphere is highly stratified. A slice through simulations for the velocity in the vertical plane shows that downflows are being swept aside by the diverging upflows. Thus, the downflows become larger and make it to deeper layers. Some of the downflows are not swept aside and disperse. Displaying the vertical velocity on horizontal planes shows the continuous change of scales from granules to supergranules. Upflows at the surface come from a small area at the bottom. Downflows at the surface converge to supergranule boundaries.
The horizontal and vertical velocities from simulations were then compared to MDI observations. At larger scales, the oscillatory component dominates, at smaller scales, the convective component dominates. Simulations were also compared to MDI observations in a k-omega diagram, a time-distance diagram, and in a diagram of f-mode travel times vs. simulated flow fields (divergence and horizontal). North-going and south-going travel time differences from MDI were compared to simulated velocities.
Note that the simulated data is available from the MDI data base: Full data sets (~200GB per hour solar time) and slices of Vxyz and T at selected depths (~2 GB per hour solar time).
After a movie of temperature and vertical velocity by Viggo Hansteen, showing non-linear wave propagation in 2D, some answers to the question "Why are linear calculations useful?" were given. They complement non-linear calculations, they are much faster than non-linear calculations, one can explore the parameter space, and one can isolate physical effects.
At the end of his talk, Stein mentioned that he is looking for a solar physics post-doc.