Statistics – Computation
Scientific paper
Oct 2000
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000dps....32.5307p&link_type=abstract
American Astronomical Society, DPS Meeting #32, #53.07; Bulletin of the American Astronomical Society, Vol. 32, p.1102
Statistics
Computation
1
Scientific paper
We report a new set of calculations which support the view that supersonic turbulent convection played a major role in the formation of the solar system. A flux-corrected transport scheme (Zalesak, J. Comp. Phys.} 31 335 1979) is used to numerically simulate thermal convection in a 2D ideal gas layer that is heated from below and is stratified gravitationally across many scale heights. The temperature T0 at the top boundary and the temperature gradient (∂ T/∂ z)1 at the lower boundary are kept constant during the computation. The initial atmosphere is superadiabatic with polytropic index m = 1, specific heats ratio γ = 1.4 and temperature contrast T1}/T{0 = 11. This layer mimics a section of the outer layer of the proto-solar cloud (Dyt & Prentice, MNRAS 296 56 1998). Because the Reynolds number of the real atmosphere is so large, motions whose scale is less than the computational grid size are represented with a Smagorinsky sub-grid scale turbulence approximation (Chan et al, Ap.J.} 263 935 1982). That is, a velocity-dependent turbulent viscosity ν t and thermal diffusivity κ t are chosen so that the high wavenumber kinetic energy spectrum follows Kolmogorov's -5/3 law. The flow soon evolves to a configuration consisting of a network of giant convective cells. At cell boundaries, the downflows are spatially concentrated and rapid. Turbulent pressures < ρ v2 >t range up to 3 times the local gas pressure pgas. The convection eliminates nearly all of the superadiabaticity in the lower 90% of the atmosphere. In the top 10%, ∂ T/∂ z increases sharply and a steep density inversion occurs, with ρ increasing by a factor of 3-4. This result gives new credibility to the modern Laplacian theory of solar system origin (Moon & Planets} 19 341 1978; ibid 73 237 1996; Phys. Lett. A} 213 253 1996). Even so, we need < ρ v2 >t ≈ 10 pgas if the proto-solar cloud is to shed discrete gas rings whose orbits match the mean planetary spacings and whose chemical condensates match the observed bulk compositions. This work was funded by the ARC.
Dyt C. P.
Prentice Andrew J. R.
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