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[53.07] Supersonic Turbulent Convection and the Origin of the Planets

A.J.R. Prentice (Monash University, Victoria, Australia), C.P. Dyt (CSIRO Div. Petroleum Resources, Bentley, Western Australia)

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, \textit{J. Comp. Phys.} \textbf{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 (\partial T/\partial 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 \gamma = 1.4 and temperature contrast T₁/T₀ = 11. This layer mimics a section of the outer layer of the proto-solar cloud (Dyt & Prentice, \textit{MNRAS} \textbf{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, \textit{Ap.J.} \textbf{263} 935 1982). That is, a velocity-dependent turbulent viscosity \nu_t and thermal diffusivity \kappa_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 \langle \rho v² \rangle_t range up to 3 times the local gas pressure p_gas. The convection eliminates nearly all of the superadiabaticity in the lower 90% of the atmosphere. In the top 10%, \partial T/\partial z increases sharply and a steep density inversion occurs, with \rho increasing by a factor of 3-4. This result gives new credibility to the modern Laplacian theory of solar system origin (\textit{Moon & Planets} \textbf{19} 341 1978; \textit{ibid} \textbf{73} 237 1996; \textit{Phys. Lett. A} \textbf{213} 253 1996). Even so, we need \langle \rho v² \rangle_t \approx 10 p_gas 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.

The author(s) of this abstract have provided an email address for comments about the abstract: andrew.prentice@sci.monash.edu.au