## Publication Abstracts

### Schilling 1994

Schilling, O., 1994: A Two-Point Closure Model of Turbulent Compressible Convection and Application to Stellar Interiors. Ph.D. thesis. Columbia University.

A theoretical two-point statistical closure model of turbulent compressible convection is developed. The model consists of two simplifying assumptions: (1) the turbulent fields are expanded in a series of eigenfunctions of the operator corresponding to the linearization of the compressible Navier-Stokes, energy, and continuity equations about a polytropic state; in the resulting spectral equations for the turbulent fields, the linear terms representing energy sources and sinks are thus replaced by the eigenvalue spectrum (growth rate) corresponding to the solution of the linear stability problem, and; (2) the equations are further simplified by invoking a homogeneity hypothesis and decoupling the Navier-Stokes equation from the continuity and energy equations by expressing all thermodynamic fluctuations in the nonlinear terms using the linear relations. The principal results of relevance to stellar modeling are: (1) the convective fluxes predicted by the closure models are smaller than the corresponding mixing-length theory flux at small convective efficiencies where superadiabaticity is most important in determining stellar structure, and; (2) compressibility effects decrease the convective flux relative to the incompressible flux at small convective efficiencies. The principal conclusions of the preliminary tests of the new convection model are: (1) at small convective efficiencies, compressible convective fluxes smaller than the incompressible convective fluxes yield solar models with larger superadiabaticity; (2) computations of two full evolutionary tracks using the compressible and incompressible fluxes for a solar-type star show a difference in surface temperature of <2% in the low-luminosity region of the pre-main-sequence branch and <1% in the red giant branch between the two tracks; (3) computations of zero-age main-sequence models from 0.5-2.0M_{—} show a difference of <1% in surface temperature between the two models, and no difference for stars more massive than the Sun, and; (4) on the basis of the qualitative differences between solar models computed using the compressible and incompressible flux, helioseismological models computed using the compressible flux are expected to yield internal sound speed and density profiles in better agreement with observational data than models using the incompressible flux. On the basis of these tests, it is concluded that: (1) the compressible flux should be used in stellar and helioseismological models, which will yield further qualitative and quantitative improvements relative to models using the incompressible flux, and; (2) relative to models using the incompressible flux, the inclusion of compressibility effects does not significantly change the main results of stellar evolution and helioseismological models, and in particular, compressibility effects are less important in red giant stars than previously believed.

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#### BibTeX Citation

@phdthesis{sc00200p, author={Schilling, O.}, title={A Two-Point Closure Model of Turbulent Compressible Convection and Application to Stellar Interiors}, year={1994}, school={Columbia University}, address={New York, N.Y.}, }

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#### RIS Citation

TY - THES ID - sc00200p AU - Schilling, O. PY - 1994 BT - A Two-Point Closure Model of Turbulent Compressible Convection and Application to Stellar Interiors PB - Columbia University CY - New York, N.Y. ER -

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