Examination of Scaling Relationships Involving Penetration Distance at the Bottom of a Stellar Convective Envelope

Details Examination of Scaling Relationships Involving Penetration Distance at the Bottom of a Stellar Convective Envelope Examination of Scaling Relationships Involving Penetration Distance at the Bottom of a Stellar Convective Envelope

Jan 2000

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000apj...529..402s&link_type=abstract

The Astrophysical Journal, Volume 529, Issue 1, pp. 402-413.

Astronomy and Astrophysics

Astronomy

13

Convection, Hydrodynamics- Stars: Interiors, Turbulence

Scientific paper

A number of studies in the recent past have proposed a variety of scaling relationships among the penetration depth (Δd) at the bottom of a convective region, the vertical velocity of the fluid (Vz), and the input flux (Fb). While a relationship of the form Δd~V3/2z has been proposed by Schmitt and coworkers on the basis of the equations of motion for buoyant plumes, Zahn proposed a similar relationship based on scaling arguments. The relationships involving Δd, Vz, and the input flux are based on recent two-dimensional numerical simulations by Hurlburt and coworkers. All these scalings were recently looked into by Singh, Roxburgh, & Chan, who performed full three-dimensional simulations of turbulent compressible convection for a stable-unstable-stable sandwich configuration. In the present study, we numerically solve the full set of Navier-Stokes equations in three dimensions in order to study the behavior of convective motions penetrating into the bottom stable layer. We take up a series of models differing in resolution or mesh size and aspect ratio with a view to examine, in greater detail, the scaling relationships between the penetration distance and other flow parameters.

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