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Astron. Astrophys. 340, 178-182 (1998)


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A study of penetration at the bottom of a stellar convective envelope and its scaling relationships

Harinder P. Singh 1, 2, 3, Ian W. Roxburgh 2 and Kwing L. Chan 1

1 Department of Mathematics, The Hong Kong University of Science & Technology, Kowloon, Hong Kong
2 Astronomy Unit, Queen Mary & Westfield College, University of London, Mile End Road, E1 4NS London, UK
3 Department of Physics, Sri Venkateswara College, University of Delhi, 110 021 New Delhi, India

Received 15 September 1997 / Accepted 3 September 1998

Abstract

A number of scaling relationships have been proposed by several authors relating the penetration depth ([FORMULA]) at the bottom of a convective region to the velocity of the penetrating motions and the input flux ([FORMULA]). These may be expressed as [FORMULA] for the case where the radiative conductivity varies smoothly from the unstable to the stable zone; [FORMULA] being the vertical velocity at the bottom of the convection zone. When the conductivity varies stepwise from one zone to another, it has been suggested that [FORMULA] for adiabatic penetration and [FORMULA] for non-adiabatic penetration. In this paper, we study the general behaviour of motions penetrating into the stable region at the bottom of a convective envelope by numerically solving the full set of Navier-Stokes equations in three dimensions. We compute a series of models which allow us to examine the scaling relationships between the penetration distance, the input flux and the vertical velocity.

Key words: convection – hydrodynamics – stars: interiors

Send offprint requests to: H.P. Singh, (hps@ttdsvc.ernet.in)

© European Southern Observatory (ESO) 1998

Online publication: November 3, 1998

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