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
Received 15 September 1997 / Accepted 3 September 1998
A number of scaling relationships have been proposed by several authors relating the penetration depth () at the bottom of a convective region to the velocity of the penetrating motions and the input flux (). These may be expressed as for the case where the radiative conductivity varies smoothly from the unstable to the stable zone; 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 for adiabatic penetration and 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, (email@example.com)
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© European Southern Observatory (ESO) 1998
Online publication: November 3, 1998