Volume 384, Number 3, March IV 2002
|Page(s)||1119 - 1123|
|Published online||15 March 2002|
Critical Richardson numbers and gravity waves
NASA, Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025, USA Dept. of Applied Physics and Mathematics, Columbia University, New York, NY 10027, USA
Corresponding author: firstname.lastname@example.org
Accepted: 7 December 2001
In this paper we present two new results. The first concerns the proper identification of the critical Richardson number Ri(cr) above which there is no longer turbulent mixing. Thus far, all studies have assumed that: However, since (cr) determines the upper limit of a laminar regime (superscript ), it has little relevance to stars where the problem is not to determine the end point of a laminar regime but the endpoint of turbulence. We show that the latter is characterized by , where t stands for turbulence, and has a value four times larger than (1): We also show that use of (2) instead of (1) changes the conclusions of recent studies. Inclusion of radiative losses (characterized by the Peclet number Pe) which weaken stable stratification and help turbulence, further changes (2) to (r stands for radiative): which, for , allows turbulence to survive far longer than (2). Finally, turbulent convection generates gravity waves that propagate into the radiative region and act as an additional source of energy. This further changes Eq. (3) to (gw stands for gravity waves): where . In conclusion, the successive inclusion of relevant physical processes leads to a chain of increasing values of : The second result concerns the dependence of the diffusivity D on Ω. We show that the commonly used expression is not correct for the regime that characterizes a stably stratified regime. The proper Ω-dependence is:
Key words: Sun: general / Sun: interior / convection / turbulence
© ESO, 2002
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.