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Semiconvection as the occasional breaking of weakly amplified internal waves

Stevenson, D. J. (1979) Semiconvection as the occasional breaking of weakly amplified internal waves. Monthly Notices of the Royal Astronomical Society, 187 (2). pp. 129-144. ISSN 0035-8711. doi:10.1093/mnras/187.2.129.

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An analysis is made of the semiconvective zones which arise in the evolution of many stars. Despite the presence of a strongly stabilizing solute gradient, growing overstable modes are possible for a slightly superadiabatic temperature gradient, because heat diffusion greatly exceeds solute diffusion or molecular viscosity. These modes are essentially identical to weakly amplified internal waves (or hydromagnetic waves if rotation and magnetic field are present). Their amplification is balanced by a cascade to higher wavevectors (caused in part by subharmonic parametric instabilities) leading to infrequent wavebreaking 'events' which provide the required redistribution of solute. Detailed quantification of this model is impractical, but a simplified analysis indicates that the ratio of the superadiabaticity to the solute gradient is at most of order (D_e/K)^(1/2) where D_e is the solute 'eddy' diffusivity and K is the thermal diffusivity. Evolutionary models require D_e << K, so the Schwarzschild-Härm criterion for semiconvection is essentially correct. A field in excess of about 10^4 gauss modifies the model somewhat, but does not invalidate it. Propagation of the waves out into the radiative envelope of the star is unimportant. The related phenomenon to semiconvection which occurs in differentiating black dwarfs (e.g. Jupiter, Saturn) is also briefly discussed.

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Stevenson, D. J.0000-0001-9432-7159
Additional Information:© 1979 Royal Astronomical Society. Received 1978 September 21; in original form 1978 July 6. I thank C. Garrett, W. Munk, J. S. Turner and G. Veronis for useful discussions.
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Official Citation:D. J. Stevenson Semiconvection as the occasional breaking of weakly amplified internal waves MNRAS (1979) Vol. 187 129-144 doi:10.1093/mnras/187.2.129 First published online June 1, 1979
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:39368
Deposited By: Tony Diaz
Deposited On:15 Jul 2013 22:21
Last Modified:09 Nov 2021 23:44

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