[mesa-users] Baroclinic Instability

[Matteo Cantiello]

Hi Craig,
sorry for the late reaction (I was out of the office).
In rigidly rotating stars (or even stars with a cylindrical rotation law) the centrifugal force can be derived from a potential. 
Equipotentials and isobars coincide, the star is barotropic (density, pressure and temperature are constant on equipotentials).
On the other hand differentially rotating stars are baroclinic. 
Barocilinicity means that density, pressure and temperature are NOT constant  on equipotentials. This allows a number of baroclinic instabilities to arise (on Earth an example of baroclinic instability are Jet-streams).
Baroclinic instabilities can mix both on "horizontal" (that in our models means on a shell) and vertical direction. The horizontal mixing feeds into "horizontal turbulence", which is at the base of the shellular approximation. 
So in a sense baroclinic instabilities "help" to retain our 1D approximation.
Concerning vertical mixing, in MESA we do include one baroclinic instability: the GSF (Goldreich-Schubert-Fricke). The formulation is linear and the implementation is diffusive, which of course makes it subject to large uncertainties. See e.g. Heger et al. 2000, and  Andre' Maeder's (2009) book. Another baroclinic instability (not included in MESA) is the ABCD instability, which is an extension of the Solberg-Hoiland
instability in the presence of thermal and compositional effects.
Hope this helps,

-M



Matteo Cantiello  |  http://matteocantiello.com/ 
Associate Specialist in Astrophysics  | Kavli Institute for Theoretical Physics
Chief Scientist and Board Member, Authorea  |  https://www.authorea.com/

On May 22, 2015, at 9:27 AM, Craig Wheeler <wheel at astro.as.utexas.edu> wrote:

> I'm interested in the physics and effects of the baroclinic
> instability in stars. I don't see that the two Paxton et al.
> manuals mention it explicitly and have looked at the Heger,
> Langer & Woosely paper where so many instabilities
> incorporated in MESA are discussed, and don't see any
> specific recipe for the BCI.
> 
> Can someone tell me where I can go to understand in
> more detail where and how BCI is incorporated in MESA?
> 
> Thanks,
> 
> Craig
> 
> -- 
> J. Craig Wheeler
> Department of Astronomy
> 2515 Speedway, Stop C1400
> Austin, TX 78712-1205
> 512-471-6407
> http://www.as.utexas.edu/~wheel
> http://ebooks.cambridge.org/ebook.jsf?bid=CBO9780511536625
> http://www.amazon.com/Krone-Ascending-ebook/dp/B00926QEGW
> 
> 
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