[mesa-users] The overshooting problem:

David Arnett wdarnett at gmail.com
Fri Jun 28 12:06:40 EDT 2013

Overshooting occurs at a turbulent boundary layer. Mechanical engineers
took decades to find acceptable ways to deal with their turbulent boundary
layers. We do not have wind tunnels that can produce stellar conditions.
Calibrating simplified convection models (mixing length theory, e.g.) has
been pushed to (beyond?) its limits. Numerical simulation shows a more
complex situation than we are used to in stellar evolution. We have a
boundary having regions of negative buoyancy (not allowed in MLT), velocity
due to both waves (no mix) and turbulence (mix), and mixing (abundance
gradients) which affect the buoyancy. When we use the Brunt frequency in
linear stability analysis,  it is via the restoring force, i.e., the
buoyancy. MLT does not know about abundance gradient effects on buoyancy,
and the overshoot algorithm probably does not either. It is a hard, coupled
problem, but it should be no surprise that our oversimplification appears
as weird behavior in the Brunt.  I take this weird behavior as a sign that
(1) it is wrong as a model of a real star, and (2) we need more work on our
boundary condition (overshooting should be a result not an add on). We are
in the process of using numerical simulations and more complete turbulence
theory  to provide a replacement for MLT; a spinoff is that various
"patches" like semi-convection and overshoot are an integral part of the
process. Unfortunately it takes time ;-(

David Arnett
Regents Professor
Steward Observatory
University of Arizona

Facts are stubborn, but statistics are more pliable.  Mark Twain
Facts do not cease to exist because they are ignored.  Aldous Huxley
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