[mesa-users] convection, mixing length, semiconvection and overshoot

[David Arnett]

If we take the mixing length to be related to physics, it must be the
integrated dissipation length for turbulence over the convective region (a
global quantity) and is related to the depth of the convection zone. It
grows with convection zone depth but seems to saturate at 3 to 4 pressure
scale heights, as many 3D simulations have now shown.

Semi-convection results from an excess of radiative flux (above radiative
flux at the adiabatic gradient) causing potential energy change by mixing
against a composition gradient. This causes advective motion much like that
seen in simulations by Toby  Wood and others (dynamic "stairsteps" in
composition), and differs from the diffusion model proposed by Norbert
Langer. This occurs away from vigorous convection zones (see below).

By using a differential equation for driving and damping, convection can be
dynamic and nonlocal, and physical boundary conditions can be defined. The
mixing boundary is where the mixing velocity (solenoidal flow) goes to
zero; the wave velocity (potential flow) continues but is usually
relatively small. The convective acceleration is negative in a "braking"
region (in order to "turn the flow back into the convective region").
Overshoot beyond this point is related to the ability of convection to
erode the neighboring stable nonconvective region, giving entrainment.

I am implementing these ideas in TYCHO for testing. So far it looks like an
improvement; we shall see. If it goes as expected I will work with Bill in
May to implement these algorithms in MESA. At present I am writing the
paper describing the physics with my collaborators.

Within this framework, use of Schwarzschild and Ledoux criteria for mixing
are over-simplifications, so be careful.
-- 
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
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <https://lists.mesastar.org/pipermail/mesa-users/attachments/20130331/3f0d1290/attachment.html>