Turbulent pressure from 3D convection...

Objections to 1D turbulent pressures

Using some kind of mixing-length (MLT) prescription for describing convection in 1D stellar models, both tex2html_wrap_inline117 and a convective velocity tex2html_wrap_inline119 come out of the procedure. These can of course be combined with some assumptions to give a turbulent pressure. Below I list some points to bear in mind when doing so:

  1. One of the main assumptions is that of an invariant velocity distribution around the mean. This means

    equation20

    where tex2html_wrap_inline121 is a form factor related to the velocity distribution function. From Fig.2 we see that this formfactor is not a constant but varies between 1.3 at the transition from convective to radiative energy transport at z = 0 to 1.9 in the bottom of the simulation. The latter though, might be a aboundary effect making 1.8 (at z=0.7) the upper limit to tex2html_wrap_inline121 .

  2. In most MLT formulations, the velocities stop abruptly when radiation takes over in the photosphere. From the Fig.1 we see how the plasma motions penetrate above the convection zone (overshoot), generating a considerable turbulent pressure. Having no overshoot, one is faced with an discontinuous pressure, so that the turbulent pressure has to be truncated in some unphysical way to allow the integration of hydrostatic equilibrium.

So all the dramatic changes in broadness and asymmetry, overshoot and possible double peakedness all seem to happen close to the top of the convection zone, - also the only region where tex2html_wrap_inline81 ever gets important. The tex2html_wrap_inline131 -ratio, peaks with 13% at z=0.1 Mm, decaying about three times faster in the overshoot region as compared to the convective zone. At the bottom of the box the turbulent pressure only contributes with 0.1% of the total pressure. It is, though, my experience and impression that 1D turbulent pressures derived from MLT convective velocities are sensible for depths greater than about 1-1.5 Mm, but this might depend on the precise MLT formulation.

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Last updated [an error occurred while processing this directive] by: trampedach@pa.msu.edu.