**Estimation of the Appropriate Length Scale to Use with the Quench Level Approximation for Obtaining Chemical Abundances**

**Michael D. Smith (NRC, NASA/GSFC)**

The ``quench level'' approximation for estimating the observed abundance
of chemically reacting species in the presence of convective dynamics
states that the chemical reaction is quenched at the level where the
time scales for the chemical reaction and for convective dynamics are
equal. The dynamical time constant, , can be computed using
, where *L* is a length scale and *K* is the vertical
eddy diffusion coefficient. Usually *K* is left as a free parameter, and
lacking any better information, *L* is taken to be a scale height.

Here we show that the length scale, *L*, can be estimated by comparing
the results of three different simple mathematical ``models'' for
convective dynamics. Each of the three models uses a different
fundamental quantity in describing the strength or efficiency of mixing
that depends on the unknown length scale, *L*, in a different way. By
demanding that the three models give consistent results, we arrive at an
independent estimate of *L*. We find that the appropriate value of *L*
is different for different chemical reactions, and can be far from a
scale height. As an example, we find that *L*=0.14 scale heights is
appropriate for the estimation of the isotopic enrichment of (D/H) in
CH over (D/H) in H . Using *L*=0.14 scale heights leads to a
value of 1.17 on Jupiter at a typical value of cm
sec compared to 1.21 when *L*=1.0 scale heights is used. This
indicates that greater care should be taken when using the quench level
approximation to estimate chemical abundances.