  Disequilibrium chemical processes have a large effect upon the spectra of
substellar objects. To study these effects, dynamical disequilibrium has been
parameterized using the quench and eddy diffusion approximations, but little
work has been done to explore how these approximations perform under realistic
planetary conditions in different dynamical regimes. As a first step in
addressing this problem, we study the localized, small scale convective
dynamics of planetary atmospheres by direct numerical simulation of fully
compressible hydrodynamics with reactive tracers using the Dedalus code. Using
polytropically-stratified, plane parallel atmospheres in 2- and 3-D, we explore
the quenching behavior of different abstract chemical species as a function of
the dynamical conditions of the atmosphere as parameterized by the Rayleigh
number. We find that in both 2- and 3-D, chemical species quench deeper than
would be predicted based on simple mixing length arguments. Instead, it is
necessary to employ length scales based on the chemical equilibrium profile of
the reacting species in order to predict quench points and perform chemical
kinetics modeling in 1-D. Based on the results of our simulations, we provide a
new length scale, derived from the chemical scale height, which can be used to
perform these calculations. This length scale is simple to calculate from known
chemical data and makes reasonable predictions for our dynamical simulations.
