Chemical quench level

A chemical quench level is where a reaction time equals the atmospheric transport time. Above it, transport is faster and carries an approximately fixed deeper abundance faster than local chemistry can restore equilibrium.

For a vertical eddy diffusivity $K_{zz}$, mixing over a length $\ell$ takes ${\tau }_{\mathrm{mix}}\sim {\ell }^2/K_{zz}$. The condition that transport outrun a chemical relaxation time therefore gives $K_{zz}\gtrsim {\ell }^2/{\tau }_{\mathrm{chem}}$. Taking $\ell =0.1H$ instead of one atmospheric scale height $H$ changes this estimate by a factor of one hundred. The atmospheric scale height itself depends on both temperature and gravity.

Atmospheric advection time shorter than the chemical relaxation time allows winds to carry a composition into regions where it differs from local thermochemical equilibrium. In a hot Jupiter, this can transport dayside carbon chemistry into the cooler nightside.

Above a chemical quench level, rapid eddy mixing can keep a species' number mixing ratio $f_A$ approximately fixed at its deeper value, provided condensation, photochemical loss, and molecular diffusion remain negligible. The species' number density is then $n_A=f_{A}p/(k_{B}T)$; constant mixing ratio does not imply constant number density. In an isothermal atmosphere, $n_A$ decreases exponentially with altitude on the atmospheric scale height.

Carbon monoxide–methane quenching freezes the CO-to-CH4 abundance ratio near the level where their interconversion time first exceeds the vertical mixing time.

Nitrogen–ammonia quenching similarly preserves a deeper N2-to-NH3 ratio above the level where chemical conversion becomes slower than atmospheric mixing.