  Observations of brown dwarfs and relatively isolated young extrasolar giant
planets have provided unprecedented details to probe atmospheric dynamics in a
new regime. Questions about mechanisms governing global circulation remain to
be addressed. Previous studies have shown that small-scale, randomly varying
thermal perturbations resulting from interactions between convection and the
overlying stratified layers can drive zonal jet streams, waves, and turbulence.
Here, we improve upon our previous general circulation model by using a
two-stream grey radiative transfer scheme to represent more realistic heating
and cooling rates. We examine the formation of zonal jets and their time
evolution, and vertical mixing of passive tracers including clouds and chemical
species. Under relatively weak radiative and frictional dissipation, robust
zonal jets with speeds up to a few hundred $\rm m\;s^{-1}$ are typical
outcomes. The off-equatorial jets tend to be pressure-independent while the
equatorial jets exhibit significant vertical wind shear. Models with strong
dissipation inhibit jet formation and have isotropic turbulence in
off-equatorial regions. Quasi-periodic oscillations of the equatorial flow with
periods ranging from tens of days to months are prevalent at relatively low
atmospheric temperatures. Sub-micron cloud particles can be transported to
several scale heights above the condensation level, while larger particles form
thinner layers. Cloud decks are inhomogeneous near their cloud tops. Chemical
tracers with chemical timescales $>10^5$ s can be driven out of equilibrium.
The equivalent vertical diffusion coefficients, $K_{\mathrm{zz}}$, for the
global-mean tracer, are diagnosed from our models and are typically on the
order of $1\sim10^2\rm m^2\;s^{-1}$. Finally, we derive an analytic estimation
of $K_{\mathrm{zz}}$ for different types of tracers under relevant conditions.
