  A variety of observations provide evidence for vigorous motion in the
atmospheres of brown dwarfs and directly imaged giant planets. Motivated by
these observations, we examine the dynamical regime of the circulation in the
atmospheres and interiors of these objects. Brown dwarfs rotate rapidly, and
for plausible wind speeds, the flow at large scales will be rotationally
dominated. We present 3D, global, numerical simulations of convection in the
interior, which demonstrate that, at large scales, the convection aligns in the
direction parallel to the rotation axis. Convection occurs more efficiently at
high latitudes than low latitudes, leading to systematic equator-to-pole
temperature differences that may reach ~1 K near the top of the convection
zone. The interaction of convection with the overlying, stably stratified
atmosphere will generate a wealth of atmospheric waves, and we argue that, as
in the stratospheres of planets in the solar system, the interaction of these
waves with the mean flow will cause a significant atmospheric circulation at
regional to global scales. At large scales, this should consist of stratified
turbulence (possibly organizing into coherent structures such as vortices and
jets) and an accompanying overturning circulation. We present an approximate
analytic theory of this circulation, which predicts characteristic horizontal
temperature variations of several to ~50 K, horizontal wind speeds of ~10-300
m/sec, and vertical velocities that advect air over a scale height in
~10^5-10^6 sec. This vertical mixing may help to explain the chemical
disequilibrium observed on some brown dwarfs. Moreover, the implied large-scale
organization of temperature perturbations and vertical velocities suggests
that, near the L/T transition, patchy clouds can form near the photosphere,
helping to explain recent observations of brown-dwarf variability in the
near-IR.
