  The formation of brown dwarfs (BDs) poses a key challenge to star formation
theory. The observed dearth of nearby ($\leq 5$ AU) brown dwarf companions to
solar-mass stars, known as the brown dwarf desert, as well as the tendency for
low-mass binary systems to be more tightly-bound than stellar binaries, have
been cited as evidence for distinct formation mechanisms for brown dwarfs and
stars. In this paper, we explore the implications of the minimal hypothesis
that brown dwarfs in binary systems originate via the same fundamental
fragmentation mechanism as stars, within isolated, turbulent giant molecular
cloud cores. We demonstrate analytically that the scaling of specific angular
momentum with turbulent core mass naturally gives rise to the brown dwarf
desert, as well as wide brown-dwarf binary systems. Further, we show that the
turbulent core fragmentation model also naturally predicts that very low-mass
(VLM) binary and BD/BD systems are more tightly-bound than stellar systems. In
addition, in order to capture the stochastic variation intrinsic to turbulence,
we generate $10^4$ model turbulent cores with synthetic turbulent velocity
fields to show that the turbulent fragmentation model accommodates a small
fraction of binary brown dwarfs with wide separations, similar to observations.
Indeed, the picture which emerges from the turbulent fragmentation model is
that a single fragmentation mechanism may largely shape both stellar and brown
dwarf binary distributions during formation.
