  We examine the possible role of turbulence in feeding the emission of
gamma-ray bursts (GRBs). Turbulence may develop in a GRB jet as the result of
hydrodynamic or current-driven instabilities. The jet carries dense radiation
and the turbulence cascade can be damped by Compton drag, passing kinetic fluid
energy to photons through scattering. We identify two regimes of turbulence
dissipation: (1) "Viscous" - the turbulence cascade is Compton damped on a
scale $\ell_{\rm damp}$ greater than the photon mean free path $\ell_\star$.
Then turbulence energy is passed to photons via bulk Comptonization by smooth
shear flows on scale $\ell_\star<\ell_{\rm damp}$. (2) "Collisionless" - the
cascade avoids Compton damping and extends to microscopic plasma scales much
smaller than $\ell_\star$. The collisionless dissipation energizes plasma
particles, which radiate the received energy; how the dissipated power is
partitioned between particles needs further investigation with kinetic
simulations. We show that the dissipation regime switches from viscous to
collisionless during the jet expansion, at a critical value of the jet optical
depth which depends on the amplitude of turbulence. Turbulent GRB jets are
expected to emit nonthermal photospheric radiation. Our analysis also suggests
revisions of turbulent Comptonization in black hole accretion disks discussed
in previous works.
