  We consider the acceleration of energetic particles by a velocity shear in
the relativistic background flow containing scattering centers. Three possible
acceleration sites for astrophysical jets are identified: (1) gradual velocity
shear parallel to the jet axis, such as a velocity profile decreasing linearly
outward with radial coordinate, (2) gradual velocity shear perpendicular to the
jet axis, such as intrinsic jet rotation, and (3) non-gradual/discontinuous,
longitudinal velocity shear at the jet-side boundary. We determine the
characteristic acceleration timescales, specify the conditions for efficient
acceleration and discuss observational features with respect to each process.
In particular, it is shown that in the case of (2) the higher energy emission
is expected to be concentrated closer to the jet axis, while in the case of (1)
and (3) the higher energy particles are likely to be located near the edges of
the jet, thus possibly leading to some form of limb-brightening.
