  Black-hole driven relativistic astrophysical jets, such as blazars and
gamma-ray bursts (GRBs), are powerful sources of electromagnetic radiation.
Their emission is powered by some energy dissipation and particle acceleration
mechanism operating in-situ at large distances from the black hole. We propose
that the formation of the dissipative structures in the jet is controlled by
the time variability of the accretion disc. We argue that the open magnetic
field lines through the black hole, which drive a strongly magnetized jet, may
have their polarity reversing over time-scales related to the growth of the
magneto-rotational dynamo in the disc. Consequently, the jet is characterized
by an alternating toroidal field polarity along its propagation axis, i.e., it
is a "striped jet". Magnetic reconnection in the current sheets that form
between the stripes dissipates the alternating-field energy and thus powers
further jet acceleration. Here, we consider a jet with a broad distribution of
stripe widths $l>l_{\rm min}$, above a dominant scale $l_{\rm min}$. We find
that the bulk acceleration of the jet, driven by the annihilation of the
stripes, is very gradual. The dissipation rate peaks at a distance $z_{\rm
peak}\sim 10^6 R_g\, (\Gamma_\infty/30)^2\, (l_{\rm min}/1000R_g)$, where
$R_{g}$ is the black-hole's gravititional radius and $\Gamma_{\infty}$ the
jet's asymptotic Lorentz factor, and exhibits a very broad plateau extending by
$\sim 4-5$ orders of magnitude in distance. The prolonged energy dissipation
accounts for the flat-to-inverted long-wavelength spectra commonly observed in
jets. The model can also account for the broad range of flaring timescales of
blazars and the fact that their bulk acceleration appears to continue out to
~100 pc scales. In GRB jets, the model predicts comparable power for the
photopsheric and Thomson-thin emission components.
