  The stellar winds of the massive stars in high-mass microquasars are thought
to be inhomogeneous. The interaction of these inhomogeneities, or clumps, with
the jets of these objects may be a major factor in gamma-ray production. Our
goal is to characterize a typical scenario of clump-jet interaction, and
calculate the contribution of these interactions to the gamma-ray emission from
these systems. We use axisymmetric, RHD simulations to model the emitting flow
in a typical clump-jet interaction. Using the simulation results we perform a
numerical calculation of the high-energy emission from one of these
interactions. The radiative calculations are done for relativistic electrons
locally accelerated at the jet shock, and the synchrotron and IC radiation
spectra are computed for different stages of the shocked clump evolution. We
also explore different parameter values, such as viewing angle and magnetic
field strength. We generalize phenomenologically the results derived from one
clump-jet interaction to multiple interactions under different wind models,
estimating the clump-jet interaction rates, and the resulting luminosities in
the GeV range. If particles are efficiently accelerated in clump-jet
interactions, the apparent gamma-ray luminosity through IC scattering with the
stellar photons can be significant even for rather strong magnetic fields and
thus efficient synchrotron cooling. Moreover, despite the standing nature or
slow motion of the jet shocks for most of the interaction stage, Doppler
boosting in the postshock flow is relevant even for mildly relativistic jets.
For clump-to-average wind density contrasts $\gtrsim 10$, clump-jet
interactions could be bright enough to match the observed GeV luminosity in
Cyg~X-1 and Cyg~X-3 when a jet is present in these sources, with required
non-thermal-to-total available power fractions $\sim 0.01$ and $0.1$,
respectively.
