We derive the convective terms in the damping which determine the structure
of the moving charge-density wave (CDW), and study the effect of a current
flowing transverse to conducting chains on the CDW dynamics along the chai
ns. In contrast to a recent prediction we find that the effect is orders of
magnitude smaller, and that contributions from transverse currents of elec
tron- and holelike quasiparticles to the force exerted on the CDW along the
chains act in the opposite directions. We discuss recent experimental veri
fication of the effect and demonstrate experimentally that geometry effects
might mimic the transverse current effect.