A theoretical model of a volcanic plume, based on applying the equations of motion in a plume-centered coordinate system, suggests that the interaction between a volcanic plume and wind causes enhanced entrainment of air and horizontal momentum, plume bending, and a decrease in plume rise height at constant eruption rate. Because of rapid dilution in the high windspeeds of the polar jet, plumes that vary over more than one order of magnitude in mass eruption rate (106 to 107--108 kg/s), if injected into the polar jet, may all attain rise heights only slightly different from that of the core of the jet, ~10 km, as opposed to 17--33 km in a still atmosphere. ¿ 2001 American Geophysical Union