A three-dimensional model of dynamics and photochemistry is used to investigate how transfers of mass and chemical constituents between the stratosphere and troposphere are influenced by changes of the residual mean circulation. Under climatological-mean conditions, the integration recovers a transfer of ozone into the extratropical troposphere that is consistent with the observed increase of tropospheric ozone during winter. Large at middle and high latitude, it reflects the downward transfer of stratospheric air, which is compensated at lower latitude by an upward transfer of tropospheric air. Changes representative of those observed between years modulate these transfers by ~10%. The structure at low latitude, however, is sensitive to the quasi-biennial oscillation's residual circulation, which interferes with the upwelling that must return mass to the stratosphere at the same rate that it is rejected at middle and high latitude. These exchanges of mass couple the circulation in the troposphere to that in the stratosphere, implying the involvement of the Hadley circulation.