First row: time evolution of the radial velocity dispersion profiles, σ_r(r), for the gS0, gSa, and gSb models. Different colors and line styles correspond to the times indicated in the second row, first panel. The bars’ CR and 2:1 OLR are shown by the dotted and solid vertical lines, respectively. Second row: same but for the vertical velocity dispersion, σ_z(r). Third row: same but for the ratio σ_z/σ_r. The slope in σ_z/σ_r outside the bar shows that the radial profile flattens more with time than the vertical one, while its overall decrease means that the disc heats more radially than vertically. This is related to the conservation of vertical action. See text for discussion.