Top: characteristic wave-related timescale (solid lines), computed using Eq. (4), as a function of the normalized radius in the radiative zone of a 1 M_⊙ red giant model, with log  T_eff = 3.16 and log  L/L_⊙ = 0.92. Colors correspond to different values for the amplitude of the differential rotation, . The red and the blue dashed lines represent the contraction or dilatation timescale and the location of the hydrogen-burning shell, respectively. Bottom: same caption and legend as the top panel, but for a 1 M_⊙ subgiant model, with log  T_eff = 3.70 and log  L/L_⊙ = 0.35.