a) Our experiments span a large range of the Reynolds number Re, which controls the turbulence intensity, and the rotation number R_Ω, introduced by Dubrulle et al. (2005), which compares shear to overall rotation. The rotation number can be used to distinguish between Rayleigh-stable flows (R_Ω ≤ −1 or R_Ω ≥ (1 − η)/η) and those that are linearly unstable (−1 < R_Ω < (1 − η)/η). b) All of our measurements for −1 < R_Ω < 0.38 are well above the linear stability curve (blue line) described by Esser & Grossmann (1996) and given by Eq. (8). The data are taken from separate experiments by van Gils et al. (2011b) (red squares) and (Paoletti & Lathrop 2011) (black circles).