Adiabatic accretion with subsonic turbulence (top: Ma ~ 0.35; bottom: 1/4 lower Mach number, i.e., Ta_t ~ 3) and e_rot = 0.3: mass PDF per bin of specific angular momentum l_z, for the gas within r< 8 kpc (cf. Fig. 4). If Ta_t< 1, turbulence widens the PDF, inducing both retrograde and prograde motions. In the opposite regime, Ta_t > 1, turbulence is too weak to induce retrograde motions: the underlying counter-clockwise rotation remains intact overall, with minor fluctuations superimposed.