This paper reports on LDA experiments in bubble columns 15.2, 23.4, and 38.4 cm in diameter. The gas fraction ranges up to 25%, but the columns are still in the bubbly regime, i.e. coalescence of bubbles is minor. It is shown that both the axial and tangential liquid velocity components can be measured with confidence, especially close to the wall. In that domain the data rates are sufficiently high to obtain time series that can be studied at high frequencies, i.e. above 1000 Hz. It is reported that the fluctuations in the velocity field are of the same order as the mean velocity. Furthermore, results on the Reynolds stresses are presented. The axial normal stress is higher than the tangential one indicating anisotropic turbulence. Furthermore, the axial normal stress shows a minimum at a radial position of 0.8 of the column radius which has not been reported before. This minimum becomes more pronounced with increasing gas fraction. The axial-tangential Reynolds shear stress is zero. A frequency analysis shows that for the higher frequencies the -5/3 power law is obeyed. At low frequencies the presence of vortical structures is found. Short-time frequency analysis indicates that these structures are well separated in space and arrive at irregular intervals.