We study the characteristic scales of quiet-Sun photospheric velocity fields along with their temperature and magnetic markers in Doppler images from the Michelson Doppler Imager aboard the SOHO satellite (SOHO/MDI) in simultaneous, Doppler, magnetic, and intensity images from the San Fernando Observatory and in full-disk magnetograms and an intensity image from National Solar Observatory (Kitt Peak). Wavelet flatness spectra show that velocity fluctuations are normally distributed (Gaussian). This is often assumed in stochastic models of turbulence but had not yet been verified observationally for the Sun. Temperature fluctuations also are Gaussian distributed, but magnetic fields are intermittent and are gathered into patterns related to flow structures. Wavelet basis functions designed to detect characteristic convection cell-flow topologies in acoustically filtered SOHO/MDI Doppler images reveal granulation scales of 0.7-2.2 Mm and supergranulation scales of 28-40 Mm. Mesogranular flows are weakly but significantly detected in the range 4-8 Mm. The systematic flows account for only 30% of the image variances at granular and supergranular scales and much less in between. The main flows for the intermediate range of 2-15 Mm are self-similar, i.e., chaotic or turbulent.