  The aim of this work is to give new observational constraints on solar
surface flows by determining the horizontal scale dependence of the velocity
and intensity fields, as represented by their power spectra, and to offer some
theoretical guidelines to interpret these spectra. We use long time series of
images taken by SOT/Hinode and reconstruct both horizontal (by granule
tracking) and vertical (by Doppler effect) velocity fields in a field of view
75x75Mm^2. At small sub-granulation scales, the kinetic energy spectral density
associated with vertical motions exhibits a k^{-10/3}-like spectrum, while the
intensity fluctuation spectrum follows a k^{-3} or k^{-17/3}-like spectrum at
the two continuum levels investigated (525 and 450 nm respectively). We discuss
the physical origin of these scalings and argue that they provide a direct
observational signature of buoyancy-driven turbulent dynamics in a strongly
thermally diffusive regime. In the mesogranulation range and up to a scale of
25Mm, we find that the vertical velocity field amplitude decreases like
L^{-3/2} with the horizontal scale L. This behaviour corresponds to a k^2
spectral power law. Still in the mesoscale range, [2.5, 10]Mm, we find that
intensity fluctuations in the blue continuum follow a power law in k^2. We show
that granule tracking cannot sample scales below 2.5Mm. We locate the
supergranulation energy peak around 30Mm and show that the emergence of a pore
erases this spectral peak. Thanks to a scale height estimate, we find that
supergranular flows are shallow. (abridged abstract).

Solar and Stellar Astrophysics