On the power spectrum of solar surface flows

Context. The surface of the Sun provides us with a unique and very detailed view of turbulent stellar convection. Studying its dynamics can therefore help us make significant progress in stellar convection modelling. Many features of solar surface turbulence like the supergranulation are still poorly understood. Aims. The aim of this work is to give new observational constraints on these 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. Methods. We use long time-series of images taken by the Solar Optical Telescope (SOT) on board the Hinode satellite; we reconstruct both horizontal (by granule tracking) and vertical (by Doppler effect) velocity fields in a field-of-view of ∼ 75×75 Mm 2 . The dynamics in the subgranulation range can be investigated with unprecedented precision thanks to the absence of seeing effects and the use of the modulation transfer function of SOT for correcting the spectra. Results. At small subgranulation scales down to 0.4 Mm the spectral density of kinetic energy associated with vertical motions exhibits a k −10/3 -like power law, while the intensity fluctuation spectrum follows either a k −17/3 or a k −3 -like power law at the two continuum levels investigated (525 and 450 nm respectively). We discuss the possible physical origin of these scalings and interpret the combined presence of k −17/3 and k −10/3 power laws for the intensity and vertical velocity as a signature of buoyancy-driven turbulent dynamics in a strongly thermally diffusive regime. In the mesogranulation range and up to a scale of 25 Mm, we find that the amplitude of the vertical velocity field decreases like λ −3/2 with the horizontal scale λ. This behaviour corresponds to a k 2 spectral power law. Still in the 2.5–10 Mm mesoscale range, we find that intensity fluctuations in the blue continuum also follow a k 2 power law. In passing we show that granule tracking cannot sample scales below 2.5 Mm. We finally further confirm the presence of a significant supergranulation energy peak at 30 Mm in the horizontal velocity power spectrum and show that the emergence of a pore erases this spectral peak. We tentatively estimate the scale height of the vertical velocity field in the supergranulation range and find 1 Mm; this value suggests that supergranulation flows are shallow.