DYNAMICS OF THE SOLAR GRANULATION .3. FRACTIONAL DIFFUSION

In most papers dealing with random motions and diffusion of small magn etic elements in the photosphere, the convective flows and in particul ar the granulation are considered as drivers of these motions. The res ults of these works have been discussed in terms of the fractal dimens ion of the granulation as seen in intensity pictures. So far neither a fractal dimension associated with the granular velocity field nor the nature of the random walks in the granular intergranular space have b een determined. Using spectrograms of high spatial resolution taken wi th the VTT at Izana (Tenerife, Spain) we investigated the granular vel ocity field in terms of its fractal nature and its diffusion propertie s. We applied the rescaled range analysis to both the velocity and int ensity fields, thus enabling us to calculate a fractal dimension as we ll as a ''diffusion'' exponent which together characterize the diffusi on properties of the granulation layers. We found a fractal dimension of the granular velocity of the same order as the fractal dimensions o f the distribution of the magnetic elements in the photosphere, and th e fractal dimension corresponding to the diffusion of the magnetic ele ments in a fractal geometry. The diffusion processes in the granulatio n layers show a subdiffusive nature characteristic of anomalous diffus ion rather than the classical Fickian diffusion. Anomalous diffusion i s often found in stochastic transport in spatially heterogeneous media . The velocity field of the granulation can be thought of as a heterog eneous turbulent medium: the granules show less turbulence than the in tergranular space.