Dynamics of fluctuation of the top location of a sandpile

We investigate the fluctuation of the top location of a sandpile numerically using the two-dimensional discrete elements method. We feed particles to a sandpile at a fixed time interval and calculate power spectra from the time series of the top location. We find that the power spectra are approximated as power functions, and their exponents increase to -1 through a plateau as the time interval decreases. For small time interval, avalanches occur continuously either on the left or right side slope of a sandpile, and the slope on which avalanches take place switches intermittently. The long time fluctuation of the top location corresponds to the switchings. For the time series of the switchings, we discuss the relation between the power spectrum and the distribution of waiting times based on analytic theories.