DYNAMIC SCALING OF RIVER-SIZE DISTRIBUTION IN THE EXTENDED SCHEIDEGGER'S RIVER NETWORK MODEL

Abstract

The scaling behavior of the river-size distribution is investigated in the river network model. The river network model is an extended version of the Scheidegger’s river model to take into account a flow-dependent meandering. It is shown that the river-size distribution ns(t) satisfies the dynamic scaling law ns(t)≈s−τf(s/tz) and the dynamic exponent z is approximately given by the exponent of the area of the drainage basin. The scaling relationship (2−τ)z=1 is found. The dynamic exponent z (or the exponent of the drainage basin) changes continuously from 1.5 (the value of the Scheidegger’s river) to 1.0 (the value of a linear river), with increasing exponent γ of the flow-dependent meandering, and the exponent τ of the river-size distribution changes from 1.33 to 1.0.