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

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 n(s)(t) satisfies the dynamic scaling law n(s)(t) approximate to s(-tau) f(s/t(z)) and the dynamic exponent z is approximately given by the exponent of the area of the drainage basin. The scaling relationship (2-tau)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 gamma of the flow-dependent meandering, and the exponent tau of the river-size distribution changes from 1.33 to 1.0.