Viewing second-order phase transitions as a metaphor for river bifurcations

Abstract

The Earth's landscape hosts a variety of patterns resulting from the interaction between a sediment-carrying fluid and an erodible boundary. Here, the morphodynamics of river bifurcations is interpreted as a second-order phase transition. A consolidated one-dimensional bifurcation model is re-examined in the light of classical Landau theory of critical phenomena. The transition from a balanced to an unbalanced flux partition is described in terms of an order parameter. The equilibrium states of the system are shown to be minima of a morphodynamic potential function. Finally, the role of a generic external forcing is investigated. A threshold value of the forcing is shown to set bounds separating two different morphodynamic responses to allogenic and autogenic dynamics.