Seepage Bifurcation as a Critical Process

Abstract:

Channel networks form beautiful and surprisingly intricate geometries, yet diligently evade comprehensive mathematical understanding. Work in recent years has shed light on this problem. Networks driven by seepage flow, in particular, have been shown to grow in a field that can be described by the Laplace equation, providing us with an understanding of valley growth and shape. However, the process by which such networks branch to form these ramified shapes is yet a mystery. We focus our attention on a highly ramified seepage valley network in Bristol, Florida. We study the behavior of flux to valley heads as a function of valley length, and use this result to motivate our discussion of branch formation. We then hypothesize that a critical groundwater flux demarcates a transition point where topographic diffusion is overcome by branching processes, and we present network-wide flux calculations, cosmogenic data, and simulation to support our claim. Our results ultimately suggest a mechanism for seepage bifurcation, and inform our understanding of pattern formation in river networks.