Convergent flow in a two-layer system and plateau development

Abstract

In order to describe the development of plateaus such as the Tibet and the Altiplano we extend the two-layer model used in a previous paper [C. A. Perazzo and J. Gratton, Phys. Fluids22, 056603 (2010)] to reproduce the evolution of mountain ranges. As before, we consider the convergent motion of a system of two liquid layers to simulate the crust and the upper mantle that form a lithospheric plate, but now we assume that the viscosity of the crust falls off abruptly at a specified depth. We derive a nonlinear differential equation for the evolution of the thickness of the crust. The solution of this equation shows that the process consists of a first stage in which a peaked range is formed and grows until its root reaches the depth where its viscosity drops. After that the range ceases to grow in height and a flat plateau appears at its top. In this second stage the plateau width increases linearly with time as its sides move outward as traveling waves. We derive simple approximate formulas for various properties of the plateau and its evolution. © 2011 American Institute of Physics.