Inferring rheology from free-surface observations

Abstract

We develop direct inversion methods for inferring the rheology of a fluid from observations of its shallow flow. First, the evolution equation for the free-surface flow of an inertia-less current with general constitutive law is derived. The relationship between the volume flux of fluid and the basal stress, Formula Presented, is encapsulated by a single function Formula Presented, which depends only on the constitutive law. The inversion method consists of (i) determining the flux and basal stress from the free-surface evolution, (ii) comparing the flux with the basal stress to constrain Formula Presented and (iii) inferring the constitutive law from Formula Presented. Examples are presente..