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 presented for both steady and transient free-surface flows demonstrating that a wide range of constitutive laws can be directly obtained. For flows in which the free-surface velocity is known, we derive a different method, which circumvents the need to calculate the flux.