论文标题
从自由地表观察中推断流变学
Inferring rheology from free-surface observations
论文作者
论文摘要
我们开发了直接的反转方法来从观察到其浅流的观察结果来推断流体的流变。首先，得出了具有一般构成定律的无惯性电流的自由表面流的演化方程。流体的体积通量与基础应力之间的关系，$τ_b$由单个函数$ f（τ_b）$封装，该功能仅取决于本构定律。反转方法包括（i）确定自由地表演化的通量和基础应力，（ii）将通量与基础应力进行比较，以限制$ f $ $ f $和（iii）从$ f $中推断本构法。为稳定和瞬态游离表面流提供了示例，表明可以直接获得广泛的本构定律。对于已知自由表面速度的流动，我们得出了一种不同的方法，该方法规避了计算通量的需求。
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, $τ_b$ is encapsulated by a single function $F(τ_b)$, 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 to the basal stress to constrain $F$ and (iii) inferring the constitutive law from $F$. 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.
