从自由表面观测推断流变学
Inferring rheology from free-surface observations
摘要：
我们开发了直接反演方法来推断流体的流变性，从其浅层流动的观察。首先，推导了具有一般本构律的无惯性流自由面流动的演化方程。流体的体积通量与基底应力之间的关系$τ_b$被封装为一个单一的函数$F(τ_b)$，它只依赖于本构关系。反演方法包括（i）从自由表面演化确定通量和基底应力，（ii）将通量与基底应力进行比较以约束$F$，以及（iii）从$F$推断本构关系。稳态和瞬态自由表面流动的例子表明，可以直接获得广泛的本构关系。对于已知自由表面速度的流动，我们推导出一种不同的方法，它避免了计算通量的需要。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
