用于自由表面浅层重力流的统一形式简化
Unified formal reduction for fluid models of free-surface shallow gravity-flows
AI总结：
本文提出了一种统一的长波简化方法，用于处理由恒定外力驱动的薄层不可压缩均质流体模型，通过数学一致性性质，为不同流变学和薄层制度定义唯一的简化模型，首次在单一框架内研究多种已知简化模型，并产生新的非牛顿 viscoelastic 流体简化模型。
摘要：
我们提出了一种统一的长波简化方法，用于处理由恒定外力驱动的薄层不可压缩均质流体模型。该方法基于一个数学一致性性质，能够唯一地定义一个简化模型，给定一种流变学和一种薄层制度。首次，据我们所知，各种已知的简化模型可以在单一数学框架内研究，适用于各种流变学（粘性与粘弹性）和各种极限制度（快速惯性流和缓慢粘性流）。此外，我们的系统方法还为粘弹性非牛顿流体生成了新的简化模型，并改进了我们之前的[1]工作。
英文摘要：
We propose a unified approach to the formal long-wave reduction of several fluid models for thin-layer incompressible homogeneous flows driven by a constant external force like gravity. The procedure is based on a mathematical coherence property that univoquely defines one reduced model given one rheology and one thin-layer regime. For the first time, as far as we know, various known reduced models can thus be investigated within a single mathematical framework, for various rheologies (viscous and viscoelastic) and various limit regimes (fast inertial flows and slow viscous flows). Furthermore, our systematic procedure also produces new reduced models for viscoelastic non-Newtonian fluids and improves on our previous work [Bouchut & Boyaval, M3AS (23) 8, 2013].
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。
