Abstract We describe three distinct stress boundary layer structures that can arise in the high Weissenberg number limit for the upper convected Maxwell (UCM) model. One is a single layer structure previously noted by M. Renardy, High Weissenberg number boundary layers for the upper convected Maxwell fluid J. Non-Newtonian Fluid Mech. 68 (1997), 125–132. The other two are double layer structures. These latter two structures extend the core flows that can be accommodated by the UCM model in the high Weissenberg regime. The three structures taken together, represent the main dominant balances that occur for the UCM equations near solid boundaries. For each structure, the leading order equations are derived in each region together with particular exact solutions when available. Importantly, the matching conditions between respective regions for each structure are also derived and explained. These stress boundary layers can arise in order one Reynolds number flows and are independent of the velocity boundary layers that can arise in high Reynolds number flows.

中文翻译：

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UCM 流体的高 Weissenberg 数边界层结构

摘要 我们描述了三种不同的应力边界层结构，它们可能出现在上对流麦克斯韦 (UCM) 模型的高魏森伯格数限制中。一个是先前由 M. Renardy、High Weissenberg 数边界层所指出的单层结构，用于上部对流麦克斯韦流体 J. Non-Newtonian Fluid Mech。68 (1997), 125-132。另外两个是双层结构。后两种结构扩展了 UCM 模型在高 Weissenberg 状态下可以容纳的核心流动。这三种结构合在一起，代表了 UCM 方程在固体边界附近发生的主要主要平衡。对于每个结构，在每个区域推导出主阶方程以及可用的特定精确解。重要的，还导出并解释了每个结构的各个区域之间的匹配条件。这些应力边界层可以按照一个雷诺数流动的顺序出现，并且与在高雷诺数流动中可能出现的速度边界层无关。