Abstract

A problem of a plane-parallel steady motion of a low-viscosity incompressible fluid that fills a rotating cylindrical cavity by half is under consideration. The Navier slip condition is imposed on a fluid — solid wall interface, and the condition of the absence of tangential stresses is imposed on a free boundary. The equation of a boundary layer considered on the entire boundary of a semicircle as a single whole is reduced to a heat equation by changing the variable. A solution to the problem is constructed in the form of a series, while corner boundary layers are ignored. Calculations and comparison with the solution constructed earlier using the finite difference method are performed.

中文翻译：

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填充圆柱腔一半的低粘度流体运动的渐近分析

摘要

一个低粘度不可压缩流体的平面平行稳定运动问题正在考虑中，该流体填充一个旋转的圆柱腔一半。Navier 滑移条件施加在流体-固体壁界面上，没有切向应力的条件施加在自由边界上。通过改变变量，将半圆的整个边界视为一个整体的边界层方程简化为热方程。该问题的解决方案以系列的形式构建，而忽略角边界层。进行计算并与之前使用有限差分法构建的解进行比较。