Boundary Layer Induced by a Potential Vortex
Boundary Layer Induced by a Potential Vortex
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势涡引起的边界层
DOI：
10.1063/1.1693691
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发表时间：
1971
影响因子：
4.6
通讯作者：
R. J. Belcher
中科院分区：
文献类型：
--
作者：
O. Burggraf;K. Stewartson;R. J. Belcher
本文对半径为a的固定圆盘上的层流边界层进行了数值计算，该圆盘的轴线与具有环流Γ的涡旋同心。计算从圆盘的边缘开始，向内向轴线继续，直到终端流动的性质变得明显。给出了边界层方程解在轴线附近的两层渐近展开式，分析所揭示的端部流动特性与数值结果吻合较好。终端边界层的结构由厚度为O[(ν/Γ)1/2R]的内层和外层组成，内层的厚度为O[(ν/Γ)1/2R]，其中的流动主要是径向的，而外层的厚度为O[(ν/Γ)1/2a]，主要是无粘性的，其中的流动恢复到外部势涡。外层的质量通量不会随着r→0而消失，这表明边界层必须以摩尔设想的方式在r=0时从表面喷发出来。
A numerical computation of the laminar boundary layer on a fixed circular disk of radius a whose axis is concentric with that of a vortex having circulation Γ is described. The computations were started at the edge of the disk and continued inward toward the axis until the properties of the terminal flow became evident. A two‐layer asymptotic expansion was formulated for the solution of the boundary‐layer equations near the axis, and the terminal‐flow properties revealed by the analysis are shown to be in excellent agreement with the numerical results. The structure of the terminal boundary layer consists of an inner layer next to the surface with thickness O[(ν/Γ)1/2r] in which the flow is primarily radial, and an outer layer with thickness O[(ν/Γ)1/2a] of predominantly inviscid nature in which the flow recovers to the external potential vortex. The mass flux in the outer layer does not vanish as r→0, indicating that the boundary layer must erupt from the surface at r=0in the manner envisioned by Moore.