Abstract

The two-dimensional laminar flow of a viscous incompressible fluid over a flat surface is considered at high Reynolds numbers. The influence exerted on the Blasius boundary layer by a body moving downstream with a low velocity relative to the plate is studied within the framework of asymptotic theory. The case in which a small external body modeled by a potential dipole moves downstream at a constant velocity is investigated. Formally, this classical problem is nonstationary, but, after passing to a coordinate system comoving with the dipole, it is described by stationary solutions of boundary layer equations on the wall moving upstream. The numerically found solutions of this problem involve closed and open separation zones in the flow field. Nonlinear regimes of the influence exerted by the dipole on the boundary layer with counterflows are calculated. It is found that, as the dipole intensity grows, the dipole-induced pressure acting on the boundary layer grows as well, which, after reaching a certain critical dipole intensity, gives rise to a singularity in the flow field. The asymptotics of the solution near the isolated singular point of the flow field is studied. It is found that, at this point, the vertical velocity grows to infinity, viscous stress vanishes, and no solution of the problem exists at higher dipole intensities.

中文翻译：

---

给定外压下上游动壁不可压缩边界层奇点的形成

摘要

粘性不可压缩流体在平坦表面上的二维层流被视为高雷诺数。在渐近理论的框架内研究了相对于板块以低速向下游移动的物体对 Blasius 边界层的影响。研究了由势偶极子建模的小型外部物体以恒定速度向下游移动的情况。形式上，这个经典问题是非平稳的，但是，在传递到与偶极子共移的坐标系后，它可以通过向上游移动的壁上的边界层方程的平稳解来描述。该问题的数值解涉及流场中的封闭和开放分离区域。计算偶极子对逆流边界层影响的非线性区域。研究发现，随着偶极子强度的增大，作用在边界层上的偶极子诱导压力也随之增大，达到一定的临界偶极子强度后，流场中会出现奇点。研究了流场孤立奇点附近解的渐近性。结果发现，此时，垂直速度增长至无穷大，粘性应力消失，并且在较高偶极子强度下，问题不存在解决方案。