The normal impingement of axisymmetric Homann stagnation-point flow on a surface executing perpendicular, planar, biaxial stretching is studied. The flow field generated is an exact solution of the steady, three-dimensional Navier–Stokes equations in the form of a similarity solution. It is shown that two sets of dual solutions exist, forming four different branches of steady solutions. For sufficiently small stretches (including compressions of the surface) the four branches exhibit a multi-branch spiralling behaviour in the surface shear stress parameter plane. The linear stability of the solutions are also examined, identifying only one stable solution for each set of parameters.

研究了轴对称Homann滞止点流在执行垂直，平面，双轴拉伸的表面上的法向碰撞。所生成的流场是以相似性解决方案的形式对稳定的三维Navier-Stokes方程进行精确求解。结果表明，存在两组对偶解，形成了稳定解的四个不同分支。对于足够小的拉伸（包括表面压缩），四个分支在表面剪切应力参数平面中表现出多分支螺旋行为。还检查了解的线性稳定性，对于每组参数仅识别出一个稳定解。