The concept of boundary layer flow, introduced in 1904 by Prandtl, is a popular field in Fluid Mechanics for engineers, physicists and mathematicians. In the classical Blasius boundary layer flow the transverse (normal) velocity reaches a finite value and remains constant in the free stream. If this finite vertical speed will be added to the free stream speed the resulting velocity in the free stream will be greater than the original velocity upstream of the plate which is irrational. This phenomenon has been marked and discussed in many Fluid Mechanics textbooks without a satisfactory explanation. In the present work we present a definite explanation by solving the complete Navier-Stokes equations. It is found that the real ambient transverse velocity is zero and not finite as it is predicted by the boundary layer theory. The same is valid in the classical free convection flow along a vertical isothermal plate.
The motion of a single heavy sphere in ambient fluid: a benchmark for interface-resolved particulate flow simulations with significant relative velocities
Transverse and lateral confinement effects on the oscillations of a free cylinder in a viscous flow
不同类型的不稳定性的自由圆柱体（直径$D$，长度$L$）已被研究在一个粘性流（速度$U$）之间的平行垂直壁的水平宽度$W$在距离$H$：的影响的限制参数$D/H$和$L/W$进行了研究。随着$D/H$的增加，从稳定流过渡到横向于壁面的振荡，然后过渡到轴相对于水平面角度振荡的颤振运动。这两种类型的振荡可以在过渡域中叠加。横向振荡的频率$f$在以下范围内与横向约束$L/W$无关：0.055 \le L/W \le 0.94 $ for a given cylinder velocity $ V_{cx} $ and increases only weakly with $ $. These results are accounted for by assuming a 2D local flow over the cylinder with a characteristic velocity independent of $ $. These results are accounted for by assuming a 2D local flow over the cylinder with a characteristic velocity independent of $ L/W $ for a given $ V_{cx} $ value. The experimental v…
