Re-examinations of the two-dimensionality of the flow and skin friction coefficient were made in a zero-pressure gradient, smooth wall, turbulent boundary layer. In order to well achieve the two-dimensionality, the balance in momentum integral equation was checked in detail. And, the wall shear stress was determined by direct measurement using a floating element device. The momentum thickness Reynolds number ranges from 840 to 6220. The present results of skin friction coefficient obtained by the direct measurement proposed an empirical formula, and the quantitative differences were evaluated between the formula and the available experimental results. On the logarithmic velocity profile, the values of Kármán constant, additive constant, and wake parameter are affected by the methods to estimate skin friction coefficient and a degree of reliability of the two-dimensional flow. The profiles of present turbulent quantities were measured carefully in the turbulent boundary layer to construct database of the two-dimensional turbulent boundary layer without pressure gradient.

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In order to investigate the mechanism of “cut and connection” phenomenon of two vortex rings, interaction of two vortex rings with equivalent circulation on the same plane in infinite region is simulated by a finite difference method solving three-dimensional Navier-Stokes equation. As the “cut and connection” occurs, the vorticity disappears in the vicinity region of two vortex rings, while the bridge is produced and then two vortex rings are connected in both sides of the region where the vorticity is canceled. Each term of the vorticity equation was examined for investigating dominant factor in cut and connection phenomenon. We found following two results; the cancellation of vorticity is due to the convection term of the vortex equation and this result is consistent with the fact that there is intensified flow in the near region of vortex rings. It is observed that the viscous term is dominant factor for the bridging and the vorticity diffusion induced connecting both the peak values or the bottom values on the distribution of the vorticity, which yields forming the bridges between two vortex rings.

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