The importance of spline functions in various fields including numerical fluid dynamics is now well recognized. While basis for univariate spline functions has been well established to be utilized for various problems, surprisingly, until the early eighties, very little information on the theory and computational methods of multivariate spline functions was known. Since then, the subject has become a rapidly growing field of mathematical research. The main purpose of this article is to outline this newly developed theory on multivariate splines. For this, some of the basic topics in univariate splines that have parallel extensions to the multivariate setting are mentioned first.

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Fluid dynamics on Wing-in-Surface Effect (WISE) craft are reviewed with special interest in the development of “Marine Slider : μ sky”. Subjects are wing theory in the surface effect, high-lift devices, pitching stability, hydrodynamics as a boat and other problems.

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The structure of vortex street in the wake of a circular cylinder was studied by using flow visualization and hot-wire technique in a low-speed wind tunnel. The lateral position of the center of a vortex in the vortex street in the visualized flow pattern is in good agreement with the lateral position of the inflection point of mean velocity distribution and also that of the maximum of vorticity distribution. However, the lateral position of the maximum turbulence intensity does not coincide with that of the center of a vortex, but it is in good agreement with the lateral position of the half value of vorticity distribution. The lateral position of the edge of the vortex core is farther outside of the position of the maximum turbulence intensity.

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To obtain a better understanding of the coupling between external disturbances and excited instability waves, the receptivity to acoustic disturbances is studied experimentally for separated flows in the leading-edge region of a flat-plate airfoil. A linear stability calculation (with parallel flow assumption) is also made on the inflectional velocity distribution near the leading edge to clarify the receptivity through identifying the instability wave excited. The results show that the separated flow in the leading-edge region is highly receptive to external disturbances and develops the instability wave, whose amplitude (in terms of u-fluctuation) is proportional to and an order of magnitude larger than that of the external sound wave. It is also shown that the excited wave is, even in the vicinity of the leading edge, very close to the eigenmode calculated from the linear stability theory. The strong receptivity of the leading-edge-separated flow is emphasized through comparing with that in the flow without separation.

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Five different aerofoil models under strong ground effect, each of them having different wing profile but with the same aspect-ratio are tested in the Low Turbulence Wind Tunnel at the Institute of Fluid Science, Tohoku University. It is important to develop and select new wing sections available for WIG-vehicles which runs very close to ground surface so that strong ground effect is utilized and sufficient stability is obtained. Angle of attack and clearance height between the trailing edge and the ground plate are varied. Result of the influence of ground clearance and angle of attack for lift, drag, and moment is reported.

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