This is a short survey of weak solutions of the Euler's equations of gas dynamics. The properties of discontinuities of the weak solutions are discussed, and flows with shock waves and contact discontinuities 'are shown to be given by weak solutions of the Euler's equations with the subsidiary entropy condition.

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This article is a review of recent studies on the effects of fluid particles upon NMR signals. Probability density of velocity of fluid particles in a circular pipe can be obtained from the first spin echo amplitude. Turbulent diffusion or Lagrangian correlation can be discussed by analyzing the second spin echo amplitude. This article has 6 sections. Section 1 summarizes the history of the study of this field. Section 2 explains the relation between NMR signals and velocity of fluid particles. In section 3, some formulas of spin echo amplitudes in laminar flow region are shown. Path integral method to analyze spin echo amplitudes in turbulent region is presented in section 4. Cumulant expansion method is presented in section 5. Observations of intermittent flow which appears in the transitional region from laminar to turbulent flow are reported in the last section.

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An experimental investigation of flow behind a backward facing step was made in the present study. Time-averaged flow patterns were measured by a pitot tube and a pulsed-wire anemometer, while time-dependent measurements were made by rotating straight and slanted hot-wires and a pulsed-wire. A data acquisition system including a traversing system of probes was used. The pulsed-wire was calibrated carefully prior to the measurements in order to minimize the influences of electrical noises. The present results thus obtained were compared with some criteria, which had been reported for flow behind a backward facing step, in order to check the accuracies of results.
After the above-mentioned examinations, the three-dimensional and time-dependent natures of flow near the time-averaged reattachment point was discussed by introducing two types of eddies generated in the shear layer.

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An analysis was made for slow simple shear flows past a rotating circular cylinder in the vicinity of a plate, on the basis of the Stokes equations. An analytical solution for the stream function was obtained, and also an analytical expression of the torque acting on the rotating circular cylinder was derived. In addition, it was clarified that various flow patterns occur for different combinations of the gap between the cylinder and plate and the angular speed of the cylinder.

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The present paper describes some measured results on the vortex shedding characteristics of a circular cylinder which is placed near a wall in a uniform flow, and forcedly vibrated in the direction perpendicular to the uniform flow. The investigation is based on a spectral analysis of the output signals from a single hot-wire located in the cylinder wake. the results clarified the characteristics of the synchronization phenomenon or so-called locking-in phenomenon of a vibrating circular cylinder near a wall.

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In order to make clear the mechanism of the velocity slip in the riser of a natural circulation heavy liquid metal MHD generation loop and to find the conditions for reducing the slip loss, the calculation of model flows and the visual simulation experiment have been performed. The calculation is based on the steady one-dimensional flow of dilute deformable bubbles and liquid two-phase model. The reduction of the bubble size, the increase in the flow velocity of liquid and the oblate deformation of bubbles are effective to reduce the slip loss. It is shown that a mercury loop can be simulated by a water loop in the reduced pressure. Such a visual simulation experimental facility has been constructed and the two-phase flow in the riser has been observed. The flow pattern changes from bubble flow to slug flow in the middle of the riser for city water, but the coalescence of bubbles is prevented effectively by adding a small amount of surface active agent. The direct measurement of the flow field in the riser shows that the cross-sectionally averaged velocity of each phase consists with the calculated one satisfactorily.

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The linear stability of unstably stratified shear flows between two horizontal parallel plates was investigated. Eigenvalue problems were solved numerically by making use of the expansion method in Chebyshev polynomials, and the critical Reyleigh numbers were obtained accurately in the Reynolds number range of [0.01, 100]. It was found that the critical Rayleigh number increases with an increase of the Raynolds number. The result strongly supports previous stability analyses except for the analysis by Makino & Ishikawa [J. Jpn. Soc. Fluid Mech. 4 (1985) 148-158] in which a decrease of the critical Rayleigh number was obtained

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