Experiments on transition to turbulence in a purely oscillatory pipe flow were performed for values of the Reynolds number Rδ, defined using the Stokes-layer thickness δ = (2ν/ω)½ and the cross-sectional mean velocity amplitude Û, from 19 to 1530 (or for values of the Reynolds number Re, defined using the pipe diameter d and Û, from 105 to 5830) and for values of the Stokes parameter λ = ½d(ω/2ν)½ (ν = kinematic viscosity and ω = angular frequency) from 1·35 to 6·19. Three types of turbulent flow regime have been detected: weakly turbulent flow, conditionally turbulent flow and fully turbulent flow. Demarcation of the flow regimes is possible on Rλ, λ or Re, λ diagrams. The critical Reynolds number of the first transition decreases as the Stokes parameter increases. In the conditionally turbulent flow, turbulence is generated suddenly in the decelerating phase and the profile of the velocity distribution changes drastically. In the accelerating phase, the flow recovers to laminar. This type of partially turbulent flow persists even at Reynolds numbers as high as Re = 5830 if the value of the Stokes parameter is high.
A reciprocating oscillatory turbulent flow in a rectangular duct is investigated experimentally by making use of a laser-Doppler velocimeter, hot-wire anemometers as well as electronic digital sampling and processing equipments.The profiles of the mean velocity, the turbulence intensities, the Reynolds stress and the turbulent-energy production rate are compared for the accelerating and decelerating phases.The characteristics of such a flow are quite different from wall turbulence which is steady in the mean. In the accelerating phase, turbulence is triggered by the shear instability at a slight distance from the wall but is suppressed and cannot develop. However, with the beginning of flow deceleration, turbulence grows explosively and violently and is maintained by the bursting type of motion.The turbulent-energy production becomes exceedingly high in the decelerating phase, but the turbulence is reduced to a very low level at the end of the decelerating phase and in the accelerating stage of reversal flow. Spectra and spatial correlations for the various phases are compared. The spectral decay in the high-frequency range for the decelerating phase with high turbulence is far steeper than that of Kolmogorov's −5/3 power law, indicating remarkably high energy dissipation by high-frequency turbulence.Notwithstanding the great difference between the ensemble-averaged characteristics of the oscillatory flow and those of steady wall turbulence, its basic processes such as ejection, sweep and interactions directed towards and away from the wall are the same as those of ‘steady’ wall turbulence.
The structure of turbulence and its role in the breaking wave dynamics within the surf zone have been investigated through laboratory experiments using several flow visualization techniques and a fibre-optic LDV system. The results indicate that there exists a characteristic structure of large-scale eddies referred to here as ‘horizontal eddies’ and ‘obliquely descending eddies’, which has a significant role in the generation of Reynolds stress and thus affects the deformation of the mean flow field. The experiments also reveal that these eddies caused by the wave breaking bring a large amount of vorticity (with non-zero average) into otherwise almost irrotational velocity fields, resulting in the generation of vorticity-related mean flow fields as well as turbulence (vorticity-containing velocity fluctuation). This means that the breaking waves in the surf zone can be regarded as pseudowaves which consist of irrotational velocity components as ‘wave motion’ and appreciable amounts of rotational mean velocity components as ‘eddying motion’ (with non-zero mean vorticity) together with turbulence. It is found that the generation of the mean rotational velocity component due to wave breaking causes considerable increase in mass and momentum transport, as compared with ordinary non-breaking waves, and thus a decrease in wave height.
Density profiles of a perdeuterated poly(methyl methacrylate) (dPMMA) film spin-coated on a substrate in water, hexane, and methanol, which are "nonsolvents" for dPMMA, were examined along the direction normal to the interface by specular neutron reflectivity (NR). The interfaces of dPMMA with the liquids were diffuse in comparison with the pristine interface with air; the interfacial width with water was thicker than that with hexane. Interestingly, in water, the dPMMA film was composed of a swollen layer and the interior region, which also contained water, in addition to the diffused layer. The interface of dPMMA with hexane was sharper than that with water. Although there were slight indications of a swollen layer for the dPMMA in hexane, the solvent molecules did not penetrate significantly into the film. On the other hand, in methanol, the whole region of the dPMMA film was strikingly swollen. To conserve mass, the swelling of the film by the nonsolvents is accompanied by an increase in the film thickness. The change in the film thickness estimated by NR was in excellent accord with the results of direct observations using atomic force microscopy (AFM). The modulus of dPMMA in the vicinity of the interfaces with liquids was also examined on the basis of force-distance curves measured by AFM. The modulus decreased closer to the outermost region of the film. The extent to which the modulus decreased in the interfacial region was consistent with the amount of liquid sorbed into the film.
Based on a dimensional consideration, the ‘−3 power law’ on the spatial spectrum of sand waves formed by flowing water Sηη(k) is derived for a large wave-number equilibrium subrange, \[ S_{\eta\eta}(k)\sim \alpha k^{-3}, \] where α is a constant depending on the angle of repose of sand particles and k denotes the wave-number.Likewise, the frequency spectrum is shown to have the ‘−3 power law’ range for higher frequencies as well as the ‘−2 power law’ range for frequencies near a spectral peak.These spectra are shown to agree with experimental data from various sources.
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