Numerical calculations are made of the torque required to sustain a wavy-vortex flow between rotating cylinders. The results are found to agree well with experimental work of Donnelly (1958), and give further confirmation of the validity of Davey, DiPrima & Stuart's (1968) analysis.

The results of an experimental investigation of a turbulent vortex street in the range 103 [lsim ] Re [lsim ] 2 × 104 are presented. The vortex street was created by the motion of a circular cylinder in a motionless fluid (mercury). Photographs obtained showed that the turbulent street, created by the vortex shedding behind the cylinder, persisted at longer downstream distances and higher Reynolds numbers than previously reported in the literature. A theory was developed to account for the experimental measurements pertaining to the change of the geometrical characteristics, h (distance between the two rows of vortices) and α (longitudinal distance between two consecutive vortices on the same row), of the street in the downstream direction. The implications of the structure of the vortex street on the entrainment mechanism of the turbulent wake are discussed. Some observations of the flow in the formation region of the vortices are discussed in relation to existing work.

The 41st EUROMECH Colloquium on flows with concentrated vorticity was held in Norwich from 17 to 21 September 1973. There were sixty-five participants from nine countries and the author was the chairman of the organizing committee.

This paper deals with local flow characteristics of subsonic turbulent jets in the presence of a cross-flow. For the various types of jet considered (a cylindrical jet and coaxial jets) the experimental results concern the axes and the velocity profiles in the plane of symmetry of the flow. In the case of the cylindrical jet, the shape of the universal axial velocity profile is defined, as are the law of velocity decay along the axis and the laws of variation of the thicknesses of the jet. Finally, the existence of a link between the axis equation and the law of axial velocity decay in the zone of similarity of the velocity profiles is established.

Experiments were conducted in two curved rectangular ducts of different radii and the results compared with flow in a straight duct. The turbulent boundary layers developing on the curved walls were examined for mean flow properties. The law of the wall takes a modified form and the usual logarithmic portion applies over a very small range of the profiles on the inner walls and a slightly larger range on the outer walls. Similarity based on a defect law did not exist for any part of the flow examined.

The response of a Pitot probe in a uniform laminar stream is commonly expressed in the form \[ P_s = P+{\textstyle\frac{1}{2}}C_{\rho} U^2, \] where Ps is the probe signal pressure, P is the stream static pressure, U is the stream speed and ρ is the fluid density. It has been found that for ordinary sphere-nosed, round-nosed and square-nosed probes \[ 1-C = K(\sin^2\theta)^m = K(U^2_n/U^2)^m, \] where θ is the angle between the velocity vector and the probe axis, and Un ≡ U sin θ is the transverse velocity component. The parameters m and K are functions of the probe geometry. These formulae also describe the performance in a turbulent stream when the probe is small compared with the turbulence scale. The evaluation of the time-averaged response is treated, and an answer is developed to the question of what it is that a Pitot probe measures in a turbulent stream. In a turbulent shear flow having the properties of a boundary layer, the reference pressure is best taken to be the static pressure at the shear-layer edge. It is shown that round-nosed probes with Di/D≃0·45 and square-nosed probes with Di/D≃0·15 then detect ${\textstyle\frac{1}{2}}\rho\overline{U}^2_x$ with good accuracy, where Di/D is the ratio of the inside and outside diameters of the Pitot tube. When measurements are made with two probes of dissimilar geometry, the differential response can be used to find the mean-square level of the transverse velocity fluctuations. Turbulence levels so measured agree closely with results from hot-wire anemometry.

Wind-tunnel turbulence behind a parallel-rod grid with jets evenly distributed along each rod is nearly isotropic. Homogeneity improvement over prior related experiments was attained by the use of controllable nozzles. Compared with the ‘passive’ case, the downwind-jet ‘active’ grid has a smaller static pressure drop across it and gives a smaller turbulence level at a prescribed distance from it, while the upwind-jet grid gives a larger static pressure drop and larger turbulence level. ‘Counterflow injection’ generates larger turbulence energy and larger scales, both events being evidently associated with instability of the jet system. This behaviour is much like that commonly observed behind passive grids of higher solidities.

If the turbulent kinetic energy is approximated as an inverse power law in distance, the (positive) exponent decreases with increasing (downwind or upwind) jet strength, corresponding to slower absolute decay rates. No peculiar decay behaviour occurs when the jet grid is ‘self-propelled’ (zero net average force), or when the static pressure drop across it is zero.

The injection does not change the general behaviour of the energy spectra, although the absolute spectra change inasmuch as the turbulence kinetic energy changes.

A study is made of uniform flow past a semi-infinite flat plate with a similarity injection distribution of boundary-layer magnitude. Attention is focused on a solution at exactly the critical injection rate for which classical boundary-layer theory predicts the blow-off singularity. Following a description of the more recent interaction analyses which also fail at the critical rate, a new theory is developed which leads to physically meaningful results. In particular, it is shown that the non-monotonic variation in wall shear with increasing injection rate near the critical value, noted by Klemp & Acrivos (1972), is real. A delicate interplay of weak pressure interactions and viscous effects is shown to be responsible for this surprising phenomenon.

The distortion of a gas bubble rising steadily in an inviscid incompressible liquid of infinite extent under the action of surface tension forces is investigated theoretically using an appropriate extension of the tensor virial theorem. A convenient parameter for distinguishing the bubble shape is the Weber number W. The virial method leads to an expression relating W and the axis ratio χ, of the transverse and longitudinal axes of the bubble. To first order in W, this relation agrees with the linear theory established by Moore (1959). Also, comparison of the results with his (1965) approximate theory reveals similar features and excellent agreement up to χ = 2. In particular, it confirms his prediction of the existence of a maximum Weber number. Although the present work does not consider the stability of these bubbles, it is interesting to note that the maximum value of 3.271 attained by W differs only by about 2.8% from the critical Weber number obtained by Hartunian & Sears (1957) for the onset of instability.

An approximate method for the study of slightly distorted spheroidal gas bubbles is also formulated and the resulting boundary-value problem solved numerically. The theory is then extended to include gravity. The joint effect of surface tension as well as gravitational forces has not been included in earlier theories. The shapes of the bubbles are traced and compared with the unperturbed spheroids. Comparisons for the velocity of bubble rise are made between the present predictions and some experimental results. In particular the results are compared with recent experimental data for the motion of gas bubbles in liquid metals.

The steady flow in and around a deformable liquid sphere moving in an unbounded viscous parabolic flow and subject to an external body force is calculated for small values of the ratio of the Weber number to the Reynolds number in the creeping-flow regime. It is found that, in addition to the drag force, the drop experiences a force orthogonal to the undisturbed flow direction. When the body force is absent (neutrally buoyant drop), this lift force tends to drive the drop inwards to the axis, where the undisturbed flow velocity is maximum, i.e., towards a position of lower velocity gradient. In the case for which the parabolic flow profile is a Poiseuille flow profile, the lift force is given by the expression. \[ {\bf F}_1 =-6\pi\mu\epsilon U_0\frac{\alpha +\frac{2}{3}}{\alpha + 1}\bigg(\frac{a}{R_0}\bigg)^4{\bf b}F[1+o(\epsilon)]. \] Here a is the radius of the undeformed sphere, R0 is the radial distance from the position of maximum undisturbed flow U0 at the profile axis to the position of zero flow, ε is the ratio of the Weber number to the Reynolds number, given by ε=μU0T−1, where μ is the external fluid viscosity and T is the surface tension of the drop, α is the ratio of the drop and external fluid viscosities, b is the radial vector from the flow axis to the centre of mass of the drop, and F is a function of α and a dimensionless parameter dependent on the body force that is determined in the analysis. Reasonable agreement is found between the observations by Goldsmith & Mason (1962) of the axial drift of liquid drops in Poiseuille flow and the predictions of the theory herein.