A theoretical method is presented for predicting the deformation and the conditions for breakup of a liquid droplet freely suspended in a general linear shear field. This is achieved by expanding the solution to the creeping-flow equations in powers of the deformation parameter ε and using linear stability theory to determine the onset of bursting. When compared with numerical solutions and with the available experimental data, the theoretical results are generally found to be of acceptable accuracy although, in some cases, the agreement is only qualitative.

Effects of moderately large Reynolds numbers R are studied by considering higher order terms in the expansions for turbulent pipe and channel flows for R → ∞. Matched asymptotic expansions using two length scales are employed to emphasize the two-layer structure of turbulent shear flows near solid walls. The effects appear as additional terms in extended forms of the law of the wall, the logarithmic velocity law, the velocity defect law and the logarithmic skinfriction law. These generalizations are critically compared with experimental results for pipe flows of Patel & Head and extremely good agreement is obtained. Also, possible applications are discussed for extending the range of skin-friction and heat-transfer devices which are based on wall similarity.

Measurements of a wall jet in a self-preserving pressure gradient are described. The quantities measured with a linearized hot-wire anemometer were the mean velocity, the turbulence stresses, triple and quadruple velocity correlations, intermittency and spectra of the longitudinal turbulence intensity. The turbulence, as well as the mean flow, reached a self-preserving state in which the ratio of the maximum velocity to the free-stream velocity was 2·65. Skin friction was also measured using the razor-blade technique in the viscous sublayer and buffer region. The values of the constants in the logarithmic law of the wall are found to be similar to those in boundary-layer and pipe flows. The skin-friction coefficient is slightly lower than that found for the wall jet in still air (Guitton 1970), but close to the formula of Bradshaw & Gee (1962) for the wall jet in an external stream with zero pressure gradient.

A balance of the terms in the turbulence energy equation is presented and discussed. The shearing stress is not zero at the point of maximum velocity but is of opposite sign to that at the wall and hence the contribution of this stress to turbulence production is negative in the outer part of the boundary-layer region. However, the total turbulence production remains positive because the contribution of the normal stresses is positive and slightly larger. The pressure—velocity gradient correlations are evaluated by difference from the Reynolds stress equations and are compared with the theoretical model of Hanjalić & Launder (1972b). Agreement is quite good in the outer region of the wall jet. The above model is also compared with the triple velocity correlations and again found to be in fair agreement.

The solution to the steady problem of an inviscid jet emerging from a symmetric nozzle of slowly varying profile is sought as an asymptotic series in the wall slope. The expansion of the solution in the region near the nozzle lip is singular at infinity, so that a matched expansion technique is evolved to solve the problem. To the order to which the solution is obtained in the present paper, the jet contraction ratio is shown to be the same as that from a nozzle formed by two inclined planes with inclination angle the same as the exit slope of the nozzle. Composite expansions are formed and used to check the consistency of expansion and matching procedures.

Investigations are made of the wave motion which arises near resonance in a tube with an applied transverse magnetic field filled with a highly electrically conducting gas and closed by two rigid walls. The wave motion is driven by the sinusoidal radiative flux emitted by one of the walls as a consequence of its oscillatory temperature; the other wall is taken to be a perfect reflector of thermal radiation. The effects of radiative transfer are treated by the use of the differential approximation. The analysis leads to the same formal governing integral equation for the solution as arises in the ordinary gasdynamic case in the absence of electromagnetic effects. Within a narrow frequency band around resonance the theory predicts the occurrence of magnetogasdynamic shock waves which become dispersed as the thermal radiation is strengthened and may be totally dispersed to leave a continuous, periodic, but not necessarily sinusoidal, wave motion. The effect of the magnetic field is to delay the onset of dispersion.

The paper examines the results of an experiment which was designed to elucidate the manner in which wave characteristics, strut geometry and aspect ratio influence the angles at which struts ventilate. The experiment was conducted using small-scale models in a towing tank which allowed the wave parameters to be varied independently. The results indicate which parameters of a seaway are most hazardous to the operation of a hydrofoil ship in high seas and suggest design features which may extend the capability range of such craft.

The properties of infinitesimal disturbances to Poiseuille flow in a circular pipe have been found for a wide range of wavenumbers through recent numerical work (Salwen & Grosch 1972; Garg & Rouleau 1972). These studies did not, however, find the least-damped disturbances. In this paper, the properties of disturbances are found in a limiting case. These disturbances are thought to have decay rates which are equal to or very close to the smallest value possible for any given large value of the Reynolds number R. For disturbances which decay in time, the limiting disturbances can be found analytically. They have the property that the axial wavenumber α tends to zero as R → ∞. The smallest decay rate -βi is given by \[ -\beta_iR = j^2_{1,1}\approx 14.7, \] where j1,1 is the first zero of the Bessel function J1. Two modes have this decay rate. One is axisymmetric with motion only in the azimuthal direction, and the other has azimuthal wavenumber n = 1. For disturbances which decay in space, the limiting solutions can be found by numerically evaluating power series. They have the property that the frequency β tends to zero as R tends to infinity. The smallest decay rate αi for these disturbances is given by αiR ≈ 21·4, corresponding to an axisymmetric mode with motion only in the azimuthal direction. A mode with azimuthal wavenumber n = 1 has a slightly larger decay rate given by αiR ≈ 28·7.

A plane harmonic sound wave is considered to be incident upon a rigid plane screen that contains a periodic rectangular array of circular or elliptical apertures, and a characterization is sought for the reflexion and transmission coefficients of the scattered waves when the relationships aperture dimension [Lt ] spacing [Lt ] wavelength apply. The problem is analysed with the help of an integral equation over a single aperture and, as a consequence of the determination of the leading terms in its asymptotic solution, some prior results for more general (that is, irregular) aperture spacing are confirmed and specific features of the interaction in the periodic arrangement are established. Similar formulations are devised and given attention for the related problems in which (i) the screen is backed by a rigid infinite plane and (ii) the apertures contain rigid pistons capable of executing normal displacements compatible with an assigned and common impedance. A section is devoted to the solution, based on expansion of its kernel, for an integral equation of the first kind with a plane circular or elliptical domain.

The two-dimensional wave pattern produced in a homogeneous rotating fluid by a forcing effect oscillating with a frequency σ′0 and travelling with a uniform speed U along a line inclined to the axis of rotation at an arbitrary angle α is studied following Lighthill's technique. It is shown how the far field changes with α and σ′0.

For all σ′0 < 2Ω, except for σ′0 = 2Ω sin α (Ω being the angular velocity of the fluid), the forcing effect excites two systems of waves. When σ′0 → 2Ω sin α one of these systems spreads out, influencing the upstream side while the other shrinks in the downstream direction. This upstream influence is to the left or to the right of the line of motion of the forcing effect (the forcing line) according as σ′0 − 2Ω sin α[lg ] 0 and increases as σ′0 − 2Ω sin α decreases. For σ′0 > 2Ω there is only a single system propagating downstream. As α varies these systems undergo a kind of rotation retaining the main features. α ≠ 0 or ½π makes the pattern asymmetric about the forcing line while a non-zero σ′0 splits the steady-case identical wave systems into two, which are otherwise coincident.

When σ′0 = 2Ω sin α the forcing effect excites straight unattenuated waves of fixed frequency travelling both ahead and behind in a ‘column’ parallel to the forcing line and enclosing it. Also there are two other systems, which propagate without penetrating into an upstream wedge. It is shown that this ‘column’ is the counterpart of the ‘Taylor column’.

The steady two-dimensional problem of reflexion of an oblique partly dispersed plane shock wave from a plane wall is studied analytically. Viscosity, diffusion and heat conduction are neglected. The thermodynamic state of the gas is assumed to be determined by the instantaneous values of the specific entropy s, pressure p and a finite number of internal state variables. Results for the flow field behind the reflected shock are obtained by a perturbation method which is based on the assumption that the influence of relaxation is relatively weak.

Measurements of the spectral components of turbulent momentum transfer for fully developed pipe flow are presented. The results indicate that near the wall (y+ < 15) two types of momentum transfer processes occur. A net positive transfer takes place in the higher frequency range of the energy-containing part of the turbulence spectrum whereas a net negative transfer returns low momentum to the wall region at the lower end of the spectrum. Examination of the turbulence at various y+ shows that the significant features of the turbulence spectra scale on frequency at any given Reynolds number, thus leading to an interpretation of the flow structure which is consistent with the hydrogen-bubble visualization data of Runstadler, Kline & Reynolds (1963). The results are consistent with a flow model in which disturbances extend from the sublayer to the core of the flow. Recent turbulent heat transfer measurements are also interpreted successfully by this model.

Experiments were carried out using models having L/D [les ] 2 and the resulting pressure distributions and vortex shedding characteristics are presented. A simple visualization technique which provides explanations of some of the measured results is described. It is concluded that splitter planes reduce the drag markedly by stabilizing the separation points and produce a wake narrower than that for a plain cylinder, raise the base pressure by as much as 50% and affect the Strouhal number to a lesser degree. Careful measurement techniques have enabled these effects to be presented accurately.

An inviscid Kármán-type vortex-shedding model is employed to show that multiple modes of vortex streets are possible, for flow around a given obstacle. This is in confirmation of various experimental observations in recent years, which were challenged by opposing claims that these were due to experimental inaccuracies.