We consider the deformation of two-dimensional drops when immersed in a slow viscous corner flow. The problem is formulated as one of analytic function theory and simplified by assuming that both the drop and the exterior fluid have the same viscosity. An approximate analysis is carried out, in which the conditions at the interface are satisfied in an average sense, and this reveals the following features of the solution. A drop of given physical properties (volume, surface tension and viscosity), when immersed in a corner flow, has no steady equilibrium shape if the rate of strain of the applied flow is too large. On the other hand, if the rate of strain is small enough for a steady solution to exist, then in general there are two possible solutions. These features are confirmed by formulating the exact problem in terms of a nonlinear integro-differential equation, which is solved numerically.

Flow and turbulence in a 50 Hz rotating-field MHD system are investigated using the hot-film constant-temperature anemometer. Factors affecting anemometer disturbances and response time are discussed. From measurements of the magnetic field at points within the liquid the distribution of MHD forces is estimated. The mean rotational velocity of the flow is of the expected order of magnitude but much less dependent on the axial co-ordinate than the corresponding MHD force. With the aid of a thermal transit-time anemometer, a weak secondary flow is detected. A note on scale-model studies of MHD systems envisaged in metallurgical applications of magnetohydrodynamics points out some basic difficulties in modelling large high-powered systems on a small scale.

The effects of swirl on internal turbulent flows are studied by conducting experiments on turbulent pipe flow with variable initial swirl. This first part of the study is primarily concerned with similarity laws. The mean velocity profiles, both away from and close to the wall, are found to admit similarity representations at sufficiently large Reynolds numbers, provided that flow reversal does not take place near the entrance. While the wall law is not sensibly dependent on swirl, the velocity defect law in its extended form is sensitive to swirl. Further, a logarithmic skin-friction law is obtained in which only the additive coefficient depends on swirl. This coefficient is found to vary linearly with the swirl angle in the range of the present experiments.

An electrical method of detecting and measuring the breakup of liquid jets is applied to the turbulent case. New data produced by this means, together with previous data, support the conjecture that the theory and understanding that were developed in connexion with the breakup of laminar jets can be used as a guide for turbulent jets as well.

Water jets are produced by vertically accelerating a rotating cone partially filled with water. It is shown that the acceleration of the parabolic meniscus results in a motion similar to that observed in a shaped explosive charge (Monroe jet). Acceleration of the cone is effected by means of an inductive electromagnetic accelerating device (conical pinch) whose theory is developed in terms of the WKB approximation. A second-order inviscid theory for the motion of the fluid in the cone in terms of the Penney-Price linearization procedure is presented and it is shown that good agreement for the jet head velocity can be achieved for low velocities. At higher velocities, experimental results appear to lag behind the theoretical ones, probably owing to the dispersal of the jet head through viscous drag with the surrounding atmosphere. The shape of the jet at early times is well represented by first-order theory.

A laser-Doppler velocimeter suitable for the measurement of mean and fluctuating flow velocities in water is described. Results of a study using this system in an axisymmetric turbulent jet of water and dilute polymer solutions are given. The laser-Doppler technique is better suited for such measurements than either Pitot tubes or heat-transfer gauges because the Doppler velocity measurements are independent of the physical properties of the fluid. Previous velocity measurements in polymer jets have suffered from the effects of the additives upon the sensors.

Turbulent round jets with Reynolds numbers between 5000 and 50000 were studied. For a jet issuing from a convergent nozzle the additives were found to have no effect upon the mean axial velocity or turbulence intensity at any point in the jet. However, for a jet issuing from a long length of circular pipe, the additives reduced the centre-line velocity and increased the turbulence level in the early part of the jet. Thus the principal effect of a polymer additive upon the jet appears to result from its effect upon the initial conditions.

A gas in a tube, one end of which is open, is driven by a periodic applied velocity or pressure at or near a resonant frequency. Damping is introduced into the system by radiation of energy through the open end. It is shown that shocks are possible at an open end and that there is a critical level of damping which ensures a continuous gas response for all frequencies. At the critical level the amplitude of the response is O(ε1/3), where ε is the amplitude of the input, and it is bounded by the amplitude predicted by linear theory. There is agreement with the qualitative experimental results available.

An analysis of the experimentally determined resonant amplitude and frequencies of oscillation of a gyroscope whose rotor contains liquid-filled cylindrical cavities reveals a surprising small amplitude instability region that is not predicted by the Stewartson instability criterion for a liquid-filled spinning top. Along with the experimental results and speculation concerning the cause of the observed phenomenon, there are presented some practical implications of the observations of use to designers of spinning vehicles containing liquid.

A body is started impulsively from rest and moves in a curved path in a stably stratified fluid. The phase configuration of the internal waves which are generated is studied using small amplitude wave theory. The theory is compared with experiment for a few special cases which include a horizontal cylinder moving in a circular path in a vertical plane, oscillating through a large amplitude in a horizontal plane, and moving with constant velocity past stationary plates. Theory and experiment show reasonable agreement except where the waves produced by the wake dominate the flow.

The waves generated in a two-dimensional fluid domain of infinite lateral extent and uniform depth by a deformation of the bounding solid boundary are investigated both theoretically and experimentally. An integral solution is developed for an arbitrary bed displacement (in space and time) on the basis of a linear approximation of the complete (nonlinear) description of wave motion. Experimental and theoretical results are presented for two specific deformations of the bed; the spatial variation of each bed displacement consists of a block section of the bed moving vertically either up or down while the time-displacement history of the block section is varied. The presentation of results is divided into two sections based on two regions of the fluid domain: a generation region in which the bed deformation occurs and a downstream region where the bed position remains stationary for all time. The applicability of the linear approximation in the generation region is investigated both theoretically and experimentally; results are presented which enable certain gross features of the primary wave leaving this region to be determined when the magnitudes of parameters which characterize the bed displacement are known. The results indicate that the primary restriction on the applicability of the linear theory during the bed deformation is that the total amplitude of the bed displacement must remain small compared with the uniform water depth; even this restriction can be relaxed for one type of bed motion.

Wave behaviour in the downstream region of the fluid domain is discussed with emphasis on the gradual growth of nonlinear effects relative to frequency dispersion duringpropagationand the subsequent breakdown of the linear theory. A method is presented for finding the wave behaviour in the far field of the downstream region, where the effects of nonlinearities and frequency dispersion have become about equal. This method is based on the use of a model equation in the far field (which includes both linear and nonlinear effects in an approximate manner) first used by Peregrine (1966) and morerecently advocated by Ben jamin, Bona & Mahony (1972) as a preferable model to the more commonly used equation of Korteweg & de Vries (1895). An input-output approach is illustrated for the numerical solution of this equation where the input is computed from the linear theory in its region of applicability. Computations are presented and compared with experiment for the case of a positive bed displacement where the net volume of the generated wave is finite and positive; the results demonstrate the evolution of a train of solitary waves (solitons) ordered by amplitude followed by a dispersive train of oscillatory waves. The case of a negative bed displacement in which the net wave volume is finite and negative (and the initial wave is negative almost everywhere) is also investigated; the results suggest that only a dispersive train of waves evolves (no solitons) for this case.

Second-order mean fields of motion and density are calculated for the two-dimensional problem of an internal gravity wave packet (the waves are predominantly of a single frequency o and wavenumber k) propagating as a wave-guide mode in an inviscid, diffusionless Boussinesq fluid of constant buoyancy frequency N, confined between horizontal boundaries. (The same mathematical analysis applies to the formally identical problem for inertia waves in a homogeneous rotating fluid.)

To leading order the mean motions turn out to be zero outside the wave packet, which consequently possesses a well-defined fluid impulse [Iscr ]. This is directed horizontally, and is given in magnitude and sense by \[ {\cal I} = \alpha{\cal M};\quad\alpha = \frac{2c_{\rm g}(c-c_{\rm g})(c+2c_{\rm g})}{c^3-4c^3_{\rm g}}. \] Here [Mscr ] is the so-called ‘wave momentum’, defined as wave energy divided by horizontal phase velocity c ≡ ω/k, and cg = c(N2–ω2)/N2, the group velocity.

If the wave packet is supposed generated by a horizontally towed obstacle, [Mscr ] appears as the total fluid impulse, but of this a portion [Mscr ]-[Iscr ] in general propagates independently away from the wave packet in the form of long waves. When the wave packet itself is totally reflected by a vertical barrier immersed in the fluid, the time-integrated horizontal force on the barrier equals 2 [Iscr ] (and not 2 [Mscr ] as might have been expected from a naive analogy with the radiation pressure of electromagnetic waves.)

The variable-coefficient Korteweg–de Vries equation \[ H_X + {\textstyle\frac{3}{2}}d^{-\frac{7}{4}}HH_{\xi} + {\textstyle\frac{1}{6}}\kappa d^{\frac{1}{2}}H_{\xi\xi\xi} = 0 \] with d = d(εX) is discussed for solitary-wave initial profiles. A straightforward asymptotic solution for ε → 0 is constructed and is shown to be non-uniform both ahead of and behind the solitary wave. The behaviour ahead is rectified by matching to the appropriate exponential form and, together with the use of conservation laws for the equation, the nature of the solution behind the solitary wave is discussed. This leads to the formulation of the solution in the oscillatory ‘tail’, which is again matched directly.

The results are applied to the development of the solitary wave into variable-depth water, and the predictions are compared with those obtained, for example, by Grimshaw (1970, 1971). Finally, the asymptotic behaviour of both the solitary wave and the oscillatory tail are assessed in the light of some numerical integrations of the equation.