Using automated laser-Doppler methods we have identified four distinct sequences of instabilities leading to turbulent convection at low Prandtl number (2·5–5·0), in fluid layers of small horizontal extent. Contour maps of the structure of the time-averaged velocity field, in conjunction with high-resolution power spectral analysis, demonstrate that several mean flows are stable over a wide range in the Rayleigh number R, and that the sequence of time-dependent instabilities depends on the mean flow. A number of routes to non-periodic motion have been identified by varying the geometrical aspect ratio, Prandtl number, and mean flow. Quasi-periodic motion at two frequencies leads to phase locking or entrainment, as identified by a step in a graph of the ratio of the two frequencies. The onset of non-periodicity in this case is associated with the loss of entrainment as R is increased. Another route to turbulence involves successive subharmonic (or period doubling) bifurcations of a periodic flow. A third route contains a well-defined regime with three generally incommensurate frequencies and no broadband noise. The spectral analysis used to demonstrate the presence of three frequencies has a precision of about one part in 104 to 105. Finally, we observe a process of intermittent non-periodicity first identified by Libchaber & Maurer at lower Prandtl number. In this case the fluid alternates between quasi-periodic and non-periodic states over a finite range in R. Several of these processes are also manifested by rather simple mathematical models, but the complicated dependence on geometrical parameters, Prandtl number, and mean flow structure has not been explained.

This paper reports on an extensive experimental study of the flows due to under-expanded axisymmetric jets impinging on flat plates. The range of plate locations extends to a point where the jet is just subsonic but the main emphasis is on the behaviour in the first shock cell. Plate inclinations from 90° to 30° were investigated by means of comprehensive surface pressure measurements and shadowgraph pictures. Wherever possible, the main features of the results have been reconstructed using inviscid analyses of the wave interactions.

The flows are shown to be extremely complex due to the local structure of the free jet and, particularly, due to interactions between shock waves in the free jet and those created by the plate. In the near field, these interactions tend to be the controlling factors but at larger distances from the nozzle, mixing effects become increasingly important.

The maximum pressure on the plate when it is inclined can be very much larger than when the plate is perpendicular, owing to the possibility of high pressure recoveries through multiple shock systems. Correlations are presented for some of the main features on perpendicular plates and it is shown that the integrated pressure loads for both normal and inclined plates can be predicted well by a simple momentum balance.

Fully developed oil flow in a smooth circular pipe at a mean Reynolds number of about 2100 was subjected to a nominally sinusoidal flow modulation at frequencies ranging from 0·05−1·75 Hz. It was observed that flow oscillation increased the critical Reynolds number and, under certain conditions, even brought about laminarization of the flow, which would be intermittently turbulent at the mean Reynolds number under quasi-steady (infinitely small oscillation frequency) conditions. The occurrence and extent of laminarization was, however, found to depend on factors such as the intermittency of turbulent puffs in the mean quasi-steady flow, frequency of oscillation, etc. Two series of experiments were performed. In one series, the oscillatory flow was almost completely laminarized. In the other series, the oscillatory flow was fully turbulent. In both the cases, instantaneous velocities in the flow were measured using laser-Doppler anemometry (LDA). The instantaneous velocity was decomposed into time-mean, periodic and random components employing ensemble-averaging techniques. The experiments indicated that the laminarized oscillatory flow behaves very similarly to laminar oscillatory flow at either end of the Strouhal-number range studied. The oscillatory turbulent flow was found to depend on both the Strouhal number and the ratio of the oscillation frequency (f) to some characteristic frequency (ft) of turbulence in the flow. The design of the present experimental facility made it possible to study the flow at f/ft ≈ 1 (‘high’ oscillation frequency), a condition that could not be attained in most previous investigations. Another unique feature of the present experiment was that the viscous sublayer and Stokes layer were both large enough (several millimetres in thickness) to allow detailed measurements to be made in these regions. It was found, that at this high frequency of oscillation, the Reynolds stresses generally remained frozen at an average state during the entire oscillation cycle. The turbulent structure showed significant departures from equilibrium at all times during the oscillation cycle. As a result, there was a net change in the time-mean velocity profile near the wall and a net increase in the time-mean wall shear stress and power loss due to friction. The observation that unsteadiness can indeed affect the mean flow behaviour in a significant way is new and contradicts the view presently held by many researchers (based on their studies at relatively low oscillation frequencies, i.e. f/ft [Lt ] 1). The data also indicated that the direct interaction between oscillation and the turbulent structure was essentially confined to the Stokes layer. The study suggests that (again contrary to the existing belief) quasi-steady turbulence models may not be adequate to describe unsteady flows when the time scale of unsteadiness is comparable to that of dominant turbulent eddies.

When a pipe, connected to reservoirs at both ends, is subjected to an oscillating compression and expansion, fluid is alternately squeezed into and out of the reservoirs, causing a considerable amount of dissipation. This and two other related geometries (involving a symmetrical channel, and a pair of circular disks) are analysed for their flow patterns and energy dissipation, as a function of frequency. It is found that, under certain circumstances, the impedance due to transverse flow can greatly exceed the acoustical impedance (due to longitudinal flow).

A technique for measuring velocity gradients in laminar flows by homodyne light scattering is presented. A theory which describes the light-scattering spectrum is derived that includes the effects of different types of linear flow fields, particle diffusion and the intensity profile in the scattering volume. The conditions which must be satisfied in order that the theory describe the experimental situation are outlined and complementary experiments are performed which both verify the theory and apply the technique. Verification is provided using the flow in a Couette device, and the flow due to single rotating cylinder in a large bath of fluid. The technique is then applied to measure the spatial variation of the shear rate in a four-roll mill.

In this paper we examine the nonlinear interaction of a forced internal gravity wave in a stratified fluid with its critical level. The representative Richardson number J is taken to be large and the undisturbed state consists of a hyperbolic-tangent velocity profile and an almost constant density gradient. It is assumed that at large values of a non-dimensional time t the flow outside the critical layer is steady, consisting of the mean shear together with a disturbance periodic in x that corresponds to the single harmonic of the incident wave of small amplitude ε. The requirements of a match across the critical layer lead to a reflected wave and a transmitted wave both of whose amplitudes are O(εe−νπ) when 1 [Lt ] t [Lt ] ε−2/3, where ν = (J − ¼)½. For ν [Gt ] 1 the layer therefore acts as a wave absorber, and the purpose of this investigation is to ascertain whether this property persists on an even longer time scale. At times t = O(ε−2/3) the layer has thickness O(ε2/3) and the first few terms of an expansion in powers of ε2/3t show that higher harmonics are forced on the outer flow, and the reflexion and transmission coefficients develop with time. The leading-order correction to these coefficients is calculated explicitly; that to the transmission coefficient is again exponentially small in ν though that to the reflexion coefficient is O(ν−1). The reflexion coefficient is therefore increasing and the critical layer begins to restore wave energy to the outer flow. Owing to the complexity of the calculation higher-order corrections are not obtained here, but the results presented are in agreement with predictions of earlier workers that the layer acts as an absorber and a reflector but not as a transmitter.

To study the mixing of a passive scalar in nearly isotropic turbulence, experiments have been made in isotropically mixed thermal fields with thermal mesh size Mθ (a) equal to the momentum mesh size M, (b) larger than M (obtained by heating only alternate rods of the turbulence generating grid), and (c) smaller than M. This last condition was achieved by inserting a fine heating screen with Mθ < M, at locations downstream of the turbulence grid. The heating screen was designed to produce negligible statistical change in the velocity field a short distance downstream. In all the heated grid experiments, for a given initial configuration of the thermal field, the intensity of temperature fluctuations θ normalized by the mean temperature rise ΔT, and the decay rate of $\overline{\theta^2} $ were both independent of the temperature of the grid. The principal effect of having Mθ > M was an increase in the relative intensity of temperature fluctuations compared with the Mθ = M case, and a marginal increase in their decay rate; contrary to expectation, the ratio R of temperature to velocity integral scales in the region of approximate homogeneity did not differ from that corresponding to Mθ = M. In heated screen experiments, the relative decay rate was independent of Mθ/M and ΔT. For the three locations of the heating screen used in these experiments, the decay rate was also independent of the relative distance xs of the heating screen from the turbulence generating grid; however, larger xs was associated with larger relative intensity of fluctuations. To a first approximation, the ratio R approached unity according to the empirical relation R = 1 − A exp [− αxθ/(UT0)], where xθ is downstream distance measured from the heating screen, and T0 is a characteristic turbulence decay time scale at x0 = 0. It was also verified that the skewness of the streamwise temperature derivative is approximately zero sufficiently downstream of the heating screen. Where the present study overlaps with previous measurements, an extensive comparison reveals several points of agreement as well as departure.

Fully developed periodic flow (with non-zero mean) of a Newtonian fluid in a rigid curved tube has been investigated both numerically and experimentally. Results are reported for the mean friction factor, the amplitude ratio and phase angle between flow rate and pressure drop, the axial velocity profile, and the wall shear stress distribution. The numerical results (obtained by a finite difference method) are restricted to rather slow flows (mean Dean number $\tilde{Dn} < 100 $), while the experimental results (extracted from instantaneous flow rate-pressure drop measurements) extend up to $\tilde{Dn} \sim 300 $. A ‘resonant’ interaction between the axial and secondary flows at intermediate frequencies appears to be a characteristic feature of periodic flow in a curved tube.

Measurements of velocity fluctuations in the wake of a thin non-lifting aerofoil are presented: in one set of experiments the flow was symmetrical, while in the other the upper surface of the aerofoil was roughened to increase the surface shear stress. Measurements were confined to the near wake, where the disturbed region lies within the inner layers of the original boundary layers; thus the boundary-layer thickness is not a relevant length scale. The practical relevance of the experiment is to the prediction of flow over aerofoils, where only the initial region of the wake significantly affects the aerofoil pressure distribution. Temperature-conditioned sampling techniques were used, one boundary layer at a time being heated so that fluid from each boundary layer could be traced within the wake. In contrast to the behaviour of merging shear layers in ducts and jets, the wake interaction involves significant fine-scale mixing; the results reveal a three-layer structure, with a fine-scale inner wake of mixed fluid separating two layers in which structural changes are confined to the region of time sharing, or internal intermittency, between mixed and unmixed fluid. The implications of the results for calculation methods are discussed.