A von Kármán vortex street generated in the usual way was subjected to a deceleration, thereby changing the ratio of longitudinal to lateral spacing between the vortices. Distortion of the individual vortices followed which resulted in annihilation of concentrated vortex regions and creation of a stationary wake flow. This wake flow was itself dynamically unstable and developed into a new vortex street of a different frequency from the initial one. The breakdown of the initial vortex street is qualitatively explained by considering the convection of a concentrated vortex region due to the motion imposed by all the other vortices.

The initial-value problem for waves generated by ground motion near a shore is solved using linear shallow water theory and an exponential bottom profile. It is found that long waves can be trapped along the coast and travel with the deep water wave speed, (gh)½. The energy in these waves decays with x−½ instead of x−1 so that more energy would be observed on this coast than expected on the basis of deep water wave amplitudes.

Using a hot wire in a turbulent boundary layer in air, an experimental study has been made of the frequent periods of activity (to be called ‘bursts’) noticed in a turbulent signal that has been passed through a narrow band-pass filter. Although definitive identification of bursts presents difficulties, it is found that a reasonable characteristic value for the mean interval between such bursts is consistent, at the same Reynolds number, with the mean burst periods measured by Kline et al. (1967), using hydrogen-bubble techniques in water. However, data over the wider Reynolds number range covered here show that, even in the wall or inner layer, the mean burst period scales with outer rather than inner variables; and that the intervals are distributed according to the log normal law. It is suggested that these ‘bursts’ are to be identified with the ‘spottiness’ of Landau & Kolmogorov, and the high-frequency intermittency observed by Batchelor & Townsend. It is also concluded that the dynamics of the energy balance in a turbulent boundary layer can be understood only on the basis of a coupling between the inner and outer layers.

The structure and growth of the internal boundary layer which forms downstream of a sudden change from a smooth to a rough surface under zero pressure gradient conditions has been studied experimentally. To keep pressure disturbances due to the roughness change small, the level of the rough surface was depressed, so that the crest of the roughness was aligned with the level of the smooth surface. It has been found that, in the region near the change, the structure of the internal layer is largely independent of that in the almost undisturbed outer layer, whilst both the zero time delay and the moving axis integral length scales in the internal layer are significantly reduced below those on the smooth wall. The growth-rate of the internal layer is similar to that of the zero pressure gradient boundary layer, whilst the level of turbulence inside the internal layer is high because of the large turbulent energy production near the rough wall. From the mixing length results, and an analysis of the turbulent energy equation, it is deduced that the internal layer flow near the wall is not in energy equilibrium, and hence the concept of inner layer similarity breaks down. From an initially self-preserving state on the smooth wall, the turbulent boundary layer approaches a second self-preserving state on the rough wall well downstream of the roughness step.

The initial-value problem for linearized perturbations is discussed, and the asymptotic solution for large time is given. For values of the Reynolds number slightly greater than the critical value, above which perturbations may grow, the asymptotic solution is used as a guide in the choice of appropriate length and time scales for slow variations in the amplitude A of a non-linear two-dimensional perturbation wave. It is found that suitable time and space variables are εt and ε½(x+a1rt), where t is the time, x the distance in the direction of flow, ε the growth rate of linearized theory and (−a1r) the group velocity. By the method of multiple scales, A is found to satisfy a non-linear parabolic differential equation, a generalization of the time-dependent equation of earlier work. Initial conditions are given by the asymptotic solution of linearized theory.

The velocity sensitivity of a resistance-wire temperature sensor is expressed in terms of sensor parameters, and the resulting errors in temperature derivative moments in isotropic turbulence are evaluated. It is shown that velocity sensitivity of a degree completely negligible for most purposes causes severe contamination of the measured third moment. The contamination terms are shown to be production rates of the mean square temperature gradient and vorticity, respectively, and therefore create positive values of measured derivative skewness. The dominant contamination term is related to the temperature spectrum through the balance equation for the mean-square temperature gradient, and calculations based on an assumed spectral form show that under typical conditions the measured skewness is large. This mechanism could provide an alternative to anisotropy as an explanation of the positive skewnesses recently measured in the atmosphere.

The drag coefficient for a family of axially symmetric ellipses of fineness ratio 4, 5 and 8 was measured using magnetically suspended models. The Reynolds number ranged up to 106. Thus, only the blockage interference is present, which may be partially allowed for by classical wind tunnel procedures. It is expected that the drag values presented here are accurate to 1%.

Simultaneous measurements of wave elevation and atmospheric pressure on wind-driven sea waves were made using a vertical wave-sensing rod and a small (23 cm diameter) pancake-shaped styrofoam buoy in which was embedded a sensitive pressure transducer; the wave probe constrained the buoy to move with the waves only in the vertical direction. Care was taken to avoid contamination of the pressure signal with dynamic pressures caused by flow distortion around the buoy.

Results are presented as power and cross-spectra of wave elevation and pressure, spectra of the fluxes of energy and momentum from the wind to the waves, and spectra of ζ the fractional increase in wave energy per radian.

The phase shifts of the pressure signal are compared with the laboratory and field results of other investigators, and with the theoretical predictions of Miles's (1957) inviscid laminar model of wave growth. Agreement is reasonably good among the experimental results, but observed phase shifts are an order of magnitude larger than the theoretically predicted values.

Integrals under the momentum flux spectra are compared in all runs with the predictions of the standard empirical formula, and in two cases are compared with the values of the total wind stress as measured with a sonic anemometer; the indication is that a large fraction of the total flux of momentum from the air to the sea goes initially into the wave field.

The ζ spectra are compared with the field results of Snyder & Cox (1966) and with the theoretical predictions of Miles's (1957) model; agreement is again good between the field results while the theory underpredicts ζ by factors of between 5 and 8.

A simple dimensionless relation is found between ζ and the ratio of wind speed to wave phase speed.

The stability of the flow induced by an impulsively started inner cylinder in a Couette flow apparatus is investigated by using a linear stability analysis. Two approaches are taken; one is the treatment as an initial-value problem in which the time evolution of the initially distributed small random perturbations of given wavelength is monitored by numerically integrating the unsteady perturbation equations. The other is the quasi-steady approach, in which the stability of the instantaneous velocity profile of the basic flow is analyzed. With the quasi-steady approach, two stability criteria are investigated; one is the standard zero perturbation growth rate definition of stability, and the other is the momentary stability criterion in which the evolution of the basic flow velocity field is partially taken into account. In the initial-value problem approach, the predicted critical wavelengths agree remarkably well with those found experimentally. The kinetic energy of the perturbations decreases initially, reaches a minimum, then grows exponentially. By comparing with the experimental results, it may be concluded that when the perturbation kinetic energy has grown a thousand-fold, the secondary flow pattern is clearly visible. The time of intrinsic instability (the time at which perturbations first tend to grow) is about ¼ of the time required for a thousandfold increase, when the instability disks are clearly observable. With the quasi-steady approach, the critical times for marginal stability are comparable to those found using the initial-value problem approach. The predicted critical wavelengths, however, are about 1½ to 2 times larger than those observed. Both of these points are in agreement with the findings of Mahler, Schechter & Wissler (1968) treating the stability of a fluid layer with time-dependent density gradients. The zero growth rate and the momentary stability criteria give approximately the same results.

The steady axially symmetric incompressible flow past a sphere is investigated for Reynolds numbers, based on the sphere diameter, in the range 0·1 to 40. The formulation is a semi-analytical one whereby the flow variables are expanded as series of Legendre functions, hence reducing the equations of motion to ordinary differential equations. The ordinary differential equations are solved by numerical methods. Only a finite number of these equations can be solved, corresponding to an approximation obtained by truncating the Legendre series at some stage. More terms of the series are required as R increases and the present calculations were terminated at R = 40. The calculated drag coefficient is compared with the results of previous investigations and with experimental data. The Reynolds number at which separation first occurs is estimated as 20·5.

The present paper, part 2, consists of an experimental investigation of the influence of a transverse magnetic field on the heat transfer of a conducting fluid (mercury) flowing in an electrically insulated pipe subjected to a uniform heat flux at the wall. Mean temperature profiles and heat transfer data are presented which demonstrate that the magnetic field inhibits the convective mechanism of heat transfer through its damping of the turbulent velocity fluctuations.

Past evidence suggests that a large-scale orderly pattern may exist in the noiseproducing region of a jet. Using several methods to visualize the flow of round subsonic jets, we watched the evolution of orderly flow with advancing Reynolds number. As the Reynolds number increases from order 102 to 103, the instability of the jet evolves from a sinusoid to a helix, and finally to a train of axisymmetric waves. At a Reynolds number around 104, the boundary layer of the jet is thin, and two kinds of axisymmetric structure can be discerned: surface ripples on the jet column, thoroughly studied by previous workers, and a more tenuous train of large-scale vortex puffs. The surface ripples scale on the boundary-layer thickness and shorten as the Reynolds number increases toward 105. The structure of the puffs, by contrast, remains much the same: they form at an average Strouhal number of about 0·3 based on frequency, exit speed, and diameter.

To isolate the large-scale pattern at Reynolds numbers around 105, we destroyed the surface ripples by tripping the boundary layer inside the nozzle. We imposed a periodic surging of controllable frequency and amplitude at the jet exit, and studied the response downstream by hot-wire anemometry and schlieren photography. The forcing generates a fundamental wave, whose phase velocity accords with the linear theory of temporally growing instabilities. The fundamental grows in amplitude downstream until non-linearity generates a harmonic. The harmonic retards the growth of the fundamental, and the two attain saturation intensities roughly independent of forcing amplitude. The saturation amplitude depends on the Strouhal number of the imposed surging and reaches a maximum at a Strouhal number of 0·30. A root-mean-square sinusoidal surging only 2% of the mean exit speed brings the preferred mode to saturation four diameters downstream from the nozzle, at which point the entrained volume flow has increased 32% over the unforced case. When forced at a Strouhal number of 0·60, the jet seems to act as a compound amplifier, forming a violent 0·30 subharmonic and suffering a large increase of spreading angle. We conclude with the conjecture that the preferred mode having a Strouhal number of 0·30 is in some sense the most dispersive wave on a jet column, the wave least capable of generating a harmonic, and therefore the wave most capable of reaching a large amplitude before saturating.

The stability of liquid layers in a porous medium under the action of viscous and surface forces is described. An extension of previous studies on the stability of a single interface in a porous medium is presented as the basis for solutions to many problems of practical interest where flow in porous media are involved.

The method of multiple scales is used to determine the temporal and spatial variation of the amplitudes and phases of capillary-gravity waves in a deep liquid at or near the third-harmonic resonant wave-number. This case corresponds to a wavelength of 2·99 cm in deep water. The temporal variation shows that the motion is always bounded, and the general motion is an aperiodic travelling wave. The analysis shows that pure amplitude-modulated waves are not possible in this case contrary to the second-harmonic resonant case. Moreover, pure phase-modulated waves are periodic even near resonance because the non-linearity adjusts the phases to yield perfect resonance. These periodic waves are found to be unstable, in the sense that any disturbance would change them into aperiodic waves.

Stratified, inviscid channel flow over a thin barrier or into an abrupt contraction is considered on the hypotheses that the upstream dynamic pressure and density gradient are constant (Long's model) for those parametric régimes in which the hypotheses are tenable for finite-amplitude disturbances, namely k < 2 for the barrier and k < 1 for the contraction, where k = NH/πU is an inverse Froude number based on the Vaisälä frequency N, the channel height H, and the upstream velocity U. Reverse flow in the neighbourhood of the forward stagnation point, which implies the formation of an upstream separation bubble, is found for certain critical ranges of k. The maximum barrier height for which the dominant lee-wave mode can exist without reversed flow either upstream or downstream of the barrier is 0·34H. The limiting case of a half space is considered briefly, and forward separation is found for κ = Nh/U > κs, where κs = 2·05 for a thin barrier and 1·8 for a semi-circular barrier. The corresponding values for reverse flow in the lee-wave field are κc = 1·73 and 1·3, respectively.

A symposium on aerodynamic noise was held at Loughborough University from 14 to 17 September 1970 under the sponsorship of the Royal Aeronautical Society and the British Acoustical Society. The objective of the meeting was to focus attention on unsolved theoretical and experimental problems which will require attention over the next few years. Areas which were covered included jet noise, nonlinear acoustics, rotor noise, and diffraction theory. The symposium was successful in bringing together several new themes in aerodynamic noise research. The most significant of these were the existence of a degree of order in turbulent jet flows, and the dominant effect of inflow conditions on rotor noise radiation. In addition an improved and unified basis for jet noise theory seems to be evolving.

The zones of influence and dependence for three-dimensional boundary-layer equations first studied by Raetz are re-examined from the viewpoint of the subcharacteristics. It is shown that in contrast, the zones of influence and dependence for a totally hyperbolic system are determined by the characteristics; for the present parabolic system of three-dimensional boundary-layer equations, the zones are determined by the characteristics and subcharacteristics. The same idea should be applicable to more general systems of equations of similar type.

Centrifugally driven circulations in a rapidly rotating cylinder of fluid heated differentially in the vertical are considered. Boundary-layer solutions obtained previously are extended to include large diameter/height aspect ratios and a centrifugal acceleration of the same magnitude as that of gravity. The ratio of convective to conductive heat transfer is small in the region of parameter space considered. The effect of the circulations on the asymptotic stability of a fluid heat from below and subjected to Coriolis force is then considered. Away from the side wall of the cylinder the basic state circulation increases the critical Rayleigh number at which gravitational instabilities occur; however, a destabilization near the side wall is possible.

We investigate steady axially symmetric small Rossby number flows in which the driving consists of prescribed axial heat sources. By letting the velocity be proportional to the shear at the bottom surface we study the effects of that boundary condition on the resulting flows.

A multi-boundary-layer structure is found in the core, surrounding the heat sources. That structure depends on the relative magnitudes of the aspect ratio, stratification parameter and Ekman number.

The flow of a continuously stratified fluid into a contraction is examined, under the assumptions that the dynamic pressure and the density gradient are constant upstream (Long's model). It is shown that a solution to the equations exists if and only if the strength of the contraction does not exceed a certain critical value which depends on the internal Froude number. For the flow of a stratified fluid over a finite barrier in a channel, it is further shown that, if the barrier height exceeds this same critical value, lee-wave amplitudes increase without bound as the length of the barrier increases. The breakdown of the model, as implied by these arbitrarily large amplitudes, is discussed. The criterion is compared with available experimental results for both geometries.