The investigation described here is an experimental study directed toward determining flow field and surface friction characteristics of a cylindrical wall jet. The flow configuration is obtained by placing a cylindrical rod along the axis of a converging nozzle. The flow field thus produced consists of a developing turbulent boundary layer co-existing with an outer fluid layer that mixes freely with quiescent surroundings. Direct measurements of fluid friction at the rod surface, performed with a hot-film element, revealed a significant effect of transverse surface curvature on the local friction factor. Velocity profiles at various axial stations exhibited similarity in the outer mixing layer, but not in the boundary layer adjacent to the surface. Representations of the velocity field in terms of law of the wall variables and defect-law variables revealed significant transverse curvature effects. The measured wall-jet velocity profiles could be satisfactorily represented in terms of a law of the wake, wherein the wake function depends on a transverse curvature parameter. In the outer mixing layer, the eddy viscosity data correspond closely to those of free jets.

To complete a previous investigation reported earlier and carried out in an air jet issuing from a 1·0ft. diameter nozzle into still air, additional measurements were made of one-point triple-velocity and two-point double-velocity correlations and the spatial mean gradients of the axial turbulent velocities. The one-point pressure/axial-velocity correlation term was evaluated by using piezo-electric ceramic elements in conjunction with total- and static-pressure probes. For the measurement of spatial mean gradients of the axial-velocity fluctuation, special probes with two parallel wires were constructed. The axial scale of turbulence was found to be almost twice as large as the other two scales. The tangential scale was the smallest. All terms of the integral and differential forms of the turbulence energy equation were evaluated throughout the region and the results are given in dimensionless form.

When attempts are made to use thin film anemometers in airflow to measure fluctuating velocity it is found that the dynamic sensitivity cannot be obtained from a steady-flow calibration. It is found that the dynamic sensitivity is considerably less than that predicted by static calibration and that the sensitivity is frequency-dependent. It is shown that thermal feedback from the substrate, on which the gauge is mounted, to the heated element is responsible for the variation of sensitivity with frequency, despite constant-temperature operation of the probe, and this variation is examined theoretically and experimentally.

The results of an experimental study of the diffraction of shock waves on plane-walled convex corners are given for a Mach number range from 1·0 to 5·0. The behaviour of the disturbances produced in the region perturbed by the corner are discussed. It is shown that the position of the slipstream and tail of the Prandtl-Meyer fan, and the velocities of the contact surface and second shock become independent of corner angle for angles greater than 75°. Comparisons with theoretical predictions of Jones, Martin & Thornhill (1951) and Parks (1952) are included. In most cases fair agreement is obtained.

Unsteady, large-amplitude motion of a viscous liquid in a long elastic tube is investigated theoretically and experimentally, in the context of physiological problems of blood flow in the larger arteries. Based on the assumptions of long wavelength and longitudinal tethering, a quasi-one-dimensional model is adopted, in which the tube wall moves only radially, and in which only longitudinal pressure gradients and fluid accelerations are important. The effects of fluid viscosity are treated for both laminar and turbulent flow. The governing non-linear equations are solved analytically in closed form by a perturbation expansion in the amplitude parameter, and, for comparison, by numerical integration of the characteristic curves. The two types of solution are compared with each other and with experimental data. Non-linear effects due to large amplitude motion are found to be not as large as those found in similar problems in gasdynamics and water waves.

Turbulence onset is considered in viscous incompressible flows. Development of fluctuations in an infinite flow with a constant gradient of mean velocity ∂U1/∂x2 = const., U2 = U3 = 0 is rigorously treated.

It is shown that two-dimensional eddy fluctuations, with infinitesimal initial amplitude A and scale of initial eddies l, increase in this flow so that the maximum ratio max ε(t)/ε(0) of their energy at the moment t to the initial energy exceeds any prescribed value as the Reynolds number R = (∂U1/∂x2) l2/v increases. The analysis of the non-linear equations obtained in the paper which describe development of fluctuations with a finite amplitude leads to the conclusion that there exists a’ stability barrier’ Ã (R) for the initial amplitude of eddy fluctuations. If A < Ã (R), then fluctuations decay as t → ∞, and if A > Ã(R) the energy of fluctuations does not decay. As R → ∞, Ã(R) → 0 according to the inequalities \[ l(\partial U_1/\partial x_2)K_2/R^{\frac{2}{3}}\leqslant \tilde{A}(R)\leqslant l(\partial U_1/\partial x_2)\,K_1/R^{\frac{2}{3}}. \] It is shown that the non-linear mechanism of preventing turbulence from decay involves generation of large-scale turbulent oscillations which then transmit energy to small-scale motions.

The described mechanism of turbulence onset from small eddies in shear flows appears to be of universal character. It is interesting that several qualitative characteristics of turbulence observed in various shear flows can be rigorously deduced even in a model where disturbances remain two-dimensional.

An experimental investigation of transition phenomena in non-steady boundary layers of sinusoidally oscillating flows was conducted, and the effect of various parameters on the transition process was observed.

The manner in which transition occurs appears to be related to a dimensionless grouping designated as the non-steady Reynolds number, (Re)NS = LΔU/2πvν. When this number exceeds a certain critical value, transition begins with turbulent bursts appearing periodically at the frequency of the free stream oscillation; these are preceded by instability waves having the appearance of a Tollmien-Schlichting instability. The transition Reynolds number depends, in this case, only on the amplitude of the free stream oscillations and not on their frequency, at least to the first order. Below a critical value of this parameter, transition occurs at a relatively constant Reynolds number which appears independent of the amplitude and frequency of the oscillation, at least over the range tested.

When the bursts appear periodically, their development appears to occur in two succeeding phases: an initial or ‘creative’ phase marked by a sequential appearance of turbulence upstream and rapid development and a latter or ‘convective’ phase marked by turbulent spots having relatively constant leading and trailing edge velocities.

The dimensionless amplitude, ΔU/U∞, of the imposed oscillations was varied from 0.014 to 0.29 while the oscillation frequencies extended from 4.5 to 62c/s. Pressure gradients imposed on the flat plate model during the course of the study are given by dCp/dx = − 0.004/ft., −0.081/ft. and 0.045/ft. where Cp = 2p/ρU2∞ and x is the distance (ft.) along the plate.

This paper describes an experimental study of the shape of a shock diffracting around a corner made up of two plane walls, for corner angles from 15 to 165° (in 15° steps) and shock Mach numbers from M0 = 1·0 to 4·0. The results are compared with profiles determined from the diffraction theory of Whitham (1957, 1959). The agreement is shown to be good for an incident shock Mach number of 3·0, and fair in other cases. The behaviour is found to follow the trends established by Lighthill (1949) in a linearized theory. Results for the Mach number of the wall shock are also presented. The shock does not degenerate to a sound wave even for large corner angles and low Mach numbers.

The flow of a viscous fluid through axially symmetric pipes and symmetrical channels is investigated under the assumption that the Reynolds number is small enough for the Stokes flow approximations to be made. It is assumed that the cross-section of the pipe or channel varies sinusoidally along the length. The flow is produced by a prescribed pressure gradient and by the variation in cross-section that occurs during the passage of a prescribed sinusoidal peristaltic wave along the walls. The theory is applied in particular to two extreme cases, peristaltic motion with no pressure gradient and flow under pressure along a pipe or channel with fixed walls and sinusoidally varying cross-section. Perturbation solutions are found for the stream function in powers of the ratio of the amplitude of the variation in the pipe radius or channel breadth to the mean radius or breadth respectively. These solutions are used to calculate, in particular, the flux through the pipe or channel for a given wave velocity in the first case and for a given pressure gradient in the second case. With a suitable notation it is possible to combine the analysis required for the two cases of pipe and channel flow.

The boundary-layer equations for the steady laminar flow of a vertical jet, including a buoyancy term caused by temperature differences, are solved by similarity methods. Two-dimensional and axisymmetric jets are treated. Exact solutions in closed form are found for certain values of the Prandtl number, and the velocity and temperature distribution for other Prandtl numbers are found by numerical integration.

The exact equations governing three-dimensional motion of an inviscid non-diffusive incompressible fluid stratified in density or of an inviscid non-diffusive gas stratified in entropy are given and briefly discussed.

The dynamics of turbulent velocity fluctuations in and somewhat outside the viscous sublayer are examined by linearizing the equations of motion around the known mean velocity profile. The rest of the boundary layer is assumed to drive the motion in the layer by means of a fluctuating pressure which is independent of distance from the wall. The equations, which are boundary-layer approximations to the Orr-Sommerfeld equations, are thus treated as a non-homogeneous system and solved by convergent power series. The solutions which exhibit the strong role of viscosity throughout the layer considered provide a model endowed with many of the known features of turbulence near a wall. In particular, the phase angle between streamwise and normal fluctuations is found to be in plausible agreement with experiments. An important role is ascribed by the solutions to the displacement of the mean velocity by the normal fluctuations. The impedance of the layer is found to be anisotropic in that it favours fluctuations with a much larger scale in the streamwise than in the spanwise direction. For such disturbances, the ratio of turbulent intensity to the intensity of the pressure fluctuations approximates the experimental ratio. According to the solutions it is primarily the spanwise component of the pressure gradient which is responsible for the intense level of turbulence very near the wall. The model apparently underestimates the amplitude ratio of normal to streamwise components of the velocity.

Laminar boundary layer on a flat plate with zero pressure gradient was excited by a solitary three-dimensional disturbance. The growth of the disturbance was studied using a 10-channel linearized d.c.-coupled hot-wire system. The development of the disturbance flow field was studied and compared with theory by Criminale & Kovasznay (1962). The experimental results indicate a departure from the theory on account of the simplifying assumptions made in the theory. Certain new results were also obtained.

Experiments performed by Fultz et al. (1959) and Stern (1959) indicate that if a flame is rotated around the bottom exterior of a pan or of a circular cylindrical annulus containing water then the fluid acquires a net vertical component of angular momentum in a direction opposite to that of the flame's motion. Stern gave an analysis showing how fluid, bounded by two horizontal plates subjected to small two-dimensional sinusoidal travelling temperature perturbations, could acquire and maintain such momentum. An assumption in Stern's analysis was that the density variations were constant between the plates. Here we shall examine the importance of the relaxation of this assumption. Also, another model, in which the upper surface of the fluid is free, is analysed, because this model conforms more closely with the experiments of Fultz et al. and Stern.

For the problem of flow between two plates we shall show that there is a net flux of momentum in the direction opposite to the motion of the thermal field for all frequencies thereof. The same result holds in the case with a free surface when conditions are comparable with those in the experiments.

In both problems the phase lag of the thermal expansion wave with height produces a skewed thermal field. This field is the most important mechanism in producing velocity correlations. It is due to these correlations and the associated Reynolds stress that the fluid acquires its momentum.

The onset of convection induced by thermal and solute concentration gradients, in a horizontal layer of a viscous fluid, is studied by means of linear stability analysis. A Fourier series method is used to obtain the eigenvalue equation, which involves a thermal Rayleigh number R and an analogous solute Rayleigh number S, for a general set of boundary conditions. Numerical solutions are obtained for selected cases. Both oscillatory and monotonic instability are considered, but only the latter is treated in detail. The former can occur when a strongly stabilizing solvent gradient is opposed by a destablizing thermal gradient. When the same boundary equations are required to be satisfied by the temperature and concentration perturbations, the monotonic stability boundary curve in the (R, S)-plane is a straight line. Otherwise this curve is concave towards the origin. For certain combinations of boundary conditions the critical value of R does not depend on S (for some range of S) or vice versa. This situation pertains when the critical horizontal wave-number is zero.

A general discussion of the possibility and significance of convection at ‘zero’ wave-number (single convection cell) is presented in an appendix.

An analysis is made of the effect of a transverse gravity field on a two-dimensional fully cavitating flow past a flat-plate hydrofoil. Under the assumption that the flow is both irrotational and incompressible, a non-linear method is developed by using conformal mapping and the solution to a mixed-boundary-value problem in an auxiliary half plane. A new cavity model, proposed by Tulin (1964a), is employed. The solution to the gravity-affected case was found by iteration; the non-gravity solution was used as the initial trial of a rapidly convergent process. The theory indicates that the lift and cavity size are reduced by the gravity field. Typical results are presented and compared to Parkin's (1957) linear theory.

The shock curvature and flow variable gradients at the tip of a pointed body caused by non-equilibrium effects are considered. Co-ordinates introduced by Chester (1956) are used since they offer a convenient way of treating the boundary conditions. The desired functions are obtained by solving numerically a system of linear ordinary differential equations. These equations have a singularity; the nature of the singularity is found analytically, and its numerical treatment is discussed. The specific non-equilibrium effect considered is vibrational relaxation in a pure diatomic gas. Representative results are given for flow of N2 over a cone for a comprehensive range of Mach number and cone angle. There is a point analogous to the Crocco point. The exact results are compared with predictions from (i) a hypersonic, small disturbance theory; (ii) the application of an integral method; (iii) characteristic calculations. In an appendix, a comparative discussion is given of results for frozen flow over ogival bodies.

This paper presents a general theoretical treatment of a new class of long stationary waves with finite amplitude. As the property in common amongst physical systems capable of manifesting these waves, the density of the (incompressible) fluid varies only within a layer whose thickness h is much smaller than the total depth, and it is h rather than the total depth that must be considered as the fundamental scale against which wave amplitude and length are to be measured. Internal-wave motions supported by the oceanic thermocline appear to be the most promising field of practical application for the theory, although applications to atmospheric studies are also a possibility.

The waves in question differ in important respects from long waves of more familiar kinds, and in § 1 their character is discussed on the basis of a comparison with solitary-wave and cnoidal-wave theories on customary lines, such as apply to internal waves in fluids of limited depth. A summary of some simple experiments is included at the end of § 1. Then, in § 2, the comparatively easy example of two-fluid systems is examined, again to illustrate principles and to prepare the way for the main analysis in § 3. This proceeds to a second stage of approximation in powers of wave amplitude, and its leading result is an equation (3·51) determining, for arbitrary specifications of the density distribution, the form of the streamlines in the layer of heterogeneous fluid. Periodic solutions of this equation are obtained, and their properties are discussed with regard to the interpretation of internal bores and wave-resistance phenomena. Solutions representing solitary waves are then obtained in the form \[ f(x) = a\lambda^2/(x^2+\lambda^2), \] where xis the horizontal co-ordinate and where aΛ = O(h2). (The latter relation between wave amplitude and length scale contrasts with the customary one, aΛ2 = O(h3)). The main analysis is developed with particular reference to systems in which the heterogeneous layer lies on a rigid horizontal bottom below an infinite expanse of homogeneous fluid; but in § 4 ways are given to apply the results to various other systems, including ones in which the heterogeneous layer is uppermost and is bounded by a free surface. Finally, in §5, three specific examples are treated: the density variation with depth is taken, respectively, to have a discontinuous, an exponential and a ‘tanh’ profile.

A horizontal fluid layer whose lower surface temperature is made to vary with time is considered. The stability analysis for this situation shows that the criterion for the onset of instability in a fluid layer which is being heated from below, depends on both the method and the rate of heating. For a fluid layer with two rigid boundaries, the minimum Rayleigh number corresponding to the onset of instability is found to be 1340. For slower heating rates the critical Rayleigh number increases to a maximum value of 1707·8, while for faster heating rates the critical Rayleigh number increases without limit.

Two specific types of heating are investigated in detail, constant flux heating and linearly varying surface temperature. These cases correspond closely to situations for which published data exist. The results are in good qualitative agreement.

A modified design of a fibre optic light probe was used for the measurement of turbulent concentration fluctuations and the spectra associated with these. The main object was to establish experimentally the nature of the scalar spectrum in the viscous-convective subrange. The existence of a spectral region with a (-1)-power law form supports the uniform straining model proposed by Batchelor (1959) for Schmidt numbers (v/D) much greater than unity. For this range, the data do not agree with the cascading process suggested by Pao (1965).

An additional object was to study further the decay of the concentration fluctuations in terms of a measure of the turbulent mixing. More specifically, the limitations of applying the isotropic stationary mixing theory of Corrsin (1957, 1964a) to a shear pipe flow situation and the validity of the earlier data for this case (Lee & Brodkey 1964; Brodkey 1966a, b; and Gegner & Brodkey 1966) were investigated.