Quantitative measurements of the structure of ejections from the wall region have been made using conditional-sampling techniques. Discrete ejections from a burst event were identified using fluorescent-dye flow visualization simultaneously with streamwise, u, and normal, v, velocity measurements. These velocity measurements, at y+ = 15, were conditionally sampled based on different phases of the ejection event. Features of the ejection which were educed from the conditional sampling were found to be very sensitive to the phase alignment. Results showed that ejections were characterized by a rapid deceleration at the leading edge followed by a strong positive velocity gradient at the trailing edge. An intense second-quadrant uv spike occurred immediately following the leading edge. This uv peak was highly correlated with a positive peak in the v velocity. The first ejection which occurred in a burst was found to be significantly more intense than the following ejections. Many characteristics of bursts which have been obtained from previous conditional-sampling studies were found to correspond to different phases of the ejection event.

The structure of normal shock waves is considered when the ratio of molecular masses mp/m of a binary mixture of inert monatomic gases is large and the density ratio ρp/ρ is of order unity or below. Generalized hydrodynamic equations, valid for arbitrary intermolecular potentials, are obtained from a hypersonic closure of the kinetic equation for the heavy gas and a near-equilibrium closure for the light component. Because the Prandtl number of the light gas and the Schmidt number of the mixture are nearly constant, the only independent transport coefficient arising in the model is the viscosity μ of the light gas, which is absorbed into a new independent position variable s. Knowledge of μ as a function of temperature thus determines the shock structure independently from the details of the intermolecular potential, allowing comparison with experiments in the complete absence of free parameters. In terms of the ratio M (frozen Mach number) between the speed of propagation and the sound speed of the light gas in the unperturbed medium, one finds that: (i) When M > 1, the behaviour is similar to that of a ‘dusty gas’, with a broad relaxation layer (outer solution) following a sharp boundary layer through which the speed of the heavy gas is almost constant (a shock within a shock). (ii) When (1 + ρp/ρ)s−½ < M < 1, the boundary layer disappears, yielding a so-called ‘fully dispersed wave’. (iii) Because the internal energy of the heavy gas is negligible, the present problem differs from previous shock studies in that, for the first time, the structure of the relaxation region is obtained algebraically in phase space, thus permitting an exhaustive study of the behaviour. From it, the overshooting solution found by Sherman (1960) is related to the unphysical degenerate branch of the outer solution arising when M > 1, showing a failure of the Chapman–Enskog theory, even for weak shocks, when the heavy gas is dilute. Also, an algebraic explanation arises for the ‘double hump structure’ observed in He–Xe shocks. (iv) When M is nearly unity, the initial boundary layer spreads out, and the structure must be obtained by integration of a numerically unstable system of three differential equations. However, the reduction of order brought about by the weak variation of the light-gas entropy at the head of the shock, results in a stable system of equations that we integrate numerically. Excellent phase-space agreement with recent shock-tube experiments of Tarczynski, Herczynski & Walenta (1986) is found for both weak and strong shocks.

In an extension of an earlier potential-flow theory using conformal mapping and source singularities in the wake region to simulate two-dimensional bluff-body flow, new mapping sequences and additional boundary conditions are presented for the application of the method to lifting airfoils fitted with upper-surface spoilers or lower-surface split flaps of arbitrary size, location, and erection angle. The only empirical input is the base pressure coefficient. Calculations are presented of pressure distribution and lift for several cases of a Joukowsky airfoil fitted with a spoiler or a split flap, and these results are compared with experimental data from wind tunnel tests. Good agreement is found.

Employing matched asymptotics, we extend the recent theory of Mei (1986) to study the phenomenon of upstream influence by a slender ship moving near the critical speed. For a special class of channel width and ship slenderness, it is shown that the response on the sea surface is essentially one-dimensional with the wave crests perpendicular to the ship's axis. In particular, solitons are radiated upstream. The hydrodynamic pressure on the ship, as well as the total sinkage force, wave resistance and trimming moment are calculated. These forces are functions of time despite the constant speed of the ship. The sinkage and trim for a ship model fixed on an advancing carriage are computed and show rapid variations across the critical speed as in the reported experiments of Graff, Kracht & Weinblum (1964). Because of the assumed slenderness of the ship, this theory does not predict two-dimensional waves in the wake. Nevertheless, there is crude agreement in the time-averaged hydrodynamic forces between theory and experiment.

A planar, sonic, underexpanded air jet induced strong and self-sustained flow oscillation. The jet was bounded by two parallel walls extending between the nozzle and the Helmholtz resonator opposite. This oscillation was characterized by large pressure amplitudes in the resonator and periodic displacement of a detached shock wave. The observed phenomena were in some measure similar to those occurring with Hartmann-Sprenger tubes. Based on the experimental results, including Mach-Zehnder interferograms and fluctuating pressure and velocity measurements, the properties of the oscillation have been described and a model for theoretical analysis has been established. Experimental and numerical investigations have made possible a description of the oscillation mechanism, which is of the relaxation type.

The time history is examined of the motion of a compound multiphase drop formed by a vapour bubble completely covered by its liquid phase in another immiscible liquid. The compound drop is growing or collapsing owing to change of phase while it is translating under buoyant forces. In the limit of large surface-tension forces the interfaces are spherical. An exact analytical solution for the fluid-mechanical part of the problem can be obtained. The heat-transfer treatment of the problem, however, requires numerical solution if we are to include convective terms along with time dependence. The drag component induced by radial velocity contributes to the total drag on the bubble in eccentric configuration. This drag force is towards the centre of the drop in the case of growth and has an effect of restoring concentricity. However, it is found that, in the case of growth, the compound drop, in general, cannot maintain its configuration of two non-intersecting eccentric spheres. On the other hand, in the case of collapse the bubble stays inside the drop if the collapse velocity is high enough. The complete analysis exhibits some interesting flow patterns relating to compound drops and bubbles. The time-dependent Nusselt number for a single bubble generally decreases with time but it may have a strong dependence on the compound-drop configuration, as well as the conductivities of the participating liquids. The radial convection opposes heat transfer but it has to compete with translatory convection, which is usually overwhelming in the case of growth.

The nonlinear periodic free oscillations of irrotational surface waves in a three-dimensional basin with a rectangular cross-section and finite depth are considered. A previous work by Verma & Keller (1962) has analysed the case when the linear natural frequencies are non-commensurate. For particular values of the parameters, however, strong internal resonance occurs (two natural frequencies are equal). Instead of the usual loss of stability and exchange of energy, it is found that the double eigenvalue generates a higher multiplicity of periodic solutions. Eight solution branches are found to be emitted by the double eigenvalues. It is also shown that perturbing the double eigenvalue results in a secondary bifurcation of periodic solutions. The direction of the branches for the multiple and secondary bifurcation changes with the depth. Finally it is shown that the formal solutions obtained are not uniformly valid and an additional expansion in the Boussinesq regime shows that the wave field changes type. One of the solutions in this regime is a field of three-dimensional cnoidal standing waves.

The flow past a circular cylinder in a rotating frame is examined when the Rossby number Ro is O(E½), where E is the Ekman number. Previous studies of the configuration have shown that, provided the ratio Ro/E½ is less than a certain critical value, the flow around the cylinder is determined by the classical potential-flow solution. However, once Ro/E½ is greater than that critical value the E1/4 layer on the surface of the cylinder, which is rather like a boundary layer in a high-Reynolds-number non-rotating fluid, can separate from the cylinder and distort the potential flow. In this study the form of the flow once separation has occurred is examined using a method analogous to the Kirchhoff free-streamline theory in a non-rotating fluid. The results are compared with published experimental and numerical data on the flow for various values of Ro/E½.

A flow circulation in a closed circular-cylindrical container is produced by a rotating lid. After a transient phase from an initial state at rest a steady-flow situation is reached for a certain parameter range. In a subspace of this parameter range an undulating meridional flow occurs that may exhibit at the axis of rotation one or several separation bubbles which are interpreted as vortex breakdown. Numerical calculations on the basis of the Navier-Stokes equations for incompressible homogeneous and Boussinesq fluids enable the study of the influence of various flow parameters on the properties of these separation bubbles. The parameters varied are the Reynolds, Prandtl, Rayleigh, and Eckert numbers together with the ratio of height to radius of the container. The numerical results are in good agreement with experiments performed by Vogel, Ronnenberg, and Escudier. The stability of the fluid motions in these experiments with respect to non-axisymmetric disturbances strongly suggests that the corresponding axisymmetric solutions of the Navier-Stokes equations are stable configurations.

Consider the Couette flow of two superposed fluids of different viscosity with the depth of the lower fluid bounded by a wall and the interface while the depth of the upper fluid is unbounded. The linear instability of this flow configuration is studied at all values of flow Reynolds number and disturbance wavelength using both asymptotic and numerical methods. Three distinct forms of instability are found which are dependent on the magnitude of two dimensionless parameters β and (α R)1/3, where β is a dimensionless wavenumber measured on a viscous lengthscale, α is a dimensionless wavenumber measured on the scale of the depth of the lower fluid and R is the Reynolds number of the lower fluid. At large β there is the short-wave instability found previously by Hooper & Boyd (1983). At small β and small (αR)1/3 there is the long-wave instability first discovered by Yih. At small β and large (αR)1/3 there is a new type of instability which arises only if the kinematic viscosity of the lower bounded fluid is less than the kinematic viscosity of the upper fluid.

Recent controlled experiments by Kachanov & Levchenko (1984) and others indicate that, during some slower kinds of transition to turbulence in boundary layers, three-dimensionality can come into play initially as a resonant-triad phenomenon, depending on the disturbance sizes present. The triad interaction, suggested theoretically in the boundary-layer context by Craik (1971) and others, is studied in the present work by means of multi-structured analysis for high characteristic Reynolds numbers. A finite-amplitude/relatively high-frequency approach leads rationally to the nonlinear triad equations, solutions for which are then obtained analytically and computationally in certain central cases of interest (temporal and spatial). The solutions have a rather chaotic spiky appearance as continual energy exchange develops between the two- and three-dimensional nonlinear modes, whose large-scale response seems governed by inviscid dynamics but subject to important, continual ‘rejuvenation’ from small- (fast-) scale viscous action in-between. The three-dimensional growth rate is thereby increased, but not the two-dimensional. Subsequently the disturbed flow enters a higher-amplitude regime similar to that studied in some related papers by the authors and co-workers. Comparisons with the experiments are very supportive of the theory (in the small and in the large), yielding both qualitative and quantitative agreement.

The frequency and damping rate of surface capillary-gravity waves in a bounded region depend on the conditions imposed where the free surface makes contact with the boundary. Extreme cases are when the free surface meets the boundary orthogonally, as in the case of pure gravity waves, and when the contact line remains fixed throughout the motion. An edge condition that models to some extent the dynamics associated with moving contact lines, but not contact-angle hysteresis, is given by making the slope of the free surface at contact proportional to its velocity. This model, which includes the two extreme cases, is used to obtain the frequency and damping rate of a standing wave between two parallel vertical walls. The effect of viscosity in the boundary layers on the walls is included and it is shown that the dissipation associated with the surface forces can exceed that produced by viscosity. The results are compared with those obtained from a number of experimental investigations, in which damping rates too large to be attributed to viscous action have been measured.

The vertical oscillation of a plate partially immersed in a non-wetting fluid produces a radiated wavetrain when the contact line between the plate and the free surface of the fluid cannot move freely along the plate. Realistic conditions to apply at the contact line when capillarity is not negligible include the dynamic variation of the contact angle and contact-angle hysteresis. Both of these effects are included in this paper and the amplitude of the radiated waves and the energy dissipation at the contact line are calculated.

This paper treats the steady flow fields generated inside and outside an initially circular, inextensible, cylindrical membrane filled with an incompressible viscous fluid when the membrane is placed in a two-dimensional shear flow of another viscous fluid. The Reynolds numbers of both the interior and exterior flows were assumed to be zero (‘creeping flow’), but no further approximations were made in the formulation. A series solution of the resulting free boundary-value problem in powers of a dimensionless shear rate parameter was constructed through fifth order. When combined with a conformal coordinate transformation this series gave accurate results for large deformations of the membrane (up to an aspect ratio of 2.5). The rather tedious algebraic manipulations required to obtain the series solution were done by computer with a symbol-manipulation program (reduce), which both formulated the boundary-value problems for each successive order and solved them. Results are presented which show how the shear rate and fluid viscosities influence the internal and external velocity and pressure fields, the membrane deformation and its ‘tank-treading’ frequency, and the membrane tension.

This work demonstrates that classical perturbation techniques combined with computer algebra offer a useful alternative to purely numerical methods for problems of this type.

The average turbulent energy dissipation is often estimated by assuming isotropy and measuring the temporal derivative of the longitudinal velocity fluctuation. In this paper, the nine major terms that make up the total dissipation have been measured in the self-preserving region of a cylinder wake for a small turbulence Reynolds number. The results indicate that local isotropy is not satisfied; the isotropic dissipation, computed by assuming isotropic relations, being smaller than the total dissipation by about 45% on the wake centreline and by about 80% near the wake edge. Indirect verification of the dissipation measurements is provided by the budget of the turbulent kinetic energy. This budget leads to a plausible distribution for the pressure diffusion term, obtained by difference.

A wave Reynolds number is the controlling parameter in Wang & Street's (1978) correlation for spray generation in developing air flow over a pool. A novel feature of the present theory is the prediction of the time-mean interfacial stress which, together with a wave-height correlation, is proposed and tested as a tool for quantifying that Reynolds number. The validation exercise shows that the results are generally acceptable, although the technique tends to underestimate the interfacial stress and droplet flux at high gas speeds. The analysis of experimental data has revealed some differences in the correlations which should be resolved.

In this paper we present the formulation and results of two-wave interactions in a spatially developing shear layer, directed at understanding and interpreting the physical mechanisms that underlie the results of quantitative observation. Our study confirms the existence of Kelly's mechanism that augments the growth of a subharmonic disturbance by extracting energy from its fundamental or vice versa. This mechanism is shown to be strongest in the region where the fundamental begins to return energy to the mean flow and the two wave modes are of comparable energy levels. It is found that the initial conditions and especially the initial phase angle between the two disturbances play a very significant role in the modal development and that of the shear layer itself. A doubling of the shear-layer thickness is shown to take place; the two successive plateaux in its growth are attributed to the peaking in the energy production rates of the fundamental and subharmonic fluctuations.

A one-dimensional wave equation is derived for water-wave propagations in a long channel with corrugated boundaries. The amplitude and the wavelength of boundary undulations are assumed to be smaller than and in the same order of magnitude as the incident wavelength, respectively. When the Bragg reflection condition (i.e. the wavenumber of the boundary undulations is twice that of the incident wavenumber) is nearly satisfied, significant wave reflection could occur. Coupled equations for transmitted and reflected wave fields are derived for the near resonant coupling. The detuning mechanism is attributed to the slight deviation in the wavenumber of the corrugated boundaries from the Bragg wavenumber. Analytical solutions are obtained for the cases where the boundary undulations are within a finite region. The application of the present theory to the design of a harbour resonator is discussed.

A passive technique of increasing entrainment was found by using a small-aspect-ratio elliptic jet. The entrainment ratio of an elliptic jet was several times greater than that of a circular jet or a plane jet. The self-induction of the asymmetric coherent structure caused azimuthal distortions which were responsible for engulfing large amounts of surrounding fluid into the jet. In an elliptic jet, an interesting feature in the initial stability process is that the thickness of the shear layer varies around the nozzle. The data indicated that instability frequency was scaled with the thinnest initial momentum thickness which was associated with the maximum vorticity. Turbulence properties were also examined and were found to be significantly different in the major- and minor-axis planes.

Experimental results and interpretations are given for transient natural convection adjacent to a suddenly heated flat vertical surface in quiescent water. The 1.24 m high surface resulted in laminar, transition and turbulent regimes downstream, in transients and in steady state, over a wide range of surface-energy input rates. Flows were visualized and velocity and temperature measurements made at various downstream locations, after imposing a uniform internal-energy generation rate within the very thin surface. Upflow development from quiescence to steady state was found to depend strongly on the downstream location x and imposed input heat flux. Laminar flow persisted into steady state, for short downstream distances. Further downstream, the flow became turbulent during the transient. Relaminarization at later time occurred only for lower flux inputs. Local measurements across the fluid layer show that the transient disturbances close to the leading edge of the surface are confined to within the final steady boundary layer. Downstream, they extend much further into the ambient. First disturbances always arose before the leading-edge-effect propagation estimates. The trend of data was in agreement with theory for a non-dimensional time τ < 85. For larger τ, turbulence instead terminated the one-dimensional transport regime simultaneously, at all downstream locations. This single value of τ also amounts to a single value of the non-dimensional thermal energy of the flow, ETT = 19.7. Disturbance frequency data early in the transient suggest the presence of a strongly selective amplification mechanism, very similar to that found in steady flows. The non-dimensional times at which local steady state was achieved were best correlated by a Fourier number, over a wide range of energy input conditions. Turbulence arising during the transient enhances the thermal transport significantly. Local convection coefficients then were found to be as much as 40% higher than the eventual steady values.