Flow past a cylinder beneath a free surface gives rise to fundamental classes of nearwake structure that are distinctly different from the wake of a completely submerged cylinder. A central feature is the generation of a vorticity layer from the free surface due to: localized separation, in the form of small-scale breaking of a free-surface wave; or complete separation from the free surface. This vorticity layer appears adjacent to a layer from the surface of the cylinder, thereby forming a jet-like flow. It is shown that the instantaneous vorticity flux on either side of this jet is rapidly balanced immediately after the onset of separation from the free surface.

We examine the steady, inviscid, supersonic flow of Bethe-Zel'dovich–Thompson (BZT) fluids in two-dimensional cascade configurations. Bethe-Zel'dovich–Thompson fluids are single-phase gases having specific heats so large that the fundamental derivative of gasdynamics, Γ, is negative over a finite range of pressures and temperatures. The equation of state is the well-known Martin–Hou equation, and the numerical scheme is the explicit predictor-corrector method of MacCormack. Numerical comparisons between BZT fluids and lighter fluids such as steam are presented. It was found that the natural dynamics of BZT fluids can result in significant reductions in the adverse pressure gradients associated with the collision of compression waves with neighbouring turbine blades. A numerical example of an entirely isentropic supersonic cascade flow is also presented.

This paper discusses self-sustaining oscillations of high-Reynolds-number shear layers and jets incident on edges and corners at infinitesimal Mach number. These oscillations are frequently sources of narrow-band sound, and are usually attributed to the formation of discrete vortices whose interactions with the edge or corner produce impulsive pressures that lead to the formation of new vorticity and complete a feedback cycle of operation. Linearized analyses of these interactions are presented in which free shear layers are modelled by vortex sheets. Detailed results are given for shear flows over rectangular wall apertures and shallow cavities, and for the classical jet–edge interaction. The operating stages of self-sustained oscillations are identified with poles in the upper half of the complex frequency plane of a certain impulse response function. It is argued that the real parts of these poles determine the Strouhal numbers of the operating stages observed experimentally for the real, nonlinear system. The response function coincides with the Rayleigh conductivity of the ‘window’ spanned by the shear flow for wall apertures and jet–edge interactions, and to a frequency dependent drag coefficient for shallow wall cavities. When the interaction occurs in the neighbourhood of an acoustic resonator, exemplified by the flue organ pipe, the poles are augmented by a sequence of poles whose real parts are close to the resonance frequencies of the resonator, and the resonator can ‘speak’ at one of these frequencies (by extracting energy from the mean flow) provided the corresponding pole has positive imaginary part.

The Strouhal numbers predicted by this theory for a shallow wall cavity agree well with data extrapolated to zero Mach number from measurements in air, and predictions for the jet–edge interaction are in excellent accord with data from various sources in the literature. In the latter case, the linear theory also agrees for all operating stages with an empirical, nonlinear model that takes account of the formation of discrete vortices in the jet.

Experiments have been carried out to study the three-dimensional characteristics of vortex shedding from a half-ellipse shape with a blunt trailing edge. In order to control the occurrence of vortex dislocations, the trailing edges of the models used were constructed with a series of periodic waves across their spans. Flow visualization was carried out in a water tunnel at a Reynolds number of 2500, based on trailing-edge thickness. A number of shedding modes were observed and the sequence of mode transitions recorded. Quantitative data were obtained from wind tunnel measurements performed at a Reynolds number of 40000. Two shedding frequencies were recorded with the higher frequency occurring at spanwise positions coinciding with minima in the chord. At these same positions the base pressure was lowest and the vortex formation length longest. Arguments are put forward to explain these observations. It is shown that the concept of a universal Strouhal number holds, even when the flow is three-dimensional. The spanwise variation in time-average base pressure is predicted using the estimated amount of time the flow spends at the two shedding frequencies.

Sources of vorticity are examined for a laboratory-generated spilling breaking wave. Two cases are studied. For the first case, based on the breaker height, the Reynolds and Froude numbers are 7370 and 2.04, respectively. The breaker is preceded by 1 mm wavelength capillary waves, with the largest amplitude-to-wavelength ratio equal to 0.18. For this case, it is found that the dominant source of vorticity flux is a viscous process, due to the deceleration of a thin layer of the surface fluid. For the second case, the Reynolds and Froude numbers based on the wave height are 1050 and 1.62, respectively. No breaking is observed for this case; rather a capillary–gravity wave is observed with 4 mm wavelength capillaries preceding the gravity wave. The largest amplitude-to-wavelength ratio of these capillaries is 0.28. This case shows that capillary waves do not contribute to the vorticity flux; rather the only dominant source of the vorticity flux into the flow is the free-surface fluid deceleration.

Lastly, a thin free-surface jet that is relatively vorticity-free is found to precede the spilling breaker. Analyses suggest that our wave-breaking phenomena can be modelled by a hydraulic jump phenomenon where the Froude number is based on the thickness of the free-surface jet, and on the velocity of the free-surface jet just prior to breaking. We believe this to be a more physically descriptive value of the Froude number. For the high-speed case, the Froude number based on the thickness of the free-surface jet is 4.78, while for the lower-speed case it is 2.14.

Understanding screech is especially important for the design of advanced aircraft because screech can cause sonic fatigue failure of aircraft structures. Although the connection between shock-cell spacing and screech frequency is well understood, the relation between non-uniformities in the shock-cell structures and the resulting amplitude, mode, and steadiness of screech have remained unexplored. This paper addresses the above issues by intentionally producing spanwise (larger nozzle dimension) variations in the shock-cell structures and studying the resulting spanwise screech mode. The spanwise-oblique shock-cell structures were produced using imperfectly expanded convergent–divergent rectangular nozzles (aspect ratio = 5) with non-uniform exit geometries. Three geometries were studied: (a) a nozzle with a spanwise uniform edge, (b) a nozzle with a spanwise oblique (single-bevelled) edge, and (c) a nozzle that had two spanwise oblique (double-bevelled) cuts to form an arrowhead-shaped nozzle. For all nozzles considered, the screech mode was antisymmetric in the transverse (smaller nozzle dimension) direction allowing focus on changes in the spanwise direction. Three types of spanwise modes were observed: symmetric (I), antisymmetric (II), and oblique (III). The following significant results emerged: (i) for all cases the screech mode corresponds with the spanwise shock-cell structure, (ii) when multiple screech modes are present, the technique presented here makes it possible to distinguish between coexisting and mutually exclusive modes, (iii) the strength of shocks 3 and 4 influences the screech source amplitude and determines whether screech is unsteady. The results presented here offer hope for a better understanding of screech and for tailoring shock-containing jets to minimize fatigue failure of aircraft components.

Two-dimensional laminar flow of an incompressible viscous fluid through a channel with a sudden expansion is investigated. A continuation method is applied to study the bifurcation structure of the discretized governing equations. The stability of the different solution branches is determined by an Arnoldi-based iterative method for calculating the most unstable eigenmodes of the linearized equations for the perturbation quantities. The bifurcation picture is extended by computing additional solution branches and bifurcation points. The behaviour of the critical eigenvalues in the neighbourhood of these bifurcation points is studied. Limiting cases for the geometrical and flow parameters are considered and numerical results are compared with analytical solutions for these cases.

Experiments document the influence of flow on the Plateau–Rayleigh (PR) instability of a near-cylindrical liquid bridge. The slightly heavy bridge is subjected to a surrounding pipe flow from bottom to top. Linear and nonlinear regimes of response are reported. Islands of stability in flow rate are observed; that is, there are bridges that are stable with flow but otherwise not. Density imbalance and flow each, on its own, is destabilizing but together they are stabilizing as recorded by a variety of measures. This nonlinear stabilization is explained in terms of the codimension-2 nature of the pitchfork bifurcation of the ‘perfect’ Plateau–Rayleigh instability.

Symme tric gravity–capillary solitary waves with decaying oscillatory tails are known to bifurcate from infinitesimal periodic waves at the minimum value of the phase speed where the group velocity is equal to the phase speed. In the small-amplitude limit, these solitary waves may be interpreted as envelope solitons with stationary crests and are described by the nonlinear Schrödinger (NLS) equation to leading order. In line with this interpretation, it would appear that one may also co nstruct asymmetric solitary waves by shifting the carrier oscillations relative to the envelope of a symmetric solitary wave. This possibility is examined here on the basis of the fifth-order Korteweg–de Vries (KdV) equation, a model for g ravity–capillary waves on water of finite depth when the Bond number is close to 1/3. Using techniques of exponential asymptotics beyond all orders of the NLS theory, it is shown that asymmetric solitary waves of the form suggested by the NLS theory in fact are not possible. On the other hand, an infinity of symmetric and asymmetric solitary-wave solution families comprising two or more NLS solitary wavepackets bifurcate at finite values of the amplitude parameter. The asymptotic results are consistent with numerical solutions of the fifth-order KdV equation. Moreover, the asymptotic theory suggests that such multi-packet gravity–capillary solitary waves also exist in the full water-wave problem near the minimum of t he phase speed.

Material flow in partially filled rotating cylinders (rotary kilns) is encountered in many practical applications of material processing, for example incineration, calcination, grain drying, etc. The flow behaviour in the cross-section is important to other transport mechanisms such as mixing and energy distribution within the bed material. The paper describes an experimental study which was carried out with the objective of understanding and improving our predictive capabilities of the rheological behaviour of granular materials in rotary cylinders. Measurement techniques similar to that used in chute flows have been employed to measure flow characteristics, e.g. particle velocities, granular temperature, and solid concentration (in the shear layer developed between the free surface and the bulk of the bed) for different materials having a wide range of coefficients of restitution. The results of the experiments provide the necessary assumptions, constraints, and data for granular flows in partially filled rotating cylinders.

A theoretical examination is made of the mechanical quasi-equilibrium stability of a horizontal, binary-mixture layer with Soret effect in the presence of a high-frequency vibrational field. The boundaries of the layer are assumed to be rigid, isothermal and impermeable. The axis of vibration is longitudinal. The study is based on the system of equations describing the behaviour of mean fields. The conditions of quasi-equilibrium are formulated. A linear stability analysis for normal modes is carried out. In the limit of long-wave disturbances the regular perturbation method is used with the wavenumber as a small parameter. For the case of an arbitrary wavenumber, the calculations are made using straight forward numerical integration. The boundaries of stability and the critical disturbance characteristics are determined for representative parameter values. Different instability mechanism and forms are discussed.

Compressible jets with various amounts of swirl and compressibility are investigated experimentally. The mixing-layer growth rate is obtained from time-averaged images of the mixing layer using the planar laser scattering (PLS) technique, and the swirl is quantified with laser Doppler velocimetry and intrusive probes. The results conclusively demonstrate that the addition of swirl to the jet increases entrainment by up to 60% compared to a corresponding non-swirling case. Instantaneous PLS images reveal modified turbulent structure in the mixing layer of the swirling-jet cases. In particular, analysis of these images indicates that both the spatial extent and amplitude of the largest turbulent fluctuations are increased when swirl is added. Based upon these results, a parameter β that correlates the observed growth-rate enhancement is proposed. This parameter is derived assuming that the streamwise vorticity, generated in the mixing layer by the addition of small amounts of swirl, causes additional turbulent mixing that increases the growth rate. When the available growth-rate data for swirling jets are plotted against this parameter, they collapse to a single curve with increased enhancement for higher values of β. This result implies that the degree of enhancement actually increases with compressibility, although the dimensional growth rates for the present compressible swirling-jet cases are still less than those of their incompressible counterparts.

The influence of compressibility upon the structure of homogeneous sheared turbulence is investigated. For the case in which the rate of shear is much larger than the rate of nonlinear interactions of the turbulence, the modification caused by compressibility to the amplification of turbulent kinetic energy by the mean shear is found to be primarily reflected in pressure–strain correlations and related to the anisotropy of the Reynolds stress tensor, rather than in explicit dilatational terms such as the pressure–dilatation correlation or the dilatational dissipation. The central role of a ‘distortion Mach number’ Md =  S[lscr ]/a, where S is the mean strain or shear rate, [lscr ] a lengthscale of energetic structures, and a the sonic speed, is demonstrated. This parameter has appeared in previous rapid-distortion-theory (RDT) and direct-numerical-simulation (DNS) studies; in order to generalize the previous analyses, the quasi-isentropic compressible RDT equations are numerically solved for homogeneous turbulence subjected to spherical (isotropic) compression, one-dimensional (axial) compression and pure shear. For pure-shear flow at finite Mach number, the RDT results display qualitatively different behaviour at large and small non-dimensional times St: when St < 4 the kinetic energy growth rate increases as the distortion Mach number increases; for St > 4 the inverse occurs, which is consistent with the frequently observed tendency for compressibility to stabilize a turbulent shear flow. This ‘crossover’ behaviour, which is not present when the mean distortion is irrotational, is due to the kinematic distortion and the mean-shear-induced linear coupling of the dilatational and solenoidal fields. The relevance of the RDT is illustrated by comparison to the recent DNS results of Sarkar (1995), as well as new DNS data, both of which were obtained by solving the fully nonlinear compressible Navier–Stokes equations. The linear quasi-isentropic RDT and nonlinear non-isentropic DNS solutions are in good general agreement over a wide range of parameters; this agreement gives new insight into the stabilizing and destabilizing effects of compressibility, and reveals the extent to which linear processes are responsible for modifying the structure of compressible turbulence.

The free-surface flow under a sluice gate is considered. The fluid is assumed to be inviscid and incompressible. The problem is solved numerically by using a boundary integral equation technique. Accurate numerical solutions are obtained when the intersection of the upstream free surface with the gate is a stagnation point. It is shown that the radiation condition is not satisfied far upstream and that there is a train of waves on the upstream free surface. For large values of the downstream Froude number F, the amplitude of the waves is so small that the upstream free surface is essentially flat. However for small values of F, the waves are of large amplitude. They ultimately approach the Stokes' limiting configuration with an angle of 120° at their crest as F is decreased.

Turbulent flow over a backward-facing step is studied by direct numerical solution of the Navier–Stokes equations. The simulation was conducted at a Reynolds number of 5100 based on the step height h and inlet free-stream velocity, and an expansion ratio of 1.20. Temporal behaviour of spanwise-averaged pressure fluctuation contours and reattachment length show evidence of an approximate periodic behaviour of the free shear layer with a Strouhal number of 0.06. The instantaneous velocity fields indicate that the reattachment location varies in the spanwise direction, and oscillates about a mean value of 6.28h. Statistical results show excellent agreement with experimental data by Jovic & Driver (1994). Of interest are two observations not previously reported for the backward-facing step flow: (a) at the relatively low Reynolds number considered, large negative skin friction is seen in the recirculation region; the peak |Cf| is about 2.5 times the value measured in experiments at high Reynolds numbers; (b) the velocity profiles in the recovery region fall below the universal log-law. The deviation of the velocity profile from the log-law indicates that the turbulent boundary layer is not fully recovered at 20 step heights behind the separation.

The budgets of all Reynolds stress components have been computed. The turbulent kinetic energy budget in the recirculation region is similar to that of a turbulent mixing layer. The turbulent transport term makes a significant contribution to the budget and the peak dissipation is about 60% of the peak production. The velocity–pressure gradient correlation and viscous diffusion are negligible in the shear layer, but both are significant in the near-wall region. This trend is seen throughout the recirculation and reattachment region. In the recovery region, the budgets show that effects of the free shear layer are still present.

The sound generated by vortex pairing in a two-dimensional compressible mixing layer is investigated. Direct numerical simulations (DNS) of the Navier–Stokes equations are used to compute both the near-field region and a portion of the acoustic field. The acoustic analogy due to Lilley (1974) is also solved with acoustic sources determined from the near-field data of the DNS. It is shown that several commonly made simplifications to the acoustic sources can lead to erroneous predictions for the acoustic field. Predictions based on the quadrupole form of the source terms derived by Goldstein (1976a, 1984) are in excellent agreement with the acoustic field from the DNS. However, despite the low Mach number of the flow, the acoustic far field generated by the vortex pairings cannot be described by considering compact quadrupole sources. The acoustic sources have the form of modulated wave packets and the acoustic far field is described by a superdirective model (Crighton & Huerre 1990). The presence of flow–acoustic interactions in the computed source terms causes the acoustic field predicted by the acoustic analogy to be very sensitive to small changes in the description of the source.