Time–frequency energy fluctuations of turbulent experimental velocity signals for Reλ≃10 and 800, are analysed using orthogonal wavelet transform. Some statistical properties of the energy bursts are analysed and discussed. The probability distribution functions (PDFs) of the energy amplitude fluctuations are investigated at different scales. Such PDFs show that the so-called non-intermittent and intermittent regions are characterized by quite different behaviour. Analysis of the wavelet coefficient scaling relations, averaged under suitable conditioning, reveals that the most energetic events localized in time and scale are responsible for the structure function (or wavelet coefficients) scaling anomalies related to intermittency. It is shown that the statistical properties which are correlated with the mechanism of the energy cascade from large to small scales are characterized by a universal behaviour. On the other hand, when the chosen statistical indicators are related to the characteristic size of turbulent structures, no universality is achieved, and a strong dependence upon the turbulent generator and Reλ is observed. This is demonstrated by analysis of the statistics of time delays between successive events which show non-universal PDFs. The mean delay between successive intermittent events is also Reλ dependent and increases for increasing Reλ.

An experimental and theoretical investigation has been carried out to understand the tonal noise generation mechanism on aerofoils at moderate Reynolds number. Experiments were conducted on a NACA0012 aerofoil section in a low-turbulence closed working section wind tunnel. Narrow band acoustic tones were observed up to 40 dB above background noise. The ladder structure of these tones was eliminated by modifying the tunnel to approximate to anechoic conditions. High-resolution flow velocity measurements have been made with a three-component laser-Doppler anemometer (LDA) which have revealed the presence of strongly amplified boundary-layer instabilities in a region of separated shear flow just upstream of the pressure surface trailing edge, which match the frequency of the acoustic tones. Flow visualization experiments have shown these instabilities to roll up to form a regular Kármán-type vortex street.

A new mechanism for tonal noise generation has been proposed, based on the growth of Tollmien–Schlichting (T–S) instability waves strongly amplified by inflectional profiles in the separating laminar shear layer on the pressure surface of the aerofoil. The growth of fixed frequency, spatially growing boundary-layer instability waves propagating over the aerofoil pressure surface has been calculated using experimentally obtained boundary-layer characteristics. The effect of boundary-layer separation has been incorporated into the model. Frequency selection and prediction of T–S waves are in remarkably good agreement with experimental data.

We have observed propagating adiabatic evaporation waves in superheated liquid dodecane, C12H26. Experiments were performed with a rapid decompression apparatus at initial temperatures of 180–300°C. Saturated dodecane in a tube was suddenly depressurized by rupturing a diaphragm. Motion pictures and still photographic images, and pressure and temperature data were obtained during the evaporation event that followed depressurization. Usually, a front or wave of evaporation started at the liquid free surface and propagated into the undisturbed regions of the metastable liquid. The evaporation wave front moved with a steady mean velocity but the front itself was unstable and fluctuating in character. At low superheats, no waves were observed until a threshold superheat was exceeded. At moderate superheats, subsonic downstream states were observed. At higher superheats, the downstream flow was choked, corresponding to a Chapman–Jouguet condition. At the most extreme superheat tested, a vapour content of over 90% was estimated from the measured data, indicating a nearly complete evaporation wave. Our results are interpreted by modelling the evaporation wave as a discontinuity, or jump, between a superheated liquid state and a two-phase liquid–vapour downstream state. Reasonable agreement is found between the model and observations; however, there is a fundamental indeterminacy that prevents the prediction of the observed wave speeds.

This paper presents a linear-stability analysis for the transition from a steady, two-dimensional thermocapillary convection in a liquid-metal layer to a periodic, three-dimensional flow involving hydrothermal waves which propagate in the directionzw normal to the plane of the base flow. There is a uniform magnetic field applied parallel to the free surface in the plane of the base flow, and there is a linear temperature gradient along the free surface in the base flow. The ratio of the layer's length to its depth, 2L, is large. The magnetic Reynolds number is small.

A key parameter is λ, the ratio of the large Hartmann number based on depth to L. The value of λ increases as either the magnetic field strength is increased or L is decreased. The results for very small values of λ agree with the results of a previous treatment of this instability without a magnetic field. As λ is increased, the critical Marangoni number and the wavenumber for the hydrothermal rolls both increase. For large values of λ, the base flow and the hydrothermal waves are confined to a free-surface layer with O(λ−2) dimensionless thickness.

The stability of an overdriven planar detonation wave is examined for a one-step Arrhenius reaction model with an order-one post-shock temperature-scaled activation energy θ in the limit of a small post-shock temperature-scaled heat release β. The ratio of specific heats, γ is taken such that (γ−1)=O(1). Under these assumptions, which cover a wide range of realistic physical situations, the steady detonation structure can be evaluated explicitly, with the reactant mass fraction described by an exponentially decaying function. The analytical representation of the steady structure allows a normal-mode description of the stability behaviour to be obtained via a two-term asymptotic expansion in β. The resulting dispersion relation predicts that for a finite overdrive f, the detonation is always stable to two-dimensional disturbances. For large overdrives, the identification of regimes of stability or instability is found to depend on a choice of distinguished limit between the heat release β and the detonation propagation Mach number D*. Regimes of instability are found to be characterized by the presence of a single unstable oscillatory mode over a finite range of wavenumbers.

Most of the studies concerning the dynamo effect are motivated by astrophysical and geophysical applications. The dynamo effect is also the subject of some experimental studies in fast breeder reactors (FBR) for they contain liquid sodium in motion with magnetic Reynolds numbers larger than unity. In this paper, we are concerned with the flow of sodium inside the core of an FBR, characterized by a strong helicity. The sodium in the core flows through a network of vertical cylinders. In each cylinder assembly, the flow can be approximated by a smooth upwards helical motion with no-slip conditions at the boundary. As the core contains a large number of assemblies, the global flow is considered to be two-dimensionally periodic. We investigate the self-excitation of a two-dimensionally periodic magnetic field using an instability analysis of the induction equation which leads to an eigenvalue problem. Advantage is taken of the flow symmetries to reduce the size of the problem. The growth rate of the magnetic field is found as a function of the flow pitch, the magnetic Reynolds number (Rm) and the vertical magnetic wavenumber (k). An α-effect is shown to operate for moderate values of Rm, supporting a mean magnetic field. The large-Rm limit is investigated numerically. It is found that α=O(Rm−2/3), which can be explained through appropriate dynamo mechanisms. Either a smooth Ponomarenko or a Roberts type of dynamo is operating in each periodic cell, depending on k. The standard power regime of an industrial FPBR is found to be subcritical.

The behaviour of a pair of corotating vortices in the wake of a flapped airfoil is experimentally studied in a water towing tank. Reynolds numbers based on total circulation of the vortices range from 1.0×104 to 6.4×104. Planar velocity vector fields and their gradients are derived from PIV images using an adaptive Lagrangian parcel tracking algorithm. Isovorticity surfaces are extracted from time series of planar vorticity data. The behaviour of the vortices is tracked by using various moments of both the probability density distribution and the spatial distribution of their streamwise vorticity. All vortices show a Lamb–Oseen circulation distribution when they are clearly identifiable. Further, vortices from the apless wing exhibit Lamb–Oseen velocity and vorticity distributions with slow growth. All corotating vortex pairs are observed to merge at about 0.8 orbit periods. First-order statistics of the flow field remain invariant during the merger. The higher-order moments of the vorticity distribution show strong time dependence, which implies three-dimensionality of the flow resulting from vortex stretching. The strengths of the individual vortices before merger are constant, and the total circulation before and after merger remains constant within the range of observations. The trajectory of the centre of vorticity remains unaffected by the merger process. The merger is preceded by a splitting of the weaker vortex into filaments which, depending on the relative strengths of the vortices, can occur in the radial direction, the axial direction, or a combination of the two. Mechanisms contributing to the merger dynamics are discussed.

Helical vortices in swirl flow are studied theoretically and experimentally.

A theory of helical vortices has been developed. It includes the following results: an analytical solution describing an elementary helical vortex structure – an infinitely thin filament; a solution for axisymmetrical vortices accounting for the helical shape of vortex lines and different laws of vorticity distribution; a formula for calculation of the self-induced velocity of helical vortex rotation (precession) in a cylindrical tube; an explanation of the zone with reverse flow (recirculation zone) arising in swirl flows; and the classification of vortex structures.

The experimental study of helical vortices was carried out in a vertical hydrodynamical vortex chamber with a tangential supply of liquid through turning nozzles. Various vortex structures were formed owing to changing boundary conditions on the bottom and at the exit section of the chamber. The hypothesis of helical symmetry is confirmed for various types of swirl flow. The stationary helical vortex structures are described (most of them for the first time) the features of which agree with the results and predictions of the theoretical model developed. They are the following: a rectilinear vortex; a composite columnar vortex; helical vortices screwed on the right or on the left; a vortex with changing helical symmetry; a double helix – two entangled vortex filaments of the same sign.

Ursell's edge waves are derived systematically using a new method. Computed profiles are then compared with the lesser known shoreline singular waves first constructed by Roseau (1958). A recent method of writing the continuous spectrum solutions on a plane beach is thereby extended to the discrete spectrum to enable the reconstruction of both types of edge waves so that, in particular, the unbounded wave profiles are more easily computed. The existence of stagnation points on the bed for standing edge waves is considered and demonstrated for the first few modes. A ramification of this is the existence of (two-dimensional-cross-shore) dividing ‘streamlines’ from the bed to the surface also, the number of which appears to equate to the modal number of the edge wave. These dividing streamlines, along with other streamlines, are computed for the first few modes of both the Ursell and the (alternative) singular waves constructed by Roseau.

It follows that these waves can also exist in the presence of solid cylinders bounded by fixed streamlines and, in particular therefore, that the hitherto unbounded Roseau waves can exist in a bounded state since a region including the origin can be removed from the flow by exploiting a dividing streamline. It is confirmed that the wavenumbers of the Roseau waves interlace those of the Ursell waves. An examination of available evidence leaves open to further research the question of whether the alternative Roseau waves have been ‘inadvertently’ observed either in the laboratory or, by means of contamination of data, in the field. Further laboratory simulations using longshore solid cylinders as ‘wave guides’ are proposed.

We study the high-harmonic surface wave associated with nonlinear diffraction and radiation of gravity waves by a near-surface circular cylinder. Based on nonlinear potential-flow theory, we show analytically, using a boundary-integral equation method, that: (a) for a circular motion of the cylinder, the leading-order outgoing radiated waves at any harmonic are generated only in one direction; (b) for a cylinder free to respond to regular incident waves, the total leading-order scattered waves at any harmonic are two orders smaller upstream of the body. These theoretical results are substantially confirmed by direct time-domain simulations of the problem.

Inertial waves are a ubiquitous feature of rapidly rotating fluids. Although much is known about their initial excitation, little is understood about their stability. Experiments indicate that they are generically unstable and in many cases catastrophically so, quickly causing the whole flow to collapse to small-scale disorder. The linear stability of two three-dimensional inertial waves observed to break down in the laboratory is considered here at experimentally small but finite Ekman numbers of [les ]10−4. Surprisingly small threshold amplitudes for instability are found. The results support the conjecture that triad resonances are the generic mechanism for secondary instability in rapidly rotating fluids but also highlight the ability of geostrophic flows to derive energy through a finite-amplitude inertial wave. This latter finding may go some way to explaining the significant mean circulations typically observed in inertial wave experiments.

The large- and small-scale vortical motions produced by ‘delta tabs’ in a two-stream shear layer have been studied experimentally. An increase in mixing was observed when the base of the triangular shaped tab was affixed to the trailing edge of the splitter plate and the apex was pitched at some angle with respect to the flow axis. Such an arrangement produced a pair of counter-rotating streamwise vortices. Hot-wire measurements detailed the velocity, time-averaged vorticity (Ωx) and small-scale turbulence features in the three-dimensional space downstream of the tabs. The small-scale structures, whose scale corresponds to that of the peak in the dissipation spectrum, were identified and counted using the peak-valley-counting technique. The optimal pitch angle, θ, for a single tab and the optimal spanwise spacing, S, for a multiple tab array were identified. Since the goal was to increase mixing, the optimal tab configuration was determined from two properties of the flow field: (i) the large-scale motions with the maximum Ωx, and (ii) the largest number of small-scale motions in a given time period. The peak streamwise vorticity magnitude [mid ]Ωx−max[mid ] was found to have a unique relationship with the tab pitch angle. Furthermore, for all cases examined, the overall small-scale population was found to correlate directly with [mid ]Ωx−max[mid ]. Both quantities peaked at θ≈±45°. It is interesting to note that the peak magnitude of the corresponding circulation in the cross-sectional plane occurred for θ≈±90°. For an array of tabs, the two quantities also depended on the tab spacing. An array of contiguous tabs acted as a solid deflector producing the weakest streamwise vortices and the least small-scale population. For the measurement range covered, the optimal spacing was found to be S≈1.5 tab widths.

The effect of surfactant on the breakup of a viscous filament, initially at rest, surrounded by another viscous fluid is studied using linear stability analysis. The role of the surfactant is characterized by the elasticity number – a high elasticity number implies that surfactant is important. As expected, the surfactant slows the growth rate of disturbances. The influence of surfactant on the dominant wavenumber is less trivial. In the Stokes regime, the dominant wavenumber for most viscosity ratios increases with the elasticity number; for filament to matrix viscosity ratios ranging from about 0.03 to 0.4, the dominant wavenumber decreases when the elasticity number increases. Interestingly, a surfactant does not affect the stability of a filament when the surface tension (or Reynolds) number is very large.

The mechanism for the generation of vorticity at a viscous free surface is described. This is a free-surface analogue of Lighthill's strategy for determining the vorticity flux at solid boundaries. In this method the zero-shear-stress and pressure boundary conditions are transformed into a boundary integral formulation suitable for the velocity–vorticity description of the flow. A vortex sheet along the free surface is determined by the pressure boundary condition, while the condition of zero shear stress determines the vorticity at the surface. In general, vorticity is generated at free surfaces whenever there is flow past regions of surface curvature. It is shown that vorticity is conserved in free-surface viscous flows. Vorticity which flows out of the fluid across the free surface is gained by the vortex sheet; the integral of vorticity over the entire fluid region plus the integral of ‘surface vorticity’ over the free surface remains constant. The implications of the present strategy as an algorithm for numerical calculations are discussed.

An approach developed recently to study the dynamics of vorticity defects in homogeneous shear flow extends naturally to the case of baroclinic, quasi-geostrophic flow. It is shown that an inviscid geostrophic flow with uniform vertical shear may be destabilized by introducing a ‘potential vorticity defect’, an arbitrarily small but sufficiently sharp and horizontally uniform change in stratification or vertical shear. The linear baroclinic problem is nearly identical to the linear homogeneous problem, with differences arising only from the boundary conditions. The nonlinear baroclinic problem differs substantially from the nonlinear homogeneous problem, as the leading-order baroclinic nonlinearity is the Jacobian of the ‘inner’ streamfunction and potential vorticity in the horizontal plane aligned with the defect. An example of the linear instability is described.