Small particle motions in standing or travelling acoustic waves are well known and extensively studied. Particle motion in weak shock waves has been studied much less, especially particle motion in periodic weak shock waves which as yet has not been dealt with.

The present study considers small particle motions caused by weak periodic shock waves in resonance tubes filled with air. A simple mathematical model is developed for resonance gas oscillations under the influence of a vibrating piston with a finite amplitude at the first acoustic resonance frequency. It is shown that a symmetrical sinusoidal piston motion generates non-symmetric periodic shock waves. A model of particle motion in such a flow field is suggested. It is found that non-symmetric shock waves cause particle drift from the middle cross-section toward the ends of the resonance tube. The velocity of particle drift is found to be of the order of Dpρp/ Trρg, where Dp is the particle diameter, Tr the period of the resonance oscillation, ρp and ρg are the particle and gas density, respectively. At the same time, the velocity drift strongly depends on the ratio τ/Tr, where τ is the particle relaxation time. Particle drift is vigorous when τ/Tr∼1 and insignificant when τ/Tr 1. Theoretical predictions of particle drift in resonance tubes are verified numerically as well as experimentally.

When the particle relaxation time is much smaller than period of the resonance oscillations particles perform oscillations around their equilibrium positions with amplitude of the order of Dpρp/ρg. It is shown that the difference in oscillation amplitude of particle of difference sizes explains coalescence of aerosol droplets observed in experiments of Temkin (1970).

The importance of the phenomena for particle separation, coagulation and transport processes is discussed.

The thermocapillary and shear-induced instabilities of a thin heated layer of liquid bounded from the top by a deformable free surface and at the bottom by a horizontally oscillating plate are studied for both Earth-bound and microgravity conditions. Finite-wavelength thermocapillary convection can be stabilized very significantly by the oscillatory shear, whereas shear-induced instabilities are greatly stabilized if the Marangoni number is negative. For long-wavelength thermocapillary convection, oscillatory shear can stabilize or destabilize the basic state, depending primarily on the imposed forcing frequency. With microgravity, significant stabilization of the dominant long-wavelength convection can be achieved by carefully selecting the imposed frequency.

Thrust-producing harmonically oscillating foils are studied through force and power measurements, as well as visualization data, to classify the principal characteristics of the flow around and in the wake of the foil. Visualization data are obtained using digital particle image velocimetry at Reynolds number 1100, and force and power data are measured at Reynolds number 40 000. The experimental results are compared with theoretical predictions of linear and nonlinear inviscid theory and it is found that agreement between theory and experiment is good over a certain parametric range, when the wake consists of an array of alternating vortices and either very weak or no leading-edge vortices form. High propulsive efficiency, as high as 87%, is measured experimentally under conditions of optimal wake formation. Visualization results elucidate the basic mechanisms involved and show that conditions of high efficiency are associated with the formation on alternating sides of the foil of a moderately strong leading-edge vortex per half-cycle, which is convected downstream and interacts with trailing-edge vorticity, resulting eventually in the formation of a reverse Kármán street. The phase angle between transverse oscillation and angular motion is the critical parameter affecting the interaction of leading-edge and trailing-edge vorticity, as well as the efficiency of propulsion.

The aspect ratio of short coin-like cylinders is defined as L/D, where L is the length and D is the diameter of the cylinder. Force and pressure measurements are extended down to L/D=0.025. The force measurements indicate an unexpected increase in drag coefficient with decreasing aspect ratio. The basic equation used to define the drag coefficient is inapplicable for very low aspect ratio and the projected area should be replaced by the side area. Surface flow visualization tests in a wind tunnel reveal the variation in both shape and size of separation bubbles, which form on the flat sides of the model. A crescent-shaped area is observed between the primary and secondary separation, followed by an unsteady re-attachment region. A strong hysteresis effect is observed in the development of the separation bubbles. The separation bubbles can be suppressed by rounding the sharp edges of the model, with considerable reduction in the drag coefficient. Finally, a flow topology is suggested consisting of two horseshoe vortices attached onto the flat sides and detached in a streamwise direction, thus forming two counter-rotating vortex pairs.

In this paper, we investigate the three-dimensional instability of a counter-rotating vortex pair to short waves, which are of the order of the vortex core size, and less than the inter-vortex spacing. Our experiments involve detailed visualizations and velocimetry to reveal the spatial structure of the instability for a vortex pair, which is generated underwater by two rotating plates. We discover, in this work, a symmetry-breaking phase relationship between the two vortices, which we show to be consistent with a kinematic matching condition for the disturbances evolving on each vortex. In this sense, the instabilities in each vortex evolve in a coupled, or ‘cooperative’, manner. Further results demonstrate that this instability is a manifestation of an elliptic instability of the vortex cores, which is here identified clearly for the first time in a real open flow. We establish a relationship between elliptic instability and other theoretical instability studies involving Kelvin modes. In particular, we note that the perturbation shape near the vortex centres is unaffected by the finite size of the cores. We find that the long-term evolution of the flow involves the inception of secondary transverse vortex pairs, which develop near the leading stagnation point of the pair. The interaction of these short-wavelength structures with the long-wavelength Crow instability is studied, and we observe significant modifications in the longevity of large vortical structures.

The formation of vortex rings generated through impulsively started jets is studied experimentally. Utilizing a piston/cylinder arrangement in a water tank, the velocity and vorticity fields of vortex rings are obtained using digital particle image velocimetry (DPIV) for a wide range of piston stroke to diameter (L/D) ratios. The results indicate that the flow field generated by large L/D consists of a leading vortex ring followed by a trailing jet. The vorticity field of the leading vortex ring formed is disconnected from that of the trailing jet. On the other hand, flow fields generated by small stroke ratios show only a single vortex ring. The transition between these two distinct states is observed to occur at a stroke ratio of approximately 4, which, in this paper, is referred to as the ‘formation number’. In all cases, the maximum circulation that a vortex ring can attain during its formation is reached at this non-dimensional time or formation number. The universality of this number was tested by generating vortex rings with different jet exit diameters and boundaries, as well as with various non-impulsive piston velocities. It is shown that the ‘formation number’ lies in the range of 3.6–4.5 for a broad range of flow conditions. An explanation is provided for the existence of the formation number based on the Kelvin–Benjamin variational principle for steady axis-touching vortex rings. It is shown that based on the measured impulse, circulation and energy of the observed vortex rings, the Kelvin–Benjamin principle correctly predicts the range of observed formation numbers.

Investigation of the linear stability problem for rapidly rotating convection on an f-plane has revealed the existence of two distinct scales in the vertical structure of the critical eigenfunctions: a small length scale whose vertical wavenumber kz is comparable with the large horizontal wavenumber k⊥ selected at onset, and a large-scale modulation which forms an envelope on the order of the layer depth d. The small-scale structure in the vertical results from a geostrophic balance imposed by the Taylor–Proudman constraint. This primary balance forces rotational alignment and confines fluid motions to planes perpendicular to the rotation axis. For convective transport in the vertical this constraint must be relaxed. This is achieved by molecular dissipation which allows weak upward (downward) spiralling of hot (cold) fluid elements across the Taylor–Proudman planes and results in a large-scale vertical modulation of the Taylor columns.

In the limit of fast rotation (i.e. large Taylor number) a multiple-scales analysis leads to the determination of a critical Rayleigh number as a function of wavenumber, roll orientation and the tilt angle of the f-plane. The corresponding critical eigenfunction represents the core solution; matching to passive Ekman boundary layers is required for a complete solution satisfying boundary conditions.

An extension of this analysis, introduced by Bassom & Zhang (1994), is used to describe strongly nonlinear two-dimensional convection, characterized by significant departures of the mean thermal field from its conduction profile. The analysis requires the solution of a nonlinear eigenvalue problem for the Nusselt number (for steady convection) and the Nusselt number and oscillation frequency (for the overstable problem). The solutions of this problem are used to calculate horizontal and vertical heat fluxes, as well as Reynolds stresses, as functions of both the latitude and roll orientation in the horizontal, and these are used to calculate self-consistently north–south and east–west mean flows. These analytical predictions are in good agreement with the results of three-dimensional simulations reported by Hathaway & Somerville (1983).

Coherent structures play an important role in the dynamics of turbulent shear flows. The ability to control coherent structures could have significant technological benefits with respect to flow phenomena such as skin friction drag, transition, mixing, and separation. This paper describes the development of an actuator concept that could be used in large arrays for actively controlling transitional and turbulent boundary layers. The actuator consists of a piezoelectrically driven cantilever mounted flush with the flow wall. When driven, the resulting flow disturbance over the actuator is a quasi-steady pair of counter-rotating streamwise vortices with common-flow away from the wall. The vortices decay rapidly downstream of the actuator; however, they produce a set of high- and low-speed streaks that persist far downstream (well over 40 displacement thicknesses). The amplitude of the actuator drive signal controls the strength of the generated vortices. The actuator is fast, compact, and generates a substantial disturbance in the flow. Its performance has been demonstrated using a small array of sensors and actuators in low-speed water laminar boundary layers with imposed steady and unsteady disturbances. Experiments are reported in which transition from a large disturbance was delayed by 40 displacement thicknesses, and in which the mean and spanwise variation of wall shear under an array of high- and low-speed streaks was substantially reduced downstream of a single transverse array of actuators.

The natural frequencies and damping rates of surface waves in a circular cylinder with pinned-end boundary conditions are calculated in terms of the gravitational Reynolds and Bond numbers, C−1 and B, and the slenderness of the cylinder Λ, in the limit C→0. We consider higher-order approximations that include the effect of viscous dissipation in the Stokes boundary layers and the bulk. A comparison with clean-surface experiments by Henderson & Miles (1994) shows a satisfactory agreement except for the first axisymmetric mode, which exhibits a 26% discrepancy. The much larger dramatic discrepancy of former theoretical predictions is hereby improved and explained.

We examine the turbulent gravitational convection which develops above a point source of buoyant fluid in a stably stratified environment in which the buoyancy frequency varies with height according to N2=N2s (z/zs)β. This generalizes the classical model of turbulent buoyant plumes rising through uniform and uniformly stratified environments originally developed by Morton et al. (1956). By analogy, the height of rise of a plume with initial buoyancy flux Fs has the form Hp= Apεp−1/2Fs1/4Ns−3/4hp (λ, β) where εp is the entrainment constant for plume motion, Ap is an O(1) constant, and the non-dimensional plume height, hp is a function of &λ=Apεp−1/2Fs1/4Ns−3/4/zs and β.

In the case β>0, the stratification becomes progressively stronger with height, and so plumes are always confined within a finite distance above the origin. Furthermore, the non-dimensional height of rise h decreases with λ. In contrast, in the case β<0, the stratification becomes progressively weaker with height, and so the non-dimensional plume height increases monotonically with λ. For slowly decaying stratification, β>−8/3, the motion is confined within a finite distance above the source. However, for each value of β with β<−8/3, there is a critical value λc(β) such that for λ<λc a plume is confined to a region near the source while for λ[ges ]λc the motion is unbounded. In the unbounded case, the motion asymptotes to the solution for a buoyant plume rising through a uniform environment, with asymptotic buoyancy flux F∞(λ)<Fs. We show that in the limiting case λ=λc, dividing bounded and unbounded motion, as z→∞ the plume asymptotes to a new similarity solution of the second kind which describes the motion of a plume in a non-uniformly stratified environment. These similarity solutions are unstable in the sense that small perturbations to the initial conditions result in very different behaviour far from the source.

Analogous results for an instantaneous release of buoyant fluid from a point source, which forms a thermal, are also presented. The model is applied to describe the motion of plumes and thermals in the upper ocean and in naturally ventilated buildings since in both cases the stratification is typically non-uniform.

Time-averaged LDA measurements and time-resolved numerical flow predictions were performed to investigate the laminar flow induced by the harmonic in-line oscillation of a circular cylinder in water at rest. The key parameters, Reynolds number Re and Keulegan–Carpenter number KC, were varied to study three parameter combinations in detail. Good agreement was observed for Re=100 and KC=5 between measurements and predictions comparing phase-averaged velocity vectors. For Re=200 and KC=10 weakly stable and non-periodic flow patterns occurred, which made repeatable time-averaged measurements impossible. Nevertheless, the experimentally visualized vortex dynamics was reproduced by the two-dimensional computations. For the third combination, Re=210 and KC=6, which refers to a totally different flow regime, the computations again resulted in the correct fluid behaviour. Applying the widely used model of Morison et al. (1950) to the computed in-line force history, the drag and the added-mass coefficients were calculated and compared for different grid levels and time steps. Using these to reproduce the force functions revealed deviations from those originally computed as already noted in previous studies. They were found to be much higher than the deviations for the coarsest computational grid or the largest time step. The comparison of several in-line force coefficients with results obtained experimentally by Kühtz (1996) for β=35 confirmed that force predictions could also be reliably obtained by the computations.

The evolution characteristics of monopolar vortices in an irrotational annular shear flow were investigated both experimentally and theoretically. The background flow was generated in a rotating tank by an appropriate source–sink configuration, while the monopolar vortex was created by withdrawing fluid for a short time. Dye-visualization studies demonstrated the gradual destruction of the vortex through a process called ‘vortex stripping’, i.e. long filaments of passive tracers were being shed from the edge of the vortex. In contrast to uniform shear flows, these filaments were asymmetrically attached to the vortex core. Furthermore, the vortex was observed to evolve in a quasi-stationary manner until its final indefinite breaking. The asymmetric stripping process could be explained by modelling both the monopolar vortex and the ambient flow simply by point vortices, and by adopting the method of contour kinematics to trace material contours in the velocity field induced by the point vortices. Furthermore, the effect of a continuous spatial vorticity distribution was investigated by applying the contour dynamics technique, in which the vortex is represented by a stack of uniform vorticity patches. The observed vortex evolution could be well captured by this latter approach.

The dynamics of a homogeneous turbulent flow subjected to a stable stratification are studied by means of direct numerical simulations (DNS) and by a two-point closure statistical EDQNM model, adapted for anisotropic flows by Cambon (1989). The purpose of this work is to investigate the validity of the anisotropic statistical model, which we refer to as the EDQNM2 model. The numerical simulations are of high resolution, 2563, which permits Reynolds numbers comparable to those of recent laboratory experiments. Thus, detailed comparisons with the wind-tunnel experiments of Lienhardt & Van Atta (1990) and Yoon & Warhaft (1990) are also presented.

The initial condition is chosen so as to test the anisotropic closure assumption of the EDQNM2 model. This choice yields a ratio of kinetic to potential energy of 2[ratio ]1. This important amount of initial potential energy drives the flow dynamics during the first Brunt–Väisälä period. Because stronger transfer rates of potential energy than of kinetic energy occur toward small scales, the heat flux is (persistently) counter gradient at those small scales. The loss of potential energy at large scales is partly made up for by conversion of vertical kinetic energy, and this sets up a down-gradient heat flux at those scales, as if no or little potential energy were present at the initial time. Thus, common features with wind-tunnel experiments (in which there is relatively little potential energy just behind the grid) are found. Interestingly, only one quantity displays a similarity law in the DNS, in the EDQNM2 model and in the experiments of Lienhardt & Van Atta (1990) and Yoon & Warhaft (1990) as well: this is the ratio of the vertical heat flux to the dissipation rate of kinetic energy, which can also be interpreted as an instantaneous mixing efficiency. Thus, this parameter seems to be independent of initial flow conditions.

Our calculations simulate a longer evolution of the flow dynamics than laboratory experiments (in which the flow develops for at most one Brunt–Väisälä period). We find that the flow dynamics change from about 1.5 Brunt–Väisälä periods. At that time, the heat flux collapses while the dissipation rate of kinetic energy displays a self-similarity law attesting that this quantity becomes driven by buoyancy forces. This permits us to link the collapse of the largest scales of the flow with the smallest scales being influenced by the buoyancy force. We finally discuss the influence of a geometrical confinement effect upon the above results.

The EDQNM2 model compares remarkably well with the DNS, with respect to previous statistical models of stably stratified turbulent flows. Insufficient decorrelation between the vertical velocity and the temperature fluctuations is however observed, but with no dynamical significance. The vortex part of the flow is also overestimated by the EDQNM2 model, but the relative difference between the model prediction and the DNS does not exceed 15% after 6 Brunt–Väisälä periods. The EDQNM2 model offers interesting perpectives because of its ability to predict the dynamics of stratified flows at high Reynolds numbers. Knowledge about small-scale behaviour will be especially useful, to build up parameterization of the subgrid scales for instance.

Viscoelastic flow instabilities can arise from gradients in elastic stresses in flows with curved streamlines. Circular Couette flow displays the prototypical instability of this type, when the azimuthal Weissenberg number Weθ is O(ε−1/2), where ε measures the streamline curvature. We consider here the effect of superimposed steady axial Couette or Poiseuille flow on this instability. For inertialess flow of an upper-convected Maxwell or Oldroyd-B fluid in the narrow gap limit (ε[Lt ]1), the analysis predicts that the addition of a relatively weak steady axial Couette flow (axial Weissenberg number Wez=O(1)) can delay the onset of instability until Weθ is significantly higher than without axial flow. Weakly nonlinear analysis shows that these bifurcations are subcritical. The numerical results are consistent with a scaling analysis for Wez[Gt ]1, which shows that the critical azimuthal Weissenberg number for instability increases linearly with Wez. Non-axisymmetric disturbances are very strongly suppressed, becoming unstable only when ε1/2Weθ= O(We2z). A similar, but smaller, stabilizing effect occurs if steady axial Poiseuille flow is added. In this case, however, the bifurcations are converted from subcritical to supercritical as Wez increases. The observed stabilization is due to the axial stresses introduced by the axial flow, which overshadow the destabilizing hoop stress. If only a weak (Wez[les ]1) steady axial flow is added, the flow is actually slightly destabilized. The analysis also elucidates new aspects of the stability problems for plane shear flows, including the exact structure of the modes in the continuous spectrum, and illustrates the connection between these problems and the viscoelastic circular Couette flow.