Showing papers in "Journal of Fluid Mechanics in 1978"

Ground effects on pressure fluctuations in the atmospheric boundary layer

Abstract: Proposals are made for modelling the pressure-containing correlations which appear in the transport equations for Reynolds stress and heat flux in a simple way which accounts for gravitational effects and the modification of the fluctuating pressure field by the presence of a wall. The predicted changes in structure are shown to agree with Young's (1975) measurements in a free stratified shear flow and with the Kansas data on the atmospheric surface layer.

A simple dynamical model of intermittent fully developed turbulence

Abstract: We present a phenomenological model of intermittency called the P-model and related to the Novikov-Stewart (1964) model. The key assumption is that in scales N &2-” only a fraction /3n of the total space has an appreciable excitation. The model, the idea of which owes much to Kraichnan (1972, 1974)’ is dynamical in the sense that we work entirely with inertial-range quantities such as velocity amplitudes, eddy turnover times and energy transfer. This gives more physical insight than the traditional approach based on probabilistic models of the dissipation. The P-model leads in an elementary way to the concept of the self-similarity dimension D, a special case of Mandelbrot’s (1974, 1976) ‘fractal dimension’. For threedimensional turbulence, the correction B to the Q exponent of the energy spectrum is equal to +( 3 - D) and is related to the exponent p of the dissipation correlation function by B = Qp (0.17 for the currently accepted value). This is a borderline case of the Mandelbrot inequality B < Qp. It is shown in the appendix that this inequality may be derived from the Navier-Stokes equation under the strong, but plausible, assumption that the inertial-range scaling laws for second- and fourth-order moments have the same viscous cut-off. The predictions of the P-model for the spectrum and for higher-order statistics are in agreement with recent conjectures based on analogies with critical phenomena (Nelkin 1975) but generally diasgree with the 1962 Kolmogorov lognormal model. However, the sixth-order structure function (8v6(Z)) and the dissipation correlation function (e(r) e(r + 1)) are related by

An exact theory of nonlinear waves on a Lagrangian-mean flow

Abstract: An exact and very general Lagrangian-mean description of the back effect of oscillatory disturbances upon the mean state is given. The basic formalism applies to any problem whose governing equations are given in the usual Eulerian form, and irrespective of whether spatial, temporal, ensemble, or ‘two-timing’ averages are appropriate. The generalized Lagrangian-mean velocity cannot be defined exactly as the ‘mean following a single fluid particle’, but in cases where spatial averages are taken can easily be visualized, for instance, as the motion of the centre of mass of a tube of fluid particles which lay along the direction of averaging in a hypothetical initial state of no disturbance.The equations for the Lagrangian-mean flow are more useful than their Eulerian-mean counterparts in significant respects, for instance in explicitly representing the effect upon mean-flow evolution of wave dissipation or forcing. Applications to irrotational acoustic or water waves, and to astrogeophysical problems of waves on axisymmetric mean flows are discussed. In the latter context the equations embody generalizations of the Eliassen-Palm and Charney-Drazin theorems showing the effects on the mean flow of departures from steady, conservative waves, for arbitrary, finite-amplitude disturbances to a stratified, rotating fluid, with allowance for self-gravitation as well as for an external gravitational field.The equations show generally how the pseudomomentum (or wave ‘momentum’) enters problems of mean-flow evolution. They also indicate the extent to which the net effect of the waves on the mean flow can be described by a ‘radiation stress’, and provide a general framework for explaining the asymmetry of radiation-stress tensors along the lines proposed by Jones (1973).

Kinematical studies of the flows around free or surface-mounted obstacles; applying topology to flow visualization

Abstract: In flows around three-dimensional surface obstacles in laminar or turbulent streamsthere are a number of points where the shear stress or where two or more component,s of the mean velocity are zero. In the first part of this paper we summarize and extend the kinematical theory for the flow near these points, particularly by emphasizing the topological classification of these points as nodes or saddles. We show that the zero-shear-stress points on the surface and on the obstacle must be such that the sum of the nodes ΣN and the sum of the saddles Σs satisfy \[ \Sigma_N -\Sigma_S = 0. \] If the obstacle has a hole through it, such as a passageway under a building, \[ \Sigma_N -\Sigma_S =-2. \] If the surface is a junction between two pipes, \[ \Sigma_N -\Sigma_S =-1. \] We also consider, in two-dimensional plane sections of the flow, the points where the components of the mean velocity parallel to the planes are zero, both in the flow and near surfaces cutting the sections. The latter points are half-nodes N′ or half-saddles S′. We find that \[ (\Sigma_N +{\textstyle\frac{1}{2}}\Sigma_{N^{\prime}}-(\Sigma_{S^{\prime}}+{\textstyle\frac{1}{2}}\Sigma_{S^{\prime}}) = 1-n, \] where n is the connectivity of the section of the flow considered.In the second part new flow-visualization studies of laminar and turbulent flows around cuboids and axisymmetric humps (i.e. model hills) are reported. A new method of obtaining a high resolution of the surface shear-stress lines was used. These studies show how enumerating the nodes and saddle points acts as a check on the inferred flow pattern.Two specific conclusions drawn from these studies are that: for all the flows we observed, there are no closed surfaces of mean streamlines around the separated flows behind three-dimensional surface obstacles, which con-tradicts most of the previous suggestions for such flows (e.g. Halitsky 1968);the separation streamline on the centre-line of a three-dimensional bluff obstacle does not, in general, reattach to the surface.

On the motion of a small viscous droplet that wets a surface

Abstract: A model for the movement of a small viscous droplet on a surface is constructed that is based on the lubrication equations and uses the dynamic contact angle to describe the forces acting on the fluid at the contact line. The problems analysed are: the spreading or retraction of a circular droplet; the advance of a thin two-dimensional layer; the creeping of a droplet or cell on a coated surface to a region of greater adhesion; the distortion of droplet shape owing to surface contamination. Relevant biological problems concerning cell movement and adhesion are described.

On the response of a poro-elastic bed to water waves

Abstract: The problem of the response of a porous elastic bed to water waves is treated analytically on the basis of the three-dimensional consolidation theory of Biot (1941). Exact solutions for the pore-water pressure and the displacements of the porous medium are obtained in closed form for the case of waves propagating over the poro-elastic bed. The theoretical results indicate that the bed response to waves is strongly dependent on the permeability k and the stiffness ratio G/K’, where G is the shear modulus of the porous medium and K’ is the apparent bulk modulus of elasticity of the pore fluid. The earlier solutions for pore-water pressure by various authors are given as the limiting cases of the present solution. For the limits G/K′ → 0 or k→ ∞, the present solution for pressure approaches the solution of the Laplace equation by Putnam (1949). For the limit G/K′→ ∞, the present solution approaches the solution of the heat conduction equation by Nakamura et al. (1973) and Moshagen & Torum (1975).The theoretical results are compared with wave tank experimental data on pore-water pressure in coarse and fine sand beds which contain small amounts of air. Good agreement between theory and experiment is obtained.

Large-scale structure in the mixing layer of a round jet

Abstract: Late transitional and turbulent flows in the mixing-layer region of a round jet are investigated for a range of Reynolds numbers by using flow-visualization and hotwire techniques. Attention is focused on the vortices in the transition region and the large eddies in the turbulent region. The interaction and coalescence of vortex rings in the transition region are described. The transition region is characterized by a growth of three-dimensional flow due to a wave instability of the cores of the vortex rings. The merging of these distorted vortices produces large eddies which can remain coherent up to the end of the potential-core region of the jet. A conditional sampling technique is used to measure eddies moving near the jet centre-line. These eddies differ significantly from the ring vortices as they are three-dimensional and contain irregular small-scale turbulence. However, when averaged, their structure is similar in cross-section to that of a vortex ring. These sampled eddies contribute greatly to local velocity fluctuations and statistical correlations. The experiments indicate a need for careful consideration of the meanings of terms such as ‘vortex’, ‘eddy’ and ‘turbulent flow’. In particular care must be taken to discriminate between the orderly, easily visualized, vortices in the transition regions of free shear flows and the less clearly visualized, but strong, large eddies in the fully developed turbulent regions.

Flow around a circular cylinder near a plane boundary

Abstract: The flow around a circular cylinder placed at various heights above a plane boundary has been investigated experimentally. The cylinder spanned the test section of a wind tunnel and was aligned with its axis parallel to a long plate and normal to the free stream. It was placed 36 diameters downstream of the leading edge of the plate and its height above the plate was varied from zero, the cylinder lying on the surface, to 3·5 cylinder diameters. The thickness of the turbulent boundary layer on the plate at the cylinder position, but with it removed from the tunnel, was equal to 0·8 of the cylinder diameter. Distributions of mean pressure around the cylinder and along the plate were measured at a Reynolds number, based on cylinder diameter, of 4·5 × 104. Spectral analysis of hot-wire signals demonstrated that regular vortex shedding was suppressed for all gaps less than about 0·3 cylinder diameters. For gaps greater than 0·3 the Strouhal number was found to be remarkably constant and the only influence of the plate on vortex shedding was to make it a more highly tuned process as the gap was reduced. Flow-visualization experiments in a smoke tunnel revealed the wake structure at various gap-to-diameter ratios.

Self-formed straight rivers with equilibrium banks and mobile bed. Part 2. The gravel river

Abstract: Rivers are capable of transporting their own bed material without altering their width. However, a naive extension of the threshold theory of canals in coarse alluvium to straight reaches of gravel rivers leads to the stable-channel paradox: transport of bed material is incompatible with a stable width. In this paper singular perturbation techniques are used to obtain a bed stress distribution which allows a mobile bed but immobile banks at bankfull or dominant discharge. This result is used to obtain regime relations for straight rivers with bed and banks composed of coarse gravel.The analysis, although dependent on a series of approximate assumptions for Reynolds-stress closure and sediment transport, provides reasonable agreement with data.

A numerical study of the deformation and burst of a viscous drop in an extensional flow

Abstract: We study the deformation and conditions for breakup of a liquid drop of viscosity λμ freely suspended in another liquid of viscosity μ with which it is immiscible and which is being sheared. The problem at zero Reynolds number is formulated exactly as an integral equation for the unknown surface velocity, which is shown to reduce to a particularly simple form when Δ = 1. This equation is then solved numerically, for the case in which the impressed shear is a radially symmetric extensional flow, by an improved version of the technique used, for Δ = 0, by Youngren & Acrivos (1976) so that we model the time-dependent distortion of an initially spherical drop. It is shown that, for a given Δ, a steady shape is attained only if the dimensionless group Ω ≡4πGμa/γ lies below a critical value Ωc(Δ), where G refers to the strength of the shear field, a is the radius of the initial spherical drop and γ is the interfacial tension. On the other hand, when Ω > Ωc the drop extends indefinitely along its long axis. The numerical results for Δ = 0·3, 0·5, 1, 2, 10 and 100 are in good agreement with the predictions of the small deformation analysis by Taylor (1932) and Barthes-Biesel & Acrivos (1973) and, at the smaller Δ, with those of slender-body theory (Taylor 1964; Acrivos & Lo 1978).

On the tones and pressure oscillations induced by flow over rectangular cavities

Abstract: Experimental measurements of the frequencies of discrete tones induced by flow over rectangular cavities were carried out over a range of low subsonic Mach numbers to provide a reliable data base for (aircraft wheel well) cavity noise consideration. A mathematical model of the cavity tones and pressure oscillation phenomenon based on the coupling between shear layer instabilities and acoustic feedback is developed to help in understanding the tone generation mechanism. Good agreement is found between discrete tone frequencies predicted by the model and experimental measurements over a wide range of Mach numbers. Evidence of tones generated by the cavity normal mode resonance mechanism at very low subsonic Mach numbers is also presented.

Free-stream turbulence near plane boundaries?

Abstract: Grid turbulence convected by a free stream past a rigid surface moving at the same speed as the free stream is analysed by boundary-layer theory and spectral methods. The turbulence is assumed to be weak, i.e. are the streamwise co-ordinate, kinematic viscosity and mean velocity respectively. Here the turbulent velocity decays to zero at the surface. Spectra variances and cross-correlations are calculated and found to compare well with measurements of turbulence near moving walls by Uzkan & Reynolds (1967) and Thomas & Hancock (1977).The results of this theory are shown to have a number of applications including the prediction of turbulence near wind-tunnel walls and near flat plates placed parallel to the flow.

An experimental study of the decay of temperature fluctuations in grid-generated turbulence

Abstract: Previous measurements of the decay rate of the fluctuation intensity of passive scalars in grid-generated turbulence show large variation. New results presented here show that the decay rate of passive temperature fluctuations produced by heating the grid is a function of the initial temperature fluctuation intensity. Although a full reason for this is wanting, spectra of the temperature fluctuations show that, by varying the heat applied to the grid, the wavenumber of the maximum in the temperature spectrum changes, indicating that the geometry of the thermal fluctuations is being altered in some way. In these experiments the one-dimensional temperature spectrum shows an anomalous slope. In order to eliminate the dependence of the decay rate of the temperature fluctuations on their intensity, we describe a new way of generating temperature fluctuations by means of placing a heated parallel array of fine wires (a mandoline) downstream from the unheated grid. Results of this experiment show that the decay rate of passive thermal fluctuations is uniquely determined by the wave-number of the initial temperature fluctuations. In this type of flow there appears to be no equilibrium value for the thermal fluctuation decay rate and hence for the mechanical/thermal time-scale ratio since the thermal fluctuation decay rate does not change within the tunnel length, which is the equivalent of nearly one turbulence decay time.

Experiments on the dynamics of a gravity current head

Abstract: Some of the dense fluid at the front of an advancing gravity current is observed to be mixed with the ambient fluid. This process continues when the cross-stream non-uniformities at the head of the current are suppressed by advancing the floor beneath the head. In the resulting two-dimensional flow regular billows are visible. This paper considers experimentally and analytically the inviscid gravity current head and specifically includes the observed mixing at the head. Experimental results were obtained with an apparatus in which the head of the gravity current was brought to rest by an opposing uniform flow. The mixing appears to occur through Kelvin-Helmholtz billows generated on the front of the head and controls the dynamics of the head. A momentum balance is used to analyse the flow and the problem is closed by quantitatively introducing the billow structure.

Asymmetric flows and instabilities in symmetric ducts with sudden expansions

Abstract: Flow visualization and laser-Doppler anemometry have been used to provide a detailed description of the velocity characteristics of the asymmetric flows which form in symmetric, two-dimensional, plane, sudden-expansion geometries. The flow and geometry boundary conditions which give rise to asymmetric flow are indicated, and the reason for the phenomenon is shown to lie in disturbances generated at the edge of the expansion and amplified in the shear layers. The spectral distributions of the fluctuations in velocity are quantitatively related to the dimensions of the two unequal regions of flow recirculation. It is also shown that the intensity of fluctuating energy in these low Reynolds number flows can be larger than that in corresponding turbulent flows.

Convection in a porous cavity

Abstract: Convection in a porous cavity driven by heating in the horizontal is analysed by a number of different techniques which yield a fairly complete description of the two-dimensional solutions. The solutions are governed by two dimensionless parameters: the Darcy-Rayleigh number R and the cavity aspect ratio A. We first find solutions valid for shallow cavities, A → 0, by using matched asymptotic expansions. These solutions are given up to O(A6R4). For A fixed, we find regular expansions in R by semi-numerical techniques, up to O(R30) in some cases. Series-improvement techniques then enable us to cover the range 0 ≤ R ≤ ∞. A limited result regarding bifurcations is noted. Finally, for R → ∞ with A fixed, we propose a self-consistent boundary-layer theory which extends previous approximate work. The results obtained by these different methods of solution are in good agreement with each other and with experiments.

Unsteady vortical and entropic distortions of potential flows round arbitrary obstacles

Abstract: The analysis concerns the alterations produced when small amplitude disturbances, including entropy and vorticity disturbances, are imposed on steady potential flows. For the most general nonacoustic incident distortion field that can be imposed on the uniform upstream flow, it is shown that the perturbation velocity at any point of the resulting unsteady compressible and vortical flow consists of a part that is a known function of the imposed upstream distortion field and the mean flow variables and a potential part that can be found by solving a linear inhomogeneous wave equation with a dipole-type source term whose strength is a known function of the imposed upstream distortion field. The theory is applied to the unsteady flow past a corner, and a closed-form analytical solution is found.

The fine-scale structure of the turbulent velocity field

Abstract: The existence of universal similarity of the fine-scale structure of turbulent velocity fields and the validity of the original Kolmogorov local similarity theory and the later reformulations were investigated. Recent studies of the fine-scale velocity field for many different flows, e.g. grid flows, wakes, jets and the atmospheric boundary layer, are shown to provide considerable evidence for the existence of Kolmogorov normalized spectral shapes which are universal in the sense that they describe the high wave-number spectral behaviour of all turbulent flow fields with a similar value of the turbulence Reynolds number Rλ. The normalized spectral shapes vary with Rλ in a manner consistent with the later reformulations. The Reynolds number dependence of the normalized spectra is demonstrated for the Rλ range from about 40 to 13 000. Expressions for the Kolmogorov normalized spectral functions are presented for three values of Rλ. Also revealed in this study is the importance of considering effects on spectra caused by deviations from Taylor's approximation in high intensity turbulent flows. Lumley's (1965) model is used to correct the high frequency portion of the measured one-dimensional spectra for these effects. An analytical solution to Lumley's expression is presented and applied to the data.

Self-formed straight rivers with equilibrium banks and mobile bed. Part 1. The sand-silt river

Abstract: Rivers and canals with perimeters composed of non-cohesive sand and silt have self-formed active beds and banks. They thus provide a most interesting fluid flow problem, for which one must determine the container as well as the flow. If bed load alone occurs across the perimeter of a wide channel, gravity will pull particles down the lateral slope of the banks; bank erosion is accomplished and the channel widens. In order to maintain equilibrium, this export of material from the banks must be countered by an import of sediment from the channel centre.The mechanism postulated for this import is lateral diffusion of suspended sediment, which overloads the flow near the banks and causes deposition. The model is formulated analytically with the aid of a series of approximate but reasonable assumptions. Singular perturbation techniques are used to define the channel geometry and obtain rational regime relations for straight channels. A comparison with data lends credence to the model.It is hoped that a first step has been made towards a more general treatment, which would include various complicating factors that are important features of natural rivers but are not essential to the maintenance of channel width. Among these factors are meandering, sediment sorting and seepage.

Models of the scalar spectrum for turbulent advection

Abstract: Several models are developed for the high-wavenumber portion of the spectral transfer function of scalar quantities advected by high-Reynolds-number, locally isotropic turbulent flow. These models are applicable for arbitrary Prandtl or Schmidt number, v/D, and the resultant scalar spectra are compared with several experiments having different v/D. The ‘bump’ in the temperature spectrum of air observed over land is shown to be due to a tendency toward a viscous-convective range and the presence of this bump is consistent with experiments for large v/D. The wavenumbers defining the transition between the inertial-convective range and viscous-convective range for asymptotically large v/D (denoted k* and k1* for the three- and one-dimensional spectra) are determined by comparison of the models with experiments. A measurement of the transitional wavenumber k1* [denoted (k1*)s] is found to depend on v/D and on any filter cut-off. On the basis of the k* values it is shown that measurements of β1 from temperature spectra in moderate Reynolds number turbulence in air (v/D = 0·72) maybe over-estimates and that the inertial-diffusive range of temperature fluctuations in mercury (v/D ≃ 0·02) is of very limited extent.

Visual observations of the flow past a sphere at Reynolds numbers between 10 4 and 10 6

Abstract: The wake configuration of a sphere has been determined by means of the surface oil-flow method, the smoke method and the tuft-grid method in a wind tunnel at Reynolds numbers ranging from 104 to 106. It was found that the wake performs a progressive wave motion at Reynolds numbers between 104 and 3·8 × 105, and that it forms a pair of stream wise line vortices at Reynolds numbers between 3·8 × 105 and 106.

On wave-action and its relatives

Abstract: Conservable quantities measuring ‘wave activity’ are discussed. The equation for the most fundamental such quantity, wave-action, is derived in a simple but very general form which does not depend on the approximations of slow amplitude modulation, linearization, or conservative motion. The derivation is elementary, in the sense that a variational formulation of the equations of fluid motion is not used. The result depends, however, on a description of the disturbance in terms of particle displacements rather than velocities. A corollary is an elementary but general derivation of the approximate form of the wave-action equation found by Bretherton & Garrett (1968) for slowlyvarying, linear waves.The sense in which the general wave-action equation follows from the classical ‘energy-momentum-tensor’ formalism is discussed, bringing in the concepts of pseudomomentum and pseudoenergy, which in turn are related to special cases such as Blokhintsev's conservation law in acoustics. Wave-action, pseudomomentum and pseudoenergy are the appropriate conservable measures of wave activity when ‘waves’ are defined respectively as departures from ensemble-, space- and time-averaged flows.The relationship between the wave drag on a moving boundary and the fluxes of momentum and pseudomomentum is discussed.

The turbulent concentration field of a methane jet

Abstract: Detailed measurements of turbulent concentration parameters in a round free methane jet up to 70 diameters downstream from the jet source are described. The concentration changes were obtained using a Raman spectrometer designed for the measurement of a methane vibrational transition function, and processed using a photon correlator. Mean and fluctuating concentration levels are given, together with the concentration probability density distribution.A theory for interpreting the statistical aspects of the signal is presented and results are compared with other data from the literature on jets of uniform and non-uniform density. It is shown that the intensity of concentration fluctuations has an asymptotic value of 28·5% in the far field region of the jet. One interesting feature of the data is the deviation from Gaussian statistics along the jet centre-line.

The continuous spectrum of the Orr-Sommerfeld equation. Part 1. The spectrum and the eigenfunctions

Abstract: It is shown that the Orr-Sommerfeld equation, which governs the stability of any mean shear flow in an unbounded domain which approaches a constant velocity in the far field, has a continuous spectrum. This result applies to both the temporal and the spatial stability problem. Formulae for the location of this continuum in the complex wave-speed plane are given. The temporal continuum eigenfunctions are calculated for two sample problems: the Blasius boundary layer and the two-dimensional laminar jet. The nature of the eigenfunctions, which are very different from the Tollmien-Schlichting waves, is discussed. Three mechanisms are proposed by which these continuum modes could cause transition in a shear flow while bypassing the usual linear Tollmien-Schlichting stage.

Large-scale motion in a turbulent boundary layer: a study using temperature contamination

Abstract: A fully developed turbulent boundary layer with a zero pressure gradient was explored by using temperature as a passive contaminant in order to study the large-scale structure. The temperature tracer was introduced into the flow field by heating the entire wall to approximately 12°C above the free-stream temperature. The most interesting observation was the existence of a sharp internal temperature front, characterized by a rapid decrease in temperature, that extended throughout the entire boundary layer. In the outer, intermittent region, the internal temperature front was always associated with the upstream side of the turbulent bulges, i.e. the ‘backs’. It extended across the entire logarithmic region and was related to the sharp acceleration associated with the bursting phenomenon near the wall. Conditional averages of the velocities measured with the temperature front revealed that it was associated with an internal shear layer. The results suggest that this shear layer provides a dynamical relationship between the large structures in the outer, intermittent region and the bursting phenomenon near the wall.

On vortex sound at low Mach number

Abstract: A transformation is described which relates the sound generated by low Mach number flow to the flow vorticity. For compact flow fields the apparent sound source is of quadrupole type and linear in the vorticity and therefore also linear in the flow velocity. This scheme is applied to the sound generated by the interaction of two identical thin vortex rings. Then a flow field with a number of compact vortices is discussed. It is found that each vortex can be replaced acoustically by a dipole related to the impulse of the vortex, plus the quadrupole just mentioned plus a spherically symmetric sound source related to the energy of the vortex. An application to low Mach number free-space turbulence shows that the generated sound is related to the vorticity correlation tensor.

Structure and entrainment in the plane of symmetry of a turbulent spot

Abstract: Laser-Doppler velocity measurements in water are reported for the flow in the plane of symmetry of a turbulent spot. The unsteady mean flow, defined as an ensemble average, is fitted to a conical growth law by using data at three streamwise stations to determine the virtual origin in x and t. The two-dimensional unsteady stream function is expressed as ψ=U^2_∞tg(ξ,η) in conical similarity co-ordinates ζ = x/U_∞t and η = y/U_∞t. In these co-ordinates, the equations for the unsteady particle displacements reduce to an autonomous system. This system is integrated graphically to obtain particle trajectories in invariant form. Strong entrainment is found to occur along the outer part of the rear interface and also in front of the spot near the wall. The outer part of the forward interface is passive. In terms of particle trajectories in conical co-ordinates, the main vortex in the spot appears as a stable focus with celerity 0·77U_∞. A second stable focus with celerity 0·64U_∞ also appears near the wall at the rear of the spot. Some results obtained by flow visualization with a dense, nearly opaque suspension of aluminium flakes are also reported. Photographs of the sublayer flow viewed through a glass wall show the expected longitudinal streaks. These are tentatively interpreted as longitudinal vortices caused by an instability of Taylor-Gortler type in the sublayer.

Hydrodynamic propulsion by large amplitude oscillation of an airfoil with chordwise flexibility

Abstract: The hydrodynamic forces due to the motion of a flexible foil in a large amplitude curved path in an inviscid incompressible flow are analysed. A parametric study of large amplitude oscillatory propulsion, with special emphasis on the effect of chordwise flexibility of the fin, is presented. This flexibility was found to increase the propulsive efficiency by up to 2% while causing small decreases in the overall thrust, compared with similar motion with rigid foils.

Bubble plumes in stratified environments

Abstract: This paper is concerned with the behaviour of buoyant plumes driven by a source of bubbles. It is shown experimentally that, when a bubble plume rises through a stratified environment, fluid can be transported vertically for some distance and then some of this fluid can leave the plume and spread out horizontally at its own density level. A simple plume model which regards the plume as a single entity is discussed in order to make a first assessment of the effects of gas expansion and bubble slip velocity in this stratified case. However, the experiments reveal a more complicated plume structure in which the bubbles remain in the centre part of the plume, and only the outer part of the plume spreads out into the environment at certain levels. On the basis of these observations a double-plume model is proposed which regards the plume as being composed of two parts: an inner circular plume (which contains all the bubbles of gas) and an outer annular plume.

An experimental map of the internal structure of a vortex breakdown

Abstract: The flow field of an 'axisymmetric' vortex breakdown has been mapped using a laser-Doppler anemometer. The interior of the recirculation zone is dominated by energetic, non-axisymmetric, low frequency periodic fluctuations. Spectra for a number of points inside this zone, as well as time-averaged swirl and axial velocity profiles both inside and outside the recirculation zone, have been obtained. The time-averaged streamlines in the interior show an unexpected two-celled structure attributed to the action of the fluctuations. Although the present experiment deals with one particular breakdown, flow-visualization studies indicate that the case examined is typical of the 'axisymmetric' form of breakdown over a range of flow conditions.