bluuebunny/crossref_metadata_2025 huggingface dataset:
Removal of Goldstein's singularity at separation, in flow past obstacles in wall layers
Authors: Smith F. T. , Daniels P. G.
Published: April 2006

It is shown that, in the flow of a viscous wall layer past a relatively steep obstacle at the wall, the Goldstein (1948) singularity generated in the classical boundary-layer approach to separation is removable in a physically sensible fashion. The removal is effected by means of a sequence of local double structures, the last of which arises just beyond separation owing to the occurrence of a further singularity which is also removable and describes the necessary complete breakaway of the viscous layer from the wall. The novel forms of the local pressure–displacement relations are the key elements allowing the solution to retain physical reality throughout. Beyond the breakaway the reattachment process takes place only at a relatively large distance downstream, before the motion returns to its original uniform shear form. The present flow configuration, the first we know of where Goldstein's singularity proves to be removable, has important applications in both internal and external flows at high Reynolds numbers and these are also discussed.
Oscillations in double-diffusive convection
Authors: Costa L. N. Da , Knobloch E. , Weiss N. O.
Published: April 2006

We have studied the transition between oscillatory and steady convection in a simplified model of two-dimensional thermosolutal convection. This model is exact to second order in the amplitude of the motion and is qualitatively accurate for larger amplitudes. If the ratio of the solutal diffusivity to the thermal diffusivity is sufficiently small and the solutal Rayleigh number, RS, sufficiently large, convection sets in as overstable oscillations, and these oscillations grow in amplitude as the thermal Rayleigh number, RT, is increased. In addition to this oscillatory branch, there is a branch of steady solutions that bifurcates from the static equilibrium towards lower values of RT; this subcritical branch is initially unstable but acquires stability as it turns round towards increasing values of RT. For moderate values of RS the oscillatory branch ends on the unstable (subcritical) portion of the steady branch, where the period of the oscillations becomes infinite. For larger values of RS a birfurcation from symmetrical to asymmetrical oscillations is followed by a succession of bifurcations, at each of which the period doubles, until the motion becomes aperiodic at some finite value of RT. The chaotic solutions persist as RT is further increased but eventually they lose stability and there is a transition to the stable steady branch. These results are consistent with the behaviour of solutions of the full two-dimensional problem and suggest that period-doubling, followed by the appearance of a strange attractor, is a characteristic feature of double-diffusive convection.
On rotating thermal convection driven by non-uniform heating from below
Authors: Hignett Phillip , Ibbetson Alan , Killworth Peter D.
Published: April 2006

Experiments are described in which a radial temperature gradient is maintained along the lower horizontal boundary of a rotating annulus containing a thermally convecting fluid; the vertical side walls and upper horizontal boundary are nominally insulating. Comparison is made with the non-rotating experiments of Rossby (1965) and the same general asymmetric circulation is observed, i.e. that of a weakly stratified interior of slowly descending fluid occupying most of the annular gap, overlying a thin thermal layer of large vertical temperature gradients, stable over the cold part of the base and statically unstable over the warmer part; the circulation is completed by a narrow region of rising motion at the warm end of the base.

A boundary-layer scaling analysis demonstrates the existence of six flow regimes, depending on the magnitude of a quantity Q defined such that Q is the square of the ratio of the (non-rotating) thermal-layer scale to the Ekman-layer scale. For small Q the flow is only weakly modified by rotation but as Q increases past unity rotation tends to thicken the thermal layer. Also presented are some numerical similarity solutions for the special case of a quadratic temperature distribution on the lower boundary and partially covering the range of Q achieved in the experiments, which is zero to ten. Above a certain critical value of Q (for the geometry used here Qc = 3·4) a baroclinic wave regime exists but is not examined in detail here although a brief discussion of an instability problem is given. Throughout comparisons are drawn between the experimental results and theoretical aspects of the problem.

It is thought that the essential features of a system thermally driven in this way have their counterparts in natural systems such as the large-scale thermally induced ocean circulation driven by the latitudinal variation of incoming solar radiation.
A nonlinear electrohydrodynamic stability analysis of a thermally stabilized plane layer of dielectric liquid
Authors: Worraker W. J. , Richardson A. T.
Published: April 2006

The nonlinear stability of a thermally stabilized horizontal plane layer of dielectric liquid subjected to unipolar charge injection at a voltage near the linear instability threshold is investigated using a normal-mode cascade analysis valid for small perturbation amplitudes. In this first analysis, the primary mode is chosen to be a system of parallel rolls whose amplitude varies aperiodically with time. The branching behaviour at the critical voltage is found to reflect the distinction, apparent in the linear instability problem, between an essentially isothermal space-charge instability and an instability dominated by the effects of an ion mobility varying with temperature. The effect of motion on heat and charge transfer through the system is also considered. Furthermore, in certain cases it appears that overstability is the preferred form of linear instability.
On vortex shedding from smooth and rough cylinders in the range of Reynolds numbers 6×103 to 5×106
Authors: Achenbach E. , Heinecke E.
Published: April 2006

The influence of surface roughness on the vortex-shedding frequency in the wake of a single cylinder has been investigated. The experiments were carried out in an atmospherical and a high-pressure wind tunnel. The tests were started with a smooth cylinder. Then the wake flow of cylinders with relative roughnesses of ks/d = 75 × 10−5, 300 × 10−5, 900 × 10−5, and 3000 × 10−5 was investigated.

For all roughness parameters tested the Strouhal number exhibited an increase in the critical flow regime. With growing roughness parameter the step in the curve became smaller. At transcritical flow conditions the Strouhal number was measured to be in the range of Sr = 0·25 ± 0·018 for all surface roughness tested. No regular vortex shedding could be observed in the critical flow range for the smooth cylinder with l/d = 3·38. When prolonging the test body to l/d = 6·75 the wake fluctuations became periodic.
Arrays of three-dimensional wave-energy absorbers
Authors: Thomas G. P. , Evans D. V.
Published: April 2006

The behaviour of a single linear array of five equally spaced semi-immersed spheres, absorbing energy in a single mode from a regular wave train, is studied both for optimal tuning and for constrained body displacement amplitudes. This is extended to consideration of two parallel rows of such devices. Finally, the spheres are replaced by identical bodies of a particular geometry, containing a strong angular variation, which are studied using a thin-ship approximation.
Newtonian flow theory for slender bodies in a dusty gas
Authors: Barron R. M. , Wiley J. T.
Published: April 2006

Hypersonic small-disturbance theory is extended to consider the problem of dusty-gas flow past thin two-dimensional bodies. The mass fraction of suspended particles is assumed to be sufficiently large that the two-way interaction between particle phase and gas phase must be considered. The system of eight governing equations is further reduced by considering the Newtonian approximation γ → 1 andM∞→ ∞. The Newtonian theory up to second order is studied and the equations are solved for the case of a thin wedge at zero angle of attack. Expressions for the streamlines, dust-particle paths, shock-wave location and all flow variables are obtained. It is seen that the presence of the dust increases the pressure along the wedge surface and tends to bend the shock wave towards the body surface. Other effects of the interaction of the two phases are also discussed.
Computation of the flow between two rotating coaxial disks: multiplicity of steady-state solutions
Authors: Holodniok M. , Kubí[cscr    ]ek M. , Hlavá[cscr    ]ek V.
Published: April 2006

A numerical investigation of the problem of rotating disks is made using the Newton-Raphson and continuation methods. The numerical analysis of the problem was performed for a sequence of values of the Reynolds number R and the ratio of angular velocities of both disks s. It was shown that for higher values of the Reynolds number it is necessary to use a large number of grid points. Continuation of the solution with respect to the parameter s indicated that a number of branches may exist. A detailed discussion for three selected values of s (s = -1, s = 0, s = 1) is presented together with a detailed comparison of our calculations with results already published in the literature.
Some vorticity theorems and conservation laws for non-barotropic fluids
Authors: Mobbs S. D.
Published: April 2006

Some theorems concerning the vorticity in barotropic flows of perfect fluids are generalized for non-barotropic flows. The generalization involves replacing the velocity in certain parts of the equations by a time-dependent quantity which is a function of the velocity and thermodynamic properties of the fluid. Results which are generalized include Kelvin's circulation theorem and conservation laws for potential vorticity and helicity. It is shown how the results can be further generalized to include dissipative effects. The possibility of using some of the results in deriving a complete set of Lagrangian conservation laws for perfect fluids is discussed.
Unsteady flow in straight alluvial streams. Part 2. Transition from dunes to plane bed
Authors: Fredsøe Jørgen
Published: April 2006

The effect of suspended sediment on the modification of individual dunes in unsteady channel flow is analyzed. The model is an extension of that developed by Fredsøe (1979), in which the change of the dune dimensions was analyzed assuming that the transport of sediment mainly occurs as bed load. By including suspended sediment, it is possible to describe dune behaviour at high sediment transport rates, for which the dunes are washed out, so the bed at sufficiently high bed shear stress becomes plane. The model is compared with laboratory experiments and the agreement is reasonable. The effect of temperature variations on dune dimensions is incorporated in the analysis.
Structure of space-time correlations of bursting phenomena in an open-channel flow
Authors: Nakagawa Hiroji , Nezu Iehisa
Published: April 2006

The present study is to investigate the structure of space-time correlations of bursting motions, such as ejections and sweeps in an open-channel flow, by a new conditional sampling analysis of the instantaneous velocity and Reynolds-stress signals measured simultaneously by two dual-sensor hot-film probes. One probe was fixed near the edge of the buffer layer, while the other probe was moved in the streamwise, vertical and spanwise directions. The sorted instantaneous Reynolds-stress signals obtained from the fixed probe were used as a detecting information of the occurrences of ejection or sweep events. The streamwise and vertical spatial characteristics of the ejection-sweep motions, and their convection process are investigated in detail. Also, the spanwise spatial properties of the high- and low-speed streaks in the bursting motions are examined experimentally by the present conditional sampling method.

Next, a qualitative model is proposed which attempts to explain the space-time structures of the bursting phenomenon, on the basis of the above anemometry information and other visual observations.
Coupling between a surface-wave spectrum and an internal wave: modulational interaction
Authors: Dysthe K. B. , Das K. P.
Published: April 2006

Using a simple three-layer model of the ocean, we study a generation mechanism for the lowest internal-wave mode by nonlinear coupling to modulations of the surface-wave spectrum. We first examine the case of a narrow-band surface-wave spectrum, applying a method developed by Alber (1978) to derive a transport equation for the spectral density. Alber demonstrated that, when the spectral width (in the main wave direction) exceeds some critical value, the spectrum is stable against modulational perturbation (i.e. the Benjamin–Feir-type instability is suppressed). We show, however, that, for a stratified ocean, a modulational instability may persist because of a coupling between a ‘modulational mode’ of the surface-wave spectrum and an internal wave. The growth rate is calculated for a simple model of the angular distribution of the spectrum. It turns out that an important parameter is 〈(∇ξ)2〉/Δθ, the ratio between the averaged square of the wave steepness, and the angular width of the spectrum.

For appreciable growth one must have roughly
\[
2\times 10^{-3}\lesssim kd \langle (\nabla\zeta)^2\rangle / \Delta\theta,
\]
where k is a characteristic wavenumber for the surface-wave spectrum, and d is the depth of the thermocline (50-100 m). This condition is probably too limiting for the above-mentioned modulational instability to be of any practical interest in the oceans.

We also consider the broad-band case of modulational interaction, and show the connection with incoherent three-wave interactions.
The instability of oscillatory plane Poiseuille flow
Authors: Von Kerczek Christian H.
Published: April 2006

The instability of oscillatory plane Poiseuille flow, in which the pressure gradient is time-periodically modulated, is investigated by a perturbation technique. The Floquet exponents (i.e. the complex growth rates of the disturbances to the oscillatory flow) are computed by series expansions, in powers of the oscillatory to steady flow velocity amplitude ratio, about the values of the growth rates of the disturbances of the steady flow. It is shown that the oscillatory flow is more stable than the steady flow for values of Reynolds number and disturbance wave number in the vicinity of the steady flow critical point and for values of frequencies of imposed oscillation greater than about one tenth of the frequency of the steady flow neutral disturbance. At very high and low values of imposed oscillation frequency, the unsteady flow is slightly less stable than the steady flow. These results hold for the values of the velocity amplitude ratio at least up to 0·25.
Self-sustained low-frequency components in an impinging shear layer
Authors: Knisely C. , Rockwell D.
Published: April 2006

Oscillations of a cavity shear layer, involving a downstream-travelling wave and associated vortex formation, its impingement upon the cavity corner, and upstream influence of this vortex-corner interaction are the subject of this experimental investigation.

Spectral analysis of the downstream-travelling wave reveals low-frequency components having substantial amplitudes relative to that of the fundamental (instability) frequency component; using bicoherence analysis it is shown that the lowest-frequency component can interact with the fundamental either to reinforce itself or to produce an additional (weaker) low-frequency component. In both cases, all frequency components exhibit an overall phase difference of almost 2kπ(k = 1, 2,…) between separation and impingement. Furthermore, the low-frequency and fundamental components have approximately the same amplitude growth rates and phase speeds; this suggests that the instability wave is amplitude-modulated at the low frequency, as confirmed by the form of instantaneous velocity traces.

At the downstream corner of the cavity, successive vortices, arising from the amplified instability wave, undergo organized variations in (transverse) impingement location, producing a low-frequency component(s) of corner pressure. The spectral content and instantaneous trace of this impingement pressure are consistent with those of velocity fluctuations near the (upstream) shear-layer separation edge, giving evidence of the strong upstream influence of the corner region.
The drift velocity of water waves
Authors: Craik A. D. D.
Published: April 2006

The important role of viscosity in producing second-order Eulerian drift currents in the presence of small-amplitude water waves was first recognized by Longuet-Higgins (1953).

The theoretical and experimental background is first reviewed. It is then shown that, contrary to previous belief, the presence of surface contamination must greatly enhance the drift velocity of short waves. We then solve an initial-value problem for the drift current associated with temporally decaying waves, thereby resolving questions raised by the work of Liu & Davis (1977), whose solution exhibits anomalous singularities. Next, the steady drift velocity of spatially decaying waves is calculated and shown to bear a close resemblance to Longuet-Higgins’ ‘conduction solution’ for unattenuated waves.

Finally, we establish that unidirectional drift currents of both surface and inter-facial waves are sure to be unstable to spanwise-periodic disturbances; the instability mechanism being identical to that first proposed by Craik (1977), and recently developed by Leibovich & Paolucci (1981), to explain the generation of Langmuir circulations.
Dynamics of an impinging jet. Part 2. The noise generation
Authors: Nosseir Nagy S. , Ho Chih-Ming
Published: April 2006

The aerodynamic noise generated by a subsonic jet impinging on a flat plate is studied from measurements of near-field and surface-pressure fluctuations. The far-field noise measured at 90° to the jet axis is found to be generated by two different physical mechanisms. One mechanism is the impinging of the large coherent structures on the plate, and the other is associated with the initial instability of the shear layer. These two sources of noise radiate to the far field via different acoustical paths.
On parametric instabilities of finite-amplitude internal gravity waves
Authors: Klostermeyer J.
Published: April 2006

The equations describing parametric instabilities of a finite-amplitude internal gravity wave in an inviscid Boussinesq fluid are studied numerically. By improving the numerical approach, discarding the concept of spurious roots and considering the whole range of directions of the Floquet vector, Mied's work is generalized to its full complexity. In the limit of large disturbance wavenumbers, the unstable disturbances propagate in the directions of the two infinite curve segments of the related resonant-interaction diagram. They can therefore be classified into two families which are characterized by special propagation directions. At high wavenumbers the maximum growth rates converge to limits which do not depend on the direction of the Floquet vector. The limits are different for both families; the disturbance waves propagating at the smaller angle to the basic gravity wave grow at the larger rate.
Magnetic levitation of liquid metals
Authors: Mestel A. J.
Published: April 2006

The process of levitation melting of metals is examined analytically and numerically for the case of axisymmetric toroidal high-frequency currents. The governing equations for the mean-velocity field and associated free-surface shape are derived under the assumption of low magnetic Reynolds number and the neglect of thermal effects. The form of the solution for high Reynolds number is discussed in general, and particularized to the case of high surface tension, in which limit a perturbation analysis about a spherical shape is presented. Finite-difference techniques are used to solve the Navier–Stokes equations in the sphere, and the surface perturbation is calculated. The asymptotic behaviour of the potential vorticity is illustrated by the numerical experiments.
Transport near a vertical ice surface melting in saline water: some numerical calculations
Authors: Carey Van P. , Gebhart Benjamin
Published: April 2006

Computed numerical results are presented for the laminar buoyancy-induced flows driven by combined thermal and saline transport near a vertical melting ice surface in saline water. Results are presented which indicate that conventional boundary-layer flow occurs for some combinations of ambient salinity and temperature in the ranges 0 to 31‰ and −1 to 20°C, respectively. These conditions are very common in terrestrial waters. The analysis used herein is the first to model fully the many complicated aspects of these flows. The present analysis includes simultaneous transport of salt and thermal energy as well as the effect of interface motion. The formulation uses the most recently available transport properties and a very accurate equation of state for the density of pure and saline water. The interface temperature and salinity, which are not known a priori, are here determined jointly from the transport equations, and from species-conservation and phase-equilibrium relations at the ice surface. At low ambient temperatures, the flow is found to be dominated by the upward saline buoyancy, resulting in upward flow. However, at high temperatures and low salinities, the downward thermal buoyancy overcomes the upward saline buoyancy near the surface to cause downward flow. For choices of ambient conditions between these extremes, the opposing saline and thermal buoyancy are about equal in strength. The resulting tendency for bi-directional flow at these intermediate circumstances caused numerical stability problems which made it impossible to obtain convergent solutions for some cases. However, calculated solutions were obtained at ambient salinities below 5‰, for ambient temperatures between 8 and 20°C, and at temperatures below 4°C, for ambient salinities between 0 and 31‰. These solutions indicate the limits of the range of conditions for which laminar boundary layer flow occurs. They further suggest that outside these ranges, the flow may be laminar and bi-directional. The very strong buoyancy which characterizes some of these conditions suggests that they may become turbulent at short downstream distances. The computed results are seen to be in excellent agreement with the limited experimental data and observations of previous studies.
An amplitude-evolution equation for linearly unstable modes in stratified shear flows
Authors: Engevik L.
Published: April 2006

A nonlinear amplitude equation of second order in time, which governs the temporal evolution of linearly unstable modes in stratified shear flows, is derived. It applies to a class of flows with continuous velocity and density profiles, and two examples of such flows are studied.

One of the flows that is studied is the stratified Couette flow with the buoyancy frequency equal to Qy2, where Q is a constant and y the vertical co-ordinate. The nonlinear amplitude equation is studied for various values of Q.

For the Garcia flow the nonlinear amplitude equation for the long-wave modes is evaluated, and it is compared with the corresponding equation in the Kelvin–Helmholtz flow, which has been found previously.
Multiple scattering in arrays of axisymmetric wave-energy devices. Part 1. A matrix method using a plane-wave approximation
Authors: Simon M. J.
Published: April 2006

A technique is developed to model the multiple scattering of surface waves in an array of axisymmetric wave-energy devices. The matrix equation which results is inverted to yield the exciting forces, the added-damping and added-mass matrices, the optimal power absorption and the optimal device responses. The matrix method is also used on the previously unstudied problem of an unconstrained array. Finite-size effects of devices are shown to be important in producing phase-shifts, which shift the uncon- strained frequency response, but leave the opt,imal energy absorption virtually unchanged.
On the oblique interaction of a large and a small solitary wave
Authors: Johnson R. S.
Published: April 2006

The steady oblique interaction of two solitary waves on the surface of water of constant depth is considered. One wave is taken to be of arbitrary (large) amplitude and the other is small with a (non-dimensional) amplitude measured by the parameter ε. A solution is sought as an asymptotic expansion, based on ε, that assumes that in some region the solution is the sum of the two waves plus interaction terms. It is shown that this expansion is not uniformly valid close to a critical angle. This angle varies from zero (parallel waves) up to about 63°, as the amplitude of the larger wave increases from infinitesimally small to the largest-possible solitary wave. I n the limit of two small waves, the details agree precisely with the results obtained by Miles (1977a).

When the angle between the two waves is dose to the critical angle, for a given large wave, an alternative asymptotic expansion is required. In this strong-interaction case, the dominant term is just the large wave but with a phase shift that is an arbitrary function of the characteristic variable associated with the small wave. This function is determined by matching to an appropriate far field, and it turns out to be proportional to the logarithm of a hypergeometric function (which itself can be expressed in terms of the associated Legendre function Pv−μ). The phase shift is then well-defined (finite, real) provided the angle is not very close to the critical value. When this occurs the phase shift can be infinite at a specific angle (which corresponds to the case |μ| = v > 0), and even closer to the critical angle (|μ| < v) the phase shift is undefined (no longer real). A real solution for the wave profile is still possible if negative amplitudes are allowed, but the resulting solution is unacceptable since the surface is then not undis- turbed at infinity. It is shown that the criterion |μ| < v matches exactly (for two small waves) with Miles’ criterion for the non-existence of a regular reflection.

For the strong interaction (and |μ| ≥ v i t is argued that the small wave cannot penetrate the large wave unchanged. The large wave suffers significant distortion (bending) in the interaction, but the small wave, if it penetrates at all, must have an amplitude O(ε). This is the main aspect of the problem which cannot be completely determined using the present methods. The difficulty can be traced to the large solitary wave which is not known in closed form: only the exponential behaviour in the ‘tail’ is used explicitly in this work.
Surface-tension-driven breakup of viscoelastic liquid threads
Authors: Goren Simon L. , Gottlieb Moshe
Published: April 2006

A linearized stability analysis is carried out for the breakup of small-diameter liquid filaments of dilute polymer solutions into droplets. Oldroyd's 8-constant model expressed in a corotational reference frame is used as the rheological equation of state. The crucial idea in this theory is the recognition that the liquid may be subject to an unrelaxed axial tension due to its prior history. If the tension is zero, the present analysis predicts that jets of shear-thinning liquids are less stable than comparable jets of Newtonian liquids; this is in agreement with previous analyses. However, when the axial tension is not zero, and provided the stress relaxation time constant is sufficiently large, the new theory predicts that the axial elastic tension can be a significant stabilizing influence. With reasonable values for the tension and stress relaxation time the theory explains the great stability observed for jets of some shear- thinning, dilute polymer solutions. The theory explains why drops produced from jets of such liquids are larger than drops from corresponding Newtonian liquids. The theory also appears capable of explaining the sudden appearance of irregularly spaced bulges on jets after long distances of t,ravel with little amplification of disturbances.
The effect of aspect ratio on longitudinal diffusivity in rectangular channels
Authors: Chatwin P. C. , Sullivan Paul J.
Published: April 2006

In a recent paper Doshi, Daiya & Gill (1978) showed that the value of Taylor's longitudinal diffusivity D for laminar flow in a channel of rectangular cross-section of breadth u and height b is about 8D0, for large values of the aspect ratio a/b, where Do is the value of the longitudinal diffusivity obtained by ignoring all variation across the channel. This superficially surprising result is confirmed by an independent method, and is shown to be caused by the boundary layers on the side walls of the channel. The primary purpose of the paper, however, is to consider the value of D in turbulent flow in a flat-bottomed channel of large aspect ratio, for which arguments based on physics are adduced in support of the formula D≈[1 + B][1 - λ(b/u)], where B and λ are positive constants independent of b. It is shown that this result is consistent with laboratory experiments by Fischer (1966). The paper concludes with a discussion of the practical effects of aspect ratio on longitudinal dispersion in channels whose cross-section is approximately rectangular.
Reflection properties of internal gravity waves incident upon a hyperbolic tangent shear layer
Authors: Duin Cornelis A. Van , Kelder Hennie
Published: April 2006

The properties of reflection and transmission of internal gravity waves incident upon a shear layer containing a critical level are investigated. The shear layer is modelled by a hyperbolic tangent profile. In the Boussinesq approximation, the differential equation governing the propagation of these waves can then be transformed into Heun's equation. For large Richardson numbers this equation can be approximated by an equation that has solutions in terms of hypergeometric functions. For these values of the Richardson number the reflection coefficient proves to be strongly dependent on the place of the critical level in the shear flow. If the Doppler-shifted frequency is an odd function of the height difference with respect to the critical level, the reflection and transmission coefficients can be evaluated in closed form.

Over-reflection is possible for sufficiently small wavenumbers and Richardson numbers. It is pointed out that over-reflection and over-transmission cannot occur in a stable flow and that resonant over-reflection is not possible in our model.
Experiments on the role of amplitude and phase modulations during transition to turbulence
Authors: Miksad R. W. , Jones F. L. , Powers E. J. , Kim Y. C. , Khadra L.
Published: April 2006

The transition of a laminar two-dimensional wake is studied experimentally to establish the role of amplitude and phase modulations in the spectral-broadening and energy-redistribution process. Multiple instability modes fo and fi are triggered by acoustic excitation. The spectrum of the fluctuating velocity field formed by the growing and interacting instabilities shows the development of a complicated side- band structure reminiscent of amplitude- and phase-modulated waves. Digital com- plex demodulation techniques are used to obtain quantitative measurements of local instantaneous amplitude and phase modulations. Measurements of the modulation time traces, their modulation indices, the lag between phase and amplitude modula- tions, and the power spectra of the modulations are presented. Our results show that both phase and amplitude modulation play a role in the transition process. The dominant modulation frequency of both amplitude and phase is that of the difference mode fv = f1−f0 produced by the interaction of the two excited instabilities. Phase modulation becomes progressively more important as transition proceeds down- stream, and seems to play the dominant role in the spectral-broadening and energy- redistribution process. Measurements of the bicoherency spectrum indicate that sideband structures, and accompanying modulations, are produced by nonlinear interactions between the low-frequency difference mode and higher-frequency in- stability modes. Some limited measurements indicate that finite-amplitude induced nonlinear dispersion effects ω(k, a2) may provide a physical mechanism by which amplitude modulations generated by nonlinear interactions can induce simultaneous phase modulations.
Finite-amplitude interfacial waves in the presence of a current
Authors: Saffman Philip G. , Yuen Henry C.
Published: April 2006

Solutions for interfacial waves of permanent form in the presence of a current wcre obtained for small-to-moderate wave amplitudes. A weakly nonlinear approximation was used to give simplc analytical solutions to second order in wave height. Numerical methods were usctl to obtain solutions for larger wave amplitudes, details are reported for a number of sclccted cases. A special class of finite-amplitude solutions, closely related to the well-known Stokes surface waves, were identified. Factors limiting the existencc of steady solutions are examined.
Three-dimensional simulations of convection in layers with tilted rotation vectors
Authors: Hathaway David H. , Somerville Richard C. J.
Published: April 2006

Three-dimensional and time-dependent numerical simulations of thermal convection are carried out for rotating layers in which the rotation vector is tilted from the vertical to represent various latitudes. The vertical component of the rotation vector produces narrow convection cells and a reduced heat flux. As this vertical component of the rotation vector diminishes in the lower latitudes, the vertical heat flux increases. The horizontal component of the rotation vector produces striking changes in the convective motions. It elongates the convection cells in a north–south direction. It also tends to turn upward motions to the west and downward motions to the east in a manner that produces a large-scale circulation. This circulation is directed to the west and towards the poles in the upper half of the layer and to the east and towards the equator in the bottom half. Since the layer is warmer on the bottom this circulation also carries an equatorward flux of heat. When the rotation vector is tilted from the vertical, angular momentum is always transported downwards and toward the equator. For rapidly rotating layers, the pressure field changes in a manner that tends to balance the Coriolis force on vertical motions. This results in an increase in the vertical heat flux as the rotation rate increases through a limited range of rotation rates.
Vortex shedding from a rectangular prism and a circular cylinder placed vertically in a turbulent boundary layer
Authors: Sakamoto Hiroshi , Arie Mikio
Published: April 2006

Measurements of the vortex-shedding frequency behind a vertical rectangular prism and a vertical circular cylinder attached to a plane wall are correlated with the characteristics of the smooth-wall turbulent boundary layer in which they are immersed. Experimental data were collected to investigate the effects of (i) the aspect ratio of these bodies and (ii) the boundary-layer characteristics on the vortex-shedding frequency. The Strouhal number for the rectangular prism and the circular cylinder, defined by S = fcw/U0 and fcd/U0 respectively, was found to be expressed by a power function of the aspect ratio h/w (or h/d). Here fc is the vortex-shedding frequency, U0 is the free-stream velocity, h is the height, w is the width and d is the diameter. As the aspect ratio is reduced, the type of vortex shedding behind each of the two bodies was found to change from the Karman-type vortex to the arch-type vortex at the aspect ratio of 2·0 for the rectangular prism and 2·5 for the circular cylinder.
Isothermal models of gas-turbine combustors
Authors: Green A. S. , Whitelaw J. H.
Published: April 2006

Measurements of mean axial velocity have been obtained in two perspex models which simulate important features of gas-turbine combustors and are compared with calculations based on the numerical solution of the three-dimensional equations that represent conservation of mass and momentum. The measurements show, for example, the effect of primary jet trajectory on the magnitude and proportion of total mass flow contained in the primary vortex. They also allow the value of the calculation method to be appraised and, in this context, it is shown that the local velocity values are subject to large errors in small regions of the flow but important parameters, such as the length of the primary vortex, are represented more than adequately for engineering purposes. Errors due to numerical approximations appear to be at least as important as those due to the two-equation turbulence model used to represent turbulent features of the flow.
General stability conditions for zonal flows in a one-layer model on the β-plane or the sphere
Authors: Ripa P.
Published: April 2006

Sufficient stability conditions are derived for a zonal flow on the β-plane or the sphere. Two conditions guarantee both shear stability (to perturbations with vanishing zonal average) and inertial stability (to longitude-independent perturbations). These conditions are not restricted to normal-mode disturbances, and are derived without making use of the quasi-geostrophic approximation. The main limitation of the model is to have only one layer.

On the β-plane, the conditions are: (i) that the product of the meridional gradient of potential vorticity and the difference between an arbitrary constant and the zonal velocity be everywhere non-negative; and (ii) that the absolute value of this difference be nowhere larger than the local phase speed of long gravity waves. Inertial stability is independently assured if the Cariolis parameter and the potential vorticity are everywhere of the same sign (this well-known condition can be easily violated near the equator, but the flow may nonetheless be stable).

If the meridional gradient of potential vorticity has everywhere the same sign, then conditions (i) and (ii) can be shown to be consequences of the conservation of a total pseudo-energy E0 and pseudomomentum P0, defined so that their lowest-order contribution is quadratic in the deviation from the fundamental state (even in the case that the perturbation is longitude-independent). Thus, if there exists a value of α such that the integral of E0 − αP0 is positive-definite, then the flow is stable. In this case, the stability conditions are valid for small, rather than infinitesimal, perturbations.

The parameters of stable flows, as guaranteed by these conditions, are investigated for the family of Gaussian jets centred at the equator; both the cases of an unbounded ocean and a semi-infinite ocean, poleward from a zonal wall, are considered. Easterlies with the width of a Kelvin wave and westerlies with that width or wider may be unstable, even though the gradient of potential vorticity is positive for any strength of the jet.
A technique for the direct measurement of volume flux of a plume
Authors: Baines W. Douglas
Published: April 2006

It is observed that an interface is established in any open-ended vertical cylinder when a plume flows in the direction of a mean flow through the cylinder. The location of the interface defines the volume flux of the plume because the total discharge in the environment has been entrained at this level. Experiments have been conducted to verify this relation and to define the limits within which the interface is established. It is found that, as the buoyancy in the plume is reduced or the area of the environment is reduced, limits do exist. An application of the interface in industrial-building ventilation is described.
Tests of subgrid models in the near-wall region using represented velocity fields
Authors: Kaneda Y. , Leslie D. C.
Published: April 2006

The 2.5-dimensional model of the turbulent field near a wall, proposed by Hatziavramidis & Hanratty (1979) and modified by Chapman & Kuhn (1981), has been used to test the subgrid models of Schumann (1973, 1975) and Moin & Kim (1982). The results are disquieting, both trends and orders of magnitude sometimes being seriously in error. It also appears that the contribution of the subgrid energy to the pseudopressure calculated in large-eddy simulations can be large, although this contribution is usually neglected. On the positive side, Leonard's model for the Leonard stress is extremely good, and Schumann's synthetic boundary condition is also found to be reliable.

These results must be taken with a grain of salt, since the tests reported in §5 show that the 2.5-dimensional model cannot reproduce important characteristics of the turbulence in the neighbourhood of y+ = 40.
Fully developed periodic turbulent pipe flow. Part 2. The detailed structure of the flow
Authors: Ramaprian B. R. , Tu S. W.
Published: April 2006

The main experimental results of the study of periodic turbulent pipe flow have been described in Part 1 of this report. In this second part, these experimental data are examined in greater detail to understand the effect of imposed oscillation on the flow structure, at moderate to large oscillation frequencies. Data on phase and amplitude and energy spectrum are used to study the effect of the imposed oscillation on the turbulence structure at these interactive frequencies of oscillation. Additional experiments which were performed to study the effect of oscillation frequency on the flow structure are also reported. Based on the present observations as well as on the data from other sources, it is inferred that turbulent shear flows respond very differently from laminar shear flows to imposed unsteadiness. A turbulent Stokes number relevant for characterizing the unsteady turbulent shear flows is identified and used to classify such flows.
The control of boundary-layer transition using a wave-superposition principle
Authors: Thomas Andrew S. W.
Published: April 2006

An experimental study has been made of the concept of controlling boundary-layer transition by superimposing in the flow Tollmien–Schlichting waves that are of equal amplitude and antiphased to the disturbances that grow and lead to transition. The cases that have been considered are transition arising from a single-frequency two-dimensional disturbance and transition arising from a nonlinear interaction between two waves of different frequency. A feedback system for controlling transition has also been studied. In each case, both hot-wire surveys and flow visualization have shown that it is possible to delay transition but that the flow cannot be restored completely to its undisturbed state. This appears to be a consequence of interactions between the very weak three-dimensional background disturbances in the flow and the primary two-dimensional waves. The implications of these findings in an implementation of the concept are discussed.
Nonlinear adjustment of a thin annular film of viscous fluid surrounding a thread of another within a circular cylindrical pipe
Authors: Hammond P. S.
Published: April 2006

A nonlinear analysis, based on lubrication theory, is presented for the adjustment under surface tension of an initially uniform annular film of viscous fluid confined within a circular cylindrical pipe. The film surrounds a thread of another viscous fluid. Small axisymmetric interfacial disturbances of sufficiently long wavelength are found to grow, leading to the break-up of the initially continuous outer film into a number of isolated rings of fixed length on the pipe wall. The implications for the rupture of fluid threads surrounded by moderately thin films in confined geometries are discussed.
The structure of the large eddies in fully developed turbulent shear flows. Part 2. The plane wake
Authors: Mumford J. C.
Published: April 2006

A set of measurements using arrays of hot-wire anemometers has been performed in the fully developed turbulent wake of a circular cylinder. The data were digitized, recorded on magnetic tape, and processed using the pattern recognition technique described in Part 1 (Mumford 1982), to yield ensemble averages of the streamwise component of the velocity fields of the large eddies in the flow.

The results indicate that the large-scale structures in the turbulent wake are predominantly the inclined ‘double-roller’ vortices described by Grant (1958). These eddies consist of two contrarotating roller-like vortices with parallel axes displaced in the spanwise direction and approximately aligned with the direction of the strain associated with the mean velocity gradient. It was found that the structures are often confined to either side of the wake centreplane, rather than extending over the entire thickness of the turbulent region. In addition, eddies of similar type tended to occur in pairs or longer groups with their centres separated in the stream direction.
Scalar diffusion in simulated helical turbulence with molecular diffusivity
Authors: Drummond I. T. , Duane S. , Horgan R. R.
Published: April 2006

We extend the simulation techniques of Kraichnan (1970, 1976) to study the effective diffusivity of a scalar field in a turbulent fluid. In our model we have introduced an adjustable helicity parameter and a technique for simulating molecular diffusivity. The results show that for non-helical turbulence the self-consistent perturbation theory of Phythian & Curtis (1978) gives excellent values for the effective diffusivity over a wide range of values for both the molecular diffusivity and the parameters describing the turbulence.

This ceases to be the case immediately the helicity is given a non-zero value. Wide departures are observed between the theoretical calculation and the simulation. Our conclusion is that non-perturbative effects are very important in the presence of helicity.
Experimental investigation of jets in a crossflow
Authors: Andreopoulos J. , Rodi W.
Published: April 2006

The paper reports on measurements in the flow generated by a jet issuing from a circular outlet in a wall into a cross-stream along this wall. For the jet-to-crossflow velocity ratios R of 0.5, 1 and 2, the mean and fluctuating velocity components were measured with a three-sensor hot-wire probe. The hot-wire signals were evaluated to yield the three mean-velocity components, the turbulent kinetic energy, the three turbulent shear stresses and, in the case of R = 0.5, the terms in the turbulent-kinetic-energy equation. The results give a quantitative picture of the complex three-dimensional mean flow and turbulence field, and the various phenomena as well as their dependence on the velocity ratio R are discussed in detail.
Long waves induced by short-wave groups over an uneven bottom
Authors: Mei Chiang C. , Benmoussa Chakib
Published: April 2006

Unidirectional and periodically modulated short waves on a horizontal or very nearly horizontal bottom are known to be accompanied by long waves which propagate together with the envelope of the short waves at their group velocity. However, for variable depth with a horizontal lengthscale which is not too great compared with the group length, long waves of another kind are further induced. If the variation of depth is only one-dimensional and localized in a finite region, then the additional long waves can radiate away from this region, in directions which differ from those of the short waves and their envelopes. There are also critical depths which define caustics for these new long waves but not for the short waves. Thus, while obliquely incident short waves can pass over a topography, these second-order long waves may be trapped on a ridge or away from a canyon.