bluuebunny/crossref_metadata_2025 huggingface dataset:
Radiation from vortex filament motion near a half plane
Authors: Crighton D. G.
Published: March 2006

The two-dimensional low Mach number sound field from the passage of a line vortex around the edge of a rigid half plane is calculated by singular perturbation methods. Simple exact expressions are given for the space-time variation of the acoustic field, and for the total radiated energy and its frequency spectrum. These expressions show in particular that the effect of the half plane is to increase the energy radiated by a nearby vortical flow by M−3, where M is a characteristic Mach number.
The stability of plane Poiseuille flow between flexible walls
Authors: Green C. H. , Ellen C. H.
Published: March 2006

This paper examines the linear stability of antisymmetric disturbances in incompressible plane Poiseuille flow between identical flexible walls which undergo transverse displacements. Using a variational approach, an approximate solution of the problem is formulated in a form suitable for computational evaluation of the (complex) wave speeds of the system. A feature of this formulation is that the varying boundary conditions (and the Orr-Sommerfeld equation) are satisfied only in the mean; this reduces the labour involved in determining the approximate solution for a variety of wall conditions without increasing the difficulty of obtaining solutions to a given accuracy. In this paper the symmetric stream function distribution across the channel is represented by a series of cosines whose coefficients are determined by the variational solution. Comparisons with previous work, both for the flexible-wall and rigid-wall problems, show that the method gives results as accurate as those obtained previously by other methods while new results, for flexible walls, indicate the presence of a higher wave-number stability boundary which joins the distorted Tollmien-Schlichting stability boundary at lower wave-numbers. In some cases this upper unstable region, which is characterized by large amplification rates, may determine the critical Reynolds number of the system.
Solitary waves in concentrated vortices
Authors: Leibovich S. , Randall J. D.
Published: March 2006

A nonlinear integro-differential equation governing finite amplitude wave propagation on concentrated vortices is solved numerically. The solution to the Cauchy problem shows a solitary wave development qualitatively similar to solutions of the Korteweg–de Vries equation. A perturbation solution of the stationary form of the evolution equation confirms the unsteady calculation.
Convection in a rotating laterally-heated annulus
Authors: Koschmieder E. L.
Published: March 2006

The convective motions in a rotating laterally-heated annulus have been studied experimentally. The main feature that differentiates this experiment from others done previously is a rigid lid which is in contact with the fluid. It has been found that the radial temperature differences at which the transition from lower symmetry to the vortex regime occur are different in the cases of positive and negative temperature gradients and that, in particular, the transition is a very strong function of Ω in the case of a negative temperature gradient. It has been observed further that the persisting vortices which form in the annulus always appear at the inner cylinder, whether the radial temperature difference is increased in a quasi-steady way, the radial temperature difference is applied suddenly while the mean temperature is maintained, the heating or cooling is applied suddenly on either the inner or outer cylinder only, thus changing the mean temperature, or whether the rotation of the annulus is started suddenly with the radial temperature difference applied beforehand. This is true regardless of whether the radial temperature gradient is positive or negative and there has not been a single instance in which a persisting vortex developed at the outer cylinder. Neither this observation nor the dependence of the transition temperature difference on Ω seems to be in agreement with the current theoretical descriptions of the annulus motions. On the other hand, the appearance of a warm cell, a counter cell and a cold cell in the time-dependent meridional motions observed in the experiments confirms the results of a numerical study of Williams (1967), which studies the symmetric motions in the annulus.
Velocity measurements made with a laser dopplermeter on the turbulent pipe flow of a dilute polymer solution
Authors: Rudd M. J.
Published: March 2006

This paper presents some new measurements which have been made on a drag-reducing polymer solution in pipe flow. A novel type of laser dopplermeter, which has been developed by the author, is briefly described and the measurements which have been obtained are given. These results and their implications are then discussed in terms of conventional models for turbulent flow in a pipe. These suggest that the polymer has very little effect upon the turbulent core of the flow, but thickens and stabilizes the viscous sublayer. The turbulent intensity inside the sublayer is unchanged but, owing to its thickening, the velocity fluctuations just outside are greater. There is not a general suppression of turbulence within the sublayer although well inside the sublayer the spanwise velocity component is found to be reduced.
A nonlinear instability burst in plane parallel flow
Authors: Hocking L. M. , Stewartson K. , Stuart J. T. , Brown S. N.
Published: March 2006

An infinitesimal centre disturbance is imposed on a fully Ldveloped plane Poiseuille flow at a Reynolds numberRslightly greater than the critical valueRcfor instability. After a long time,t, the disturbance consists of a modulated wave whose amplitudeAis a slowly varying function of position and time. In an earlier paper (Stewartson & Stuart 1971) the parabolic differential equation satisfied byAfor two-dimensional disturbances was found; the theory is here extended to three dimensions. Although the coefficients of the equation are coinples, a start is made on elucidating the properties of its solutions by assuming that these coefficients are real. It is then found numerically and confirmed analytically that, for a finite value of (R-Rc)t, the amplitudeAdevelops an infinite peak at the wave centre. The possible relevance of this work to the phenomenon of transition is discussed.
Note on the stability of a boundary layer on a concave wall with suction
Authors: Kobayashi Ryoji
Published: March 2006

The purpose of this paper is to consider theoretically how the homogeneous suction from a slightly concave permeable wall will affect the instability of the laminar boundary layer to the onset of longitudinal vortices. The curves of neutral stability and of several growth factors of the vortices are given. The critical values of the Görtler parameter Gc, and the wavenumber σc, based on the momentum thickness of the boundary layer, are found: Gc = 1·17 and σc = 0·22.
Finite amplitude instability of second-order fluids in plane Poiseuille flow
Authors: McIntire Larry V. , Lin C. H.
Published: March 2006

The hydrodynamic stability of plane Poiseuille flow of second—order fluids to finite amplitude disturbances is examined using the method of Stuart, and Watson as extended by Reynolds & Potter. For slightly non-Newtonian fluids subcritical instabilities are predicted. No supercritical equilibrium states are expected if the entire spectrum of disturbance wavelengths is present. Possible implications with respect to the Toms phenomenon are discussed.
On prediction of the turbulent flow over a wavy boundary
Authors: Davis Russ E.
Published: March 2006

The importance of fluctuating turbulent stresses in the flow over a wave is examined. It is shown that anisotropic stresses, which are most likely to be turbulent Reynolds stresses, are essential to the process of energy flow to the wave. Two fundamentally different methods of predicting fluctuating turbulent Reynolds stresses are examined. One method makes use of a phenomenological closure of the conservation equation for the turbulent Reynolds stresses and is similar to the turbulent boundary-layer calculation scheme of Bradshaw, Ferriss & Atwell (1967). The second method is based on the assumption that the turbulent stresses are determined by the recent history of velocity shear experienced by a fluid parcel and results in a viscoelastic constitutive relation for the turbulence; in the limit of shortest’ memory’ this relation becomes the eddy viscosity model proposed by Hussain & Reynolds (1970). Comparison of predicted and measured values of surface pressure indicates that the eddy viscoelasticity model can explain measured pressure distributions but the comparison is not conclusive. Suggestions for further measurements are made.
Flow separation at the upstream edge of a square-edged broad-crested weir
Authors: Moss W. D.
Published: March 2006

A simple model is suggested to explain the flow mechanism at the upstream edge of a square-edged broad-crested weir. The separation bubble that may be seen to occur at this point is treated as an area of constant static head, while the main flow outside the bubble is deemed to be irrotational and divided from the bubble by a free streamline. If this model is accepted, the flow pattern will be such that energy requirements will be met along the free surface and the streamline bounding the bubble while, within these boundaries, the Laplace equation will be satisfied at every point. Accordingly, a solution satisfying these conditions is established by the use of a relaxation technique.

In practice, it is likely that the cavity flow within the bubble will be bounded not by a single streamline but by a turbulent mixing zone and that there will be some increase in pressure near the point of re-attachment. Nevertheless, the surface profile and flow pattern observed in experiments show fair agreement with those predicted using the simple model. Whilst acknowledging, then, that the bubble and the zone bounding it are in fact of a more complex character, we may say that this simplified treatment affords a sound model of the main flow and so permits a better understanding of the action of the square-edged broad-crested weir.
Variational properties of steady fall in Stokes flow
Authors: Weinberger H. F.
Published: March 2006

It is shown that for a given body and a given orientationgthere is always a position of the centre of mass which produces a stable falling motion in a very viscous fluid withgvertical and, in general, with a spin about the vertical axis. The corresponding terminal settling speed is bounded by means of several variational principles.

Relations between the terminal speeds for falls with different downward directions and between the terminal speed and the geometry of the body are deduced. In particular, it is proved that for a large class of slender bodies the first approximation to the drag obtained from the slender-body theory of Burgers (1938) is correct. It follows that the ratio of the terminal speeds for falls with the long axis vertical and horizontal is near two.
Boundary-layer velocity profiles in a swirling convergent flow field
Authors: Houlihan T. M. , Hornstra D. J.
Published: March 2006

Velocity distributions within the boundary layer of a swirling flow of incompressible fluid in a convergent conical nozzle have been investigated. Theoretical calculations with boundary conditions more appropriate to physically existent situations discounted the existence of 'super-velocities’ within the boundary layer. Parallel experimental investigations demonstrated an interdependence of core and boundary-layer flows which precluded the maintenance of the flow conditions required by the analysis.
An instability of internal gravity waves
Authors: Smith Ronald
Published: March 2006

When water is slightly stratified, internal gravity waves are considerably shorter than surface waves of comparable frequency. Here, this fact is exploited in demonstrating that an internal wave is unstable when it forms part of a resonant triad with a surface wave and another internal wave whose wave number is approximately equal to that of the original internal wave. It is suggested that in a system where there are two classes of waves of comparable frequencies but greatly differing wavelengths the short waves may be expected to generate long waves by this mechanism.
Experimental investigations of the stability of channel flows. Part 2. Two-layered co-current flow in a rectangular channel
Authors: Kao Timothy W. , Park Cheol
Published: March 2006

The stability of the laminar co-current flow of two fluids, oil and water, in a rectangular channel was investigated experimentally, with and without artificial excitation. For the ratio of viscosity explored, only the disturbances in water grew in the beginning stages of transition to turbulence. The critical water Reynolds number, based upon the hydraulic diameter of the channel and the superficial velocity defined by the ratio of flow rate of water to total cross-sectional area of the channel, was found to be 2300. The behaviour of damped and growing shear waves in water was examined in detail using artificial excitation and briefly compared with that observed in Part 1. Mean flow profiles, the amplitude distribution of disturbances in water, the amplification rate, wave speed and wavenumbers were obtained. A neutral stability boundary in the wave-number, water Reynolds number plane was also obtained experimentally.

It was found that in natural transition the interfacial mode was not excited. The first appearance of interfacial waves was actually a manifestation of the shear waves in water. The role of the interface in the transition range from laminar to turbulent flow in water was to introduce and enhance spanwise oscillation in the water phase and to hasten the process of breakdown for growing disturbances.
Dynamic calibration of inclined and crossed hot wires
Authors: Morrison G. L. , Perry A. E. , Samuel A. E.
Published: March 2006

Single inclined hot wires and X-wires are calibrated directly for absolute turbulence intensity measurements by oscillating the wire probe sinusoidally with accurately known motion in a steady stream. The usual static method of calibration shows serious discrepancies and uncertainties when compared with this new procedure. The new method also provides a check on the small perturbation linearity of inclined wires.
Physiological fluid dynamics: a survey?
Authors: Lighthill M. J.
Published: March 2006

Section 1 is in the nature of a general survey of fluid flows within the human body : including the lungs (airflow in the airways and the special characteristics of the pulmonary blood circulation), the general systemic circulation of the blood, and the urinary tract. Problems of the microcirculation, including blood flow in the narrower capillaries, gas exchange with the terminal airways (alveoli), and exchange of gas and nutrients with peripheral tissue, are treated in the more specialized second section, which describes in some detail modern views concerning peripheral resistance.
An experiment on the stability of small disturbances in a stratified free shear layer
Authors: Scotti R. S. , Corcos G. M.
Published: March 2006

A statically stable stratified free shear layer was formed within the test section of a wind tunnel by merging two uniform streams of air after uniformly heating the top stream. The two streams were accelerated side by side in a contraction section. The resulting sheared thermocline thickened gradually as a result of molecular diffusion and was characterized by nearly self-similar temperature (odd), velocity (odd) and Richardson number (even) profiles. The minimum Richardson numberJ0could be adjusted over the range 0·07 ≥J0≥ 0·76; the Reynolds number Re varied between 30 and 70. Small periodic disturbances were introduced upstream of the test section by a fine wire oscillating in the thermocline. The wire generated a narrow horizontal beam of internal waves, which propagated downstream and remained confined within the thermocline. The growth or decay of these waves was observed in the test section. The results confirm the existence of a critical Richardson number the value of which is in plausible agreement with theoretical predictions (J0≅ 0·22 for the Reynolds number of the experiment). The growth rate is a function of the wavenumber and is somewhat different from that computed for the same Reynolds and Richardson numbers, but the calculation assumed velocity and density profiles which were also somewhat different.
On the hydromagnetic stability of a rotating fluid annulus
Authors: Acheson D. J.
Published: March 2006

A non-dissipative fluid rotates uniformly in the annular region between two infinitely long cylinders and is permeated by a magnetic field varying with distance from the axis of rotation. The hydromagnetic stability of this system is examined theoretically. When the magnetic field is azimuthal the system can always be rendered stable to axisymmetric disturbances by sufficiently rapid rotation (Michael 1954). Unless the magnetic field everywhere decreases with radius, however, the system may be unstable to non-axisymmetric disturbances even when the rotation speed exceeds a typical Alfvén speed by many orders of magnitude. ‘Slow’ hydromagnetic waves, akin to those invoked in a recent theory of the geomagnetic secular variation (Hide 1966), may then be generated by the spatial variations of the magnetic field. All unstable waves so generated propagate against the basic rotation, i.e. ‘westward’, when the field is azimuthal, and this property is in fact remarkably insensitive to variations in both magnitude and direction of the imposed field.
Some effects of intense turbulence on the aerodynamics of a circular cylinder at subcritical Reynolds number
Authors: Surry David
Published: March 2006

The effect, of high intensity large-scale free-stream turbulence on the flow past a rigid circular cylinder has been studied experimentally a t subcritical Reynolds numbers. Grids were used to produce homogeneous turbulence fields with longitudinal scales ranging from 0·36 to 4·40 cylinder diameters and with longitudinal intensities greater than 10%. Power and cross-spectra of the turbulence components (the ‘system input’) have been measured in order to carefully define the turbulence characteristics.

In the response experiments, a special model measured arbitrary two-point pressure correlations. Subsequent integrations yielded the specbral properties of the unsteady lift and drag. Measurements of mean drag and Strouhal frequency indicate that to some extent even severe large-scale turbulence can be considered to be qualitatively equivalent to an increase in the effective Reynolds number. Vortex shedding is not seriously disrupted by severe turbulence, but is affected more by low than by high frequencies. The unsteady lift response is still dominated by the vortex shedding, whereas the unsteady drag becomes primarily a response to turbulence. The cross-spectra of the drag forces for the one turbulence case examined overlay well when plotted against lateral separation divided by wavelength. This has enabled a ‘describing function’ for the drag response to turbulence to be derived. This describing function is the central element needed for the calculation of the structural response of such cylinders in the drag direction.
On the breakup of accelerating liquid drops
Authors: Harper E. Y. , Grube G. W. , Chang I-Dee
Published: March 2006

An accelerating liquid drop, under the action of surface tension, is shown to be unstable to small disturbances above a first critical value of the Bond number. Both numerical and second-order asymptotic methods are employed in order to characterize the normal-mode response and the neutral-stable modes at larger values of the Bond number. The transient response of an initially spherical drop that is accelerated by the flow of an external gas is studied as an initial-value problem. A unified theory, that includes acceleration as well as aerodynamic effects, is presented in order to account for the complete dynamic range of Weber and Bond numbers. The results are compared with experimental observations that range from continuous vibration to irreversible aerodynamic distortion and unstable shattering.
A note on the laminar mixing of two uniform parallel semi-infinite streams
Authors: Klemp J. B. , Acrivos Andreas
Published: March 2006

According to classical boundary-layer theory, when two uniform parallel streams are brought into contact at large Reynolds number (R) the location of the dividing streamline remains indeterminate to O(R−½) if both streams are subsonic and semi-infinite in extent. It is demonstrated here that this indeterminacy is a fundamental property of such a system which cannot be resolved, as Ting (1959) proposed, by balancing the pressure across the viscous mixing region to higher order in R.
The vortex street in the wake of a vibrating cylinder
Authors: Griffin Owen M. , Votaw Charles W.
Published: March 2006

The von Kármán vortex streets formed in the wakes of vibrating smooth cylinders and cables were studied using a hot-wire anemometer and flow visualization by fog injection in a wind tunnel. All the experiments took place in the flow regime where the vibration and vortex-shedding frequencies lock together, or synchronize, to control the formation of the wake. Since the flow in the vortex formation region is fundamental to further understanding of the interaction between a vibrating bluff obstacle and its wake, detailed measurements were made of the formation-region flow for Reynolds numbers between 120 and 350. The formationregion length is shown to be a fundamental parameter for the wake, and is dependent on a shedding parameterSt* related to the natureally occurring Strouhal number for the von Kármán street. The effects of vibration amplitude and frequency on the mean and fluctuating velocity fields in the wake become apparent when the downstream displacement is scaled with the formation length. The von Kármán vortex street behind a vibrating cylinder is divided into three predominant flow regimes: the formation, stable and unstable regions. Fundamental differences exist in the vortex streets generated behind stationary and vibrating cylinders, but many classical characteristics, including the manner of vortex breakdown in the unstable region, are shared by the two systems.
Steady two-dimensional viscous flow in a jet
Authors: Capell K.
Published: March 2006

An idealized two-dimensional flow due to a point source ofxmomentum is discussed. In the far field the flow is modelled by a jet region of large vorticity outside which the flow is potential. After use of the transformation\[ \zeta^3 = (\xi + i\eta)^3 = x + iy, \]the equations suggest naively obvious asymptotic expansions for the stream function in these two regions, namely\[ \sum_{n=0}^{\infty}\xi^{1-n}f_n(\eta)\quad {\rm and}\quad\sum_{n=0}^{\infty}\xi^{1-n}F_n(\eta/\xi) \]respectively. Consistency in matching these expansions is achieved by including logarithmic terms associated with the occurrence of eigensolutions.Fnis easy to find andJncan be found in closed form so the inner and outer eigensolutions may be fully determined along with the complete structure of the expansions.
Structure of the Reynolds stress near the wall
Authors: Willmarth W. W. , Lu S. S.
Published: March 2006

Experimental studies of the flow field near the wall in a turbulent boundary layer using hot-wire probes are reported. Measurements of the productuvare studied using the technique of conditional sampling with a large digital computer to single out special events (bursting) when large contributions to turbulent energy and Reynolds stress occur. The criterion used to determine when the productuvis sampled is that the streamwise velocity at the edge of the sublayer should have attained a certain value. With this simple criterion we find that 60% of the contribution to$\overline{uv}$is produced when the sublayer velocity is lower than the mean. This result is true at both low,Rθ= 4230, and high,Rθ= 38 000, Reynolds numbers. With a more strict sampling criterion, that the filtered sublayer velocity at two side-by-side points should be simultaneously low and decreasing, individual contributions to$\overline{uv}$as large as 62$\overline{uv}$have been identified. Additional measurements using correlations between truncateduandvsignals reveal that the largest contributions to the Reynolds stress and turbulent energy occur whenu< 0,v> 0 during an intense bursting process and the remainder of the contributions occur during a less intense recovery process. Thus, contributions to the turbulent energy production and Reynolds stress at a point near the wall are of relatively large magnitude, short duration and occur intermittently. A rough measure of the intermittency factor foruvat a point near the wall is 0·55 since 99% of the contribution to$\overline{uv}$is made during only 55% of the total time.
The equilibrium configuration of a slowly rotating mass of liquid in the presence of a poloidal magnetic field
Authors: Sozou C.
Published: March 2006

The equilibrium configuration of a slowly rotating self-gravitating perfectly conducting inviscid liquid, in the presence of a small poloidal magnetic field, is considered for a case where the electric current is a simple function of the distance from the axis of rotation. Owing to the coupling of the magnetic field with the rotation the electric current may reverse direction. This could make the magnetic field zero on certain surfaces and impose restrictions on the parameters of the problem. A perturbation expansion of the nearly spherical surface of the liquid is constructed.
Kelvin waves on oceanic boundaries
Authors: Miles John W.
Published: March 2006

The primitive Kelvin wave (on a rotating, semi-infinite, plane sheet of water of uniform depth bounded by a vertical wall) is corrected for the effects of the Earth's curvature, the reduction in depth over the continental shelf, and bends in the coastline. The results are of interest for coastal propagation of the tides; numerical examples are given for the California coastline. It is found that the Earth's curvature reduces the wave speed south of Cape Mendocmo by 8–10% (the possible range for other coastlines is roughly ± 15%) and that the continental shelf reduces the wave speed by 2−8%. The off-shore mass transport (which vanishes identically for the primitive Kelvin wave) induced by curvature and/or the shelf also is calculated. The analysis of Packham & Williams (1968) for diffraction of a Kelvin wave by a corner is extended to obtain explicit results for the phase of the transmission coefficient. It is found that a sustained change in the direction of the coastline may induce a phase shift of the order of an hour (1·3 hours for the bend at Cape Mendocino), but that small distortions of the coastline without a sustained change in direction have negligible effects on the transmitted Kelvin wave at tidal frequencies.
Waves generated in the configuration of a magnetically confined and field-permeated axisymmetric jet
Authors: Chee-Seng Lim
Published: March 2006

A cylindrical MGD configuration comprising an electrically conducting, infinitely extended (cylindrical) jet which is both permeated and contained by stream-aligned magnetic fields is considered. Axisymmetric perturbations are then generated by exposure to a stationary, weak, azimuthal current source. Ignoring relativistic and dissipative effects, asymptotic solutions complying with a radiation condition are established for the steady state. Generally speaking, the disturbed system propagates a discrete superposition of wave functions, each of which is uniquely obtained for either the upstream or downstream region. In the non-trivial cases, there is no axial wave attenuation. However, transverse attenuations are experienced within the fluid-free enveloping field. The various jet-flow regimes are thoroughly examined. It is found, in particular, that a single stationary wave is produced upstream wheneverM< 1,M2+A2[ges ] 2 and λβ < 1, while ifM> 1 andA> 1 an infinity of discrete stationary waves occurs downstream.MandAbeing, respectively, the Mach and Alfvén numbers of the jet; λβ is a parameter involvingM, AandA0(an interface Alfvén number).
Viscous interaction over concave and convex surfaces at hypersonic speeds
Authors: Mohammadian S.
Published: March 2006

The growth of hypersonic boundary layers over both concave and convex surfaces is described, the strong-viscous-interaction equation due to Cheng et al. (1961) for curved surfaces with sharp leading edges being solved asymptotically for small and large arguments. Both the asymptotic solution for large arguments and a numerical integration predict an oscillatory behaviour of the boundary-layer thickness on concave surfaces. A modification of Cheng's theory, as suggested by Sullivan (1968) and Stollery (1970), is also examined and compared with experimental data reported here. The experiments were conducted in air using a hypersonic gun tunnel under cold wall conditions at M∞ = 12·25. They included measurement of surface pressure, heat-transfer distributions and schlieren studies for concave and convex models.
Nonlinear baroclinic instability of a continuous zonal flow of viscous fluid
Authors: Drazin P. G.
Published: March 2006

Nonlinear instability of a zonal flow of slightly viscous Boussinesq fluid in a rapidly rotating frame is studied mathematically by the method of normal mode cascade, the flow being along a rectangular channel with horizontal and vertical rigid walls. Viscosity is represented approximately by supposing that its only effects occur in Ekman layers near the top and bottom walls of the channel, after the linear model of Barcilon. Self-interaction of one slightly unstable mode is found to lead to equilibration with supercritical instability. Also, interactions of two slightly unstable modes plausibly lead to equilibration. These results are related to the literature of experiments on differentially heated, rotating annuli.
Dissipation and breakdown of a wing-tip vortex
Authors: Mager A.
Published: March 2006

The solutions of the incompressible quasi-cylindrical momentum-integral equations describing the flow in the viscous core of a wing-tip vortex are obtained in a closed form and are shown to have two distinct branches. The discontinuities of these solutions have infinite axial gradients and therefore, following Hall, are assumed to signal the inception of the vortex breakdown. Benjamin's finite transition, with its excess flow force dissipated, is shown to give results equivalent to a sudden cross-over, upstream of the discontinuity, from one branch solution to another. The critical point of such a cross-over is downstream from the cross-over, at the discontinuity. Sarpkaya's experimental data, and the nature of the solutions ahead of the discontinuity, suggest that the physical manifestation of the discontinuity is the spiral breakdown, whereas the cross-over seems to be related to the rapidly expanding and subsequently contracting axisymmetric bubble. This therefore implies that the beginning of the spiral breakdown is the all important disturbance which triggers off not only the downstream asymmetric departure of the flow from its quasi-cylindrical form but also the formation of the upstream axisymmetric cross-over bubble. Solutions for the turbulent flow downstream from the spiral breakdown indicate that the wing-tip vortex breakdown can result in an appreciable reduction of the maximum circumferential velocity and should thus lessen the danger that trailing vortices present to following aircraft.
Water-drop response to sudden accelerations
Authors: Simpkins P. G. , Bales E. L.
Published: March 2006

The deformation of initially spherical drops of radius r0 subjected to an external flow of velocity u is experimentally examined for a large range of Weber and Bond numbers. Observations of the changes in the response are compared with recent analytical predictions. The data show that beyond a critical Weber number the response ceases to be vibratory and becomes monotonic with time. Subsequently, it is found that, although the response is unstable, the deformation imposed by the external aerodynamic pressure distribution remains the dominant factor. Measurements of the drag coefficient yield a mean value ofCD = 2·5 over a large Reynolds-number range. The time at which Taylor instability occurs is shown to be inversely proportional to Bond number to the one-quarter power. There is little evidence of the instability occurring until a normalized time $t^{*} = (\epsilon^{\frac{1}{2}}\bar{t}u/r_0)$ is approximately unity; here ε is the gas/liquid density ratio (ρ/ρ′) and $\bar{t}$ is the real time.
Wave motion of low-tension interfaces with electrical double layers
Authors: Miller C. A.
Published: March 2006

An approximate solution is developed for the system of equations describing flow and ion transport in a diffuse electrical double layer slightly perturbed from equilibrium. The approximation is valid only when the potential difference across the diffuse layer is small, less than about 25 mV. When the approximate solution is used to study wave motion of low-tension interfaces, it is found chat ion transport in diffuse layers slows down interfacial motion in both stable and unstable situations. Although the slowing effect is relatively small (a few per cent or less) when the small potential approximation applies, the form of the solution suggests that the effect could be significant for potential differences in the 50–100 mV range, which exist in many systems of interest. There are also indications that the slowing effect can significantly influence wave motion of thin liquid films with diffuse layers, e.g. soap films, although a detailed analysis of the thin-film situation is not carried out.
Statistical mechanics of the Burgers model of turbulence
Authors: Tatsumi Tomomasa , Kida Shigeo
Published: March 2006

The velocity field of the Burgers one-dimensional model of turbulence at extremely large Reynolds numbers is expressed as a train of random triangular shock waves. For describing this field statistically the distributions of the intensity and the interval of the shock fronts are defined. The equations governing the distributions are derived taking into account the laws of motion of the shock fronts, and the self-preserving solutions are obtained. The number of shock fronts is found to decrease with time t as t−α, where α (0 [les ] α < 1) is the rate of collision, and consequently the mean interval increases as tα. The distribution of the intensity is shown to be the exponential distribution. The distribution of the interval varies with α, but it is proved that the maximum entropy is attained by the exponential distribution which corresponds to α = ½. For α = ½, the turbulent energy is shown to decay with time as t−1, in good agreement with the numerical result of Crow & Canavan (1970).
A point explosion in an arbitrary atmosphere
Authors: Treve Y. M. , Manley O. P.
Published: March 2006

It is shown that the method developed by Laumbach & Probstein (1969) for an exponential atmosphere can be extended to the case of an arbitrary atmospheric density distribution. Results are given for various burst-point altitudes in a model atmosphere and compared with those corresponding to an exponential atmosphere.
The rheology of a suspension of nearly spherical particles subject to Brownian rotations
Authors: Leal L. G. , Hinch E. J.
Published: March 2006

A set of constitutive equations, valid for arbitrary linear bulk flows, is derived for a dilute suspension of nearly spherical, rigid particles which are subject to rotary Brownian couples. These constitutive equations are subsequently applied to find the resulting stress patterns for a variety of time-dependent bulk flow fields. The rheological responses are found to exhibit many of the same qualitative features as have been observed in recent experimental investigations of polymeric solutions and other complex materials.
Conditionally sampled measurements near the outer edge of a turbulent boundary layer
Authors: Antonia R. A.
Published: March 2006

The conditional sampling technique is used to measure ensemble averages of the longitudinal and normal velocity fluctuations u and v respectively and of the Reynolds shear stress fluctuations uv both within the turbulent and irrotational regions near the outer edge of a turbulent boundary layer. The measurements are made in both a smooth- and a rough-wall boundary layer under zero-pressure-gradient conditions. The smooth- and rough-wall results are qualitatively similar but the magnitude of the rough-wall averages is higher than that of the smooth- wall averages, corresponding with the higher value of wall shear stress on the rough surface. The maximum shear stress value encountered within a burst represents a significant proportion of the wall shear stress.

The statistical properties of the turbulence within the burst are close but not quite identical to the nearly Gaussian properties of the inner region of the boundary layer. During an attempt to distinguish between bursts of different ages or strengths at the time of measurement, it was found that bursts of relatively short duration travel at much the same longitudinal velocity as the local mean U and contribute little to the local shear stress. The longer and less frequent bursts have a mean velocity smaller than U and a maximum shear stress comparable to the shear stress at the wall.
The boundary layer in a shock tube
Authors: And J. D. A. Walker , Dennis S. C. R.
Published: March 2006

The boundary layer that forms on the walls of a shock tube, after the diaphragm which initially separates two gases at different pressures is burst, is investigated. Both the driver and driven gases are assumed to have the same thermal properties and the shock tube wall is maintained at constant temperature. Crocco variables are used and a method is presented for solving the compressible boundary-layer equations within the tube in similarity variables. Three cases, corresponding to different initial pressure ratios of the driver and driven gases, are calculated which are representative of weak and medium-strength shock and expansion waves.
On the unsteady expansion of a gas into a near vacuum
Authors: Grundy R. E.
Published: March 2006

This note intends to clarify the way in which the expansion of an initially uniform gas into an ambient atmosphere degenerates into an expansion into a perfect vacuum. The starting-point is a paper by Greenspan & Butler (1962) in which certain tentative remarks are made reprding this question. We show that the flow consists of an infinite-strength contact front coinciding with the gasvacuum interface of the perfect-vacuum expansion, driving an infinite-strength shock into the vacuum ahead of it. The ga,s-vacuum interface and the shock are separated a t all times even though the density of the gas through which the shock travels vanishes in the vacuum limit.
On the radiation and scattering of short surface waves. Part 1
Authors: Leppington F. G.
Published: March 2006

The radiation and scattering of time-periodic surface waves by partially immersed objects is investigated in the short-wave asymptotic limit ε → 0, where ε is a non-dimensional wavelength. Details are given for the prototype radiation and scattering problems in which the fluid has infinite depth and the body is a two-dimensional dock of finite width and zero thickness. The solutions are then generalized to deal with other two-dimensional geometries, with the restriction that the ends of the obstacle are horizontal for a distance of many wavelengths. The method of matched expansions is used. A first approximation ϕ0, presumed to be a good estimate for the potential throughout most of the fluid region, is obtained by replacing the free-surface condition by its formal limit ϕ0 = 0. In the vicinity of the ends of the obstacle, the correct surface condition is used but the geometry of the problem is simplified. The remaining surface layers are dealt with by superimposing on the function ϕ0 regular wave trains of the appropriate amplitude.
Three-dimensional MHD duct flows with strong transverse magnetic fields. Part 3. Variable-area rectangular ducts with insulating walls
Authors: Walker J. S. , Ludford G. S. S. , Hunt J. C. R.
Published: March 2006

The general analysis developed in Parts 1 and 2 of three-dimensional duct flows subject to a strong transverse magnetic field is used to examine the flow in diverging ducts of rectangular cross-section, the walls of which are electrically non-conducting. A dramatically different flow is found in this case from that studied in Part 2, where the side walls parallel to the magnetic field were highly conducting. Now it is found that the core velocity normalized with respect to the mean velocity is of O(M−½) while the velocity in the side-wall boundary layers is of O(M½), so that these boundary layers carry most of the flow. The problem of entry is solved by analysing the change from fully developed Hartmann flow in a rectangular duct to the flow in the diverging duct. It is found that the disturbance in the upstream duct decays exponentially. The analysis of the side-wall boundary layers is more difficult than that in Part 1 on account of the different boundary conditions and requires the solution of two coupled integro-differential equations. Numerical solutions are obtained for a duct whose width increases linearly in the flow direction.
Solution of the wedge entry problem by numerical conformal mapping
Authors: Hughes O. F.
Published: March 2006

An accurate quasi-analytic method of solution is presented for the classical hydrodynamics problem of the constant-velocity entry of a prismatic wedge into a weightless incompressible inviscid fluid. The method uses the Wagner function W, which reduces the problem to the determination of a mapping function Λ = [Lscr ](W) for the hodograph. [Lscr ](W) is constructed by using the hodograph for an unsymmetric diamond together with a modifying or ‘preparatory’ trans-formation. A computer method of conformal mapping is developed and is used to obtain this latter transformation. Results are presented for the case of a 90° wedge and show that the solution is both more accurate than previous solutions, having an error of less than 1 %, and more complete, as it portrays the entire flow field and furnishes information about the functional dependence among the variables.
Numerical solution of the Navier-Stokes equations for symmetric laminar incompressible flow past a parabola
Authors: Davis R. T.
Published: March 2006

Symmetric laminar incompressible flow past a parabolic cylinder is considered for all Reynolds numbers. In the limit as the Reynolds number based on nose radius of curvature goes to zero, the solution for flow past a semi-infinite flat plate is obtained. All solutions are found by using an implicit alternating direction method to solve the time-dependent Navier-Stokes equations. The solutions found are compared with various other exact and approximate solutions. Results are presented for skin friction, surface pressure, friction drag and pressure drag. The numerical method developed is of particular interest since it combines the alternating direction method with the implicit method for solving the boundary-layer equations. This leads to fast convergence and may be of use in other problems.
Quantitative schlieren measurements in a supersonic turbulent jet
Authors: Davis M. R.
Published: March 2006

This paper describes the results of a series of measurements made using a single beam schlieren system to investigate the density fluctuations present in the initial region of a supersonic axisymmetric turbulent jet with a Mach number of 1-82 in the flow a t the nozzle exit. A preheater was used to reduce the difference between the jet static temperature and that of the surrounding air to a relatively low level. The results show that significant density fluctuations are present in the potential core of the jet and that the distribution of fluctuating intensity across the shear layer differs from that obtained with a subsonic jet without preheating.
Long wave generation on a sloping beach
Authors: And E. O. Tuck , Hwang Li-San
Published: March 2006

A general solution of the linear long-wave equation is obtained for arbitrary ground motion on a uniformly sloping beach. Numerical results are presented for specific shapes and time histories of ground motion. Near-shore large amplitude waves are also investigated using non-linear theory.
Plasma motions in narrow capillary flow
Authors: Fitz-Gerald J. M.
Published: March 2006

Plasma motions in the gaps between successive red cells in narrow-capillary blood flow are obtained in an idealized model, using a series of eigenfunctions to represent the disturbance to a basic Poiseuille flow created by the cells. The flow is matched, in the narrow entry and exit regions, to the lubrication flow in the constricted zone around the red cell (Fitz-Gerald 1969). Basically, the circulating toroidal motion predicted by Prothero & Burton (1961) is obtained in a reference frame in which the cells are considered stationary. Small secondary circulations are also found near the axis and close to the red cells, whose intensity is controlled by the amount of leakback past the cells. Zones of high shear are found along the capillary wall and in some cases on part of the red-cell face; implications of this for mass transport are discussed (see §4). Because of the unusual behaviour of the slowest-decaying dominant eigenfunction circulation and wall shearincreaseas the cell spacing decreases, contrary to expectation, until the spacing becomes very small indeed.
A soliton on a vortex filament
Authors: Hasimoto Hidenori
Published: March 2006

The intrinsic equation governing the curvature K and the torsion τ of an isolated very thin vortex filament without stretching in an incompressible inviscid fluid is reduced to a non-linear Schrödinger equation
\[
\frac{{\rm l}}{i}\frac{\partial \psi}{\partial t} = \frac{\partial^2\psi}{\partial s^2}+{\textstyle\frac{1}{2}}(|\psi|^2+A)\psi,
\]
where t is the time, s the length measured along the filament, ψ is the complex variable
\[
\psi = \kappa\exp\left(i\int_0^{s}\tau \,ds\right)
\]
and is a function oft. It is found that this equation yields a solution describing the propagation of a loop or a hump of helical motion along a line vortex, with a constant velocity 2τ. The relation to the system of intrinsic equations derived by Betchov (1965) is discussed.
Some comments on heat-transfer laws for fine wires
Authors: Bradbury L. J. S. , Castro I. P.
Published: March 2006

The semi-empirical heat-transfer laws of Collis & Williams (1959) and Davies & Fisher (1964) give values of the heat-transfer rates for the flow past fine wires which are generally very different from one another. This paper describes some measurements of heat-transfer and convective time constants which show that the relationship of Collis & Williams is the more representative expression.
Fluid mechanics of the cochlea. Part 1
Authors: Lesser M. B. , Berkley D. A.
Published: March 2006

The physiology of the cochlea (part of the inner ear) is briefly examined in conjunction with a description of the ‘place’ theory of hearing. The role played fluid motions is seen to be of importance, and some attempts to bring fluid mechanics into a theory of hearing are reviewed. Following some general fluid-mechanical considerations a potential flow model of the cochlea is examined in some detail. A basic difference between this and previous investigations is that here we treat anenclosedtwo-dimensional cavity as opposed to one-dimensional and open two-dimensional models studied earlier. Also the two time-scale aspect of the problem, as a possible explanation for nonlinear effects in hearing, has not previously been considered. Thus observations on mechanical models indicate that potential flow models are applicable for times of the same scale as the frequency of the driving acoustic inputs. For larger time scales mechanical models show streaming motions which dominate the qualitative flow picture. The analytical study of these effects is left for a future paper.