bluuebunny/crossref_metadata_2025 huggingface dataset:
The effect of rotation on the simpler modes of motion of a liquid in an elliptic paraboloid
Authors: Ball F. K.
Published: March 2006

The six simplest modes of motion are considered and three rotational effects investigated:

The effect of the rotation of the earth.

The effect of the rotation of the container.

The effect of the rotation of the liquid within the container.

The first two are shown to be equivalent for motion in a paraboloid, and the last two are also equivalent when the paraboloid iscircular. In the case of an elliptic paraboloid the last is rather more difficult and one must first derive a solution of the non-linear equations representing ‘elliptic rotation’ and then consider deviations from it.

The changes in frequency consequent on the rotation are derived in all three cases for all six modes. In the case of the earth's rotation the disposition and character of the amphidromic (nodal) points and the amphidromic waves that rotate round these points are investigated in detail. One mode is particularly interesting because it has four amphidromic points, the waves rotate in a positive sense around two of these and in a negative sense round the other two.
On the stability of the asymptotic suction boundary-layer profile
Authors: Hughes T. H. , Reid W. H.
Published: March 2006

This paper presents a discussion of some aspects of the linear stability problem for the asymptotic suction profile. An exact solution of the inviscid equation is first obtained in terms of the usual hypergeometric function and its analytical continuation. This exact solution provides both a corrected version of an earlier treatment by Freeman and an independent check on the more general method suggested for solving the inviscid equation numerically. Various approximations to the characteristic equation, and hence to the curve of neutral stability, are then considered. In particular, it is found that, in a consistent asymptotic treatment of the related adjoint problem, at least one viscous correction to the singular inviscid solution must be considered. Based on the present results for the adjoint problem, it is suggested that Tollmien's original treatment of the viscous corrections must be slightly modified.
The stability of laminar boundary layers at separation
Authors: Hughes T. H. , Reid W. H.
Published: March 2006

The effect of an adverse pressure gradient on the stability of a laminar boundary layer is considered in the limiting case when the skin friction at the wall vanishes, i.e. when U′(0) = 0. Such flows are not absolutely unstable as might have been expected but have a minimum critical Reynolds number of the order of 25. General results are given for the asymptotic behaviour of both the upper and lower branches of the neutral curve and a complete neutral curve is obtained for Pohlhausen's simple fourth-degree polynomial profile at separation.
Weak waves in relaxing flows
Authors: Wegener Peter P. , Chu Boa-Teh , Klikoff W. A.
Published: March 2006

Theoretical and experimental investigations are described of the linearized wave equation of supersonic flow with a single relaxation process. Firing-range experiments using a known model gas mixture with a single relaxation process are discussed. Qualitatively, it is shown that weak conical and spherical waves decay as predicted by theory. In addition, this decay can be determined quantitatively for conical disturbances; and, satisfactory agreement with theory is found. For application to unknown relaxation processes, it is suggested that observation of the damping of weak waves provides an additional tool for the study of fast rate processes.
Report on the first European Mechanics Colloquium, on the Coanda effect
Authors: Wille R. , Fernholz H.
Published: March 2006

The first in a new series of European research conferences in mechanics was held in Berlin on 5 and 6 April 1965. The subject was the Coanda effect, or boundary layers and jets on highly curved walls. Participation was restricted to about 40 people, invited on the basis of their active interest in the subject. These Colloquia are intended to have an informal, workshop-like, character, and formal papers are not normally available, nor will any full proceedings be published. The first author was the chairman of the Colloquium. The following account of the scientific developments of the Colloquium has been prepared to make them widely available. The references quoted give further details of the work discussed at the Colloquium and of related previous work.
Hypersonic strong-interaction similarity solutions for flow past a flat plate
Authors: Bush William B.
Published: March 2006

The hypersonic strong-interaction regime for the flow of a viscous, heat-conducting compressible fluid past a flat plate is analysed using the Navier–Stokes equations as a basis. It is assumed that the fluid is a perfect gas having constant specific heats, a constant Prandtl number σ, whose numerical value is of order one, and a viscosity coefficient varying as a power, ω, of the absolute temperature. Limiting forms of solutions are studied as the free-stream Mach numberM, the free-stream Reynolds number based on the plate lengthRL, and the interaction parameterx= {(γM2)2+ω/RL}½, go to infinity.

Through the use of asymptotic expansions and matching, it is shown that, for (1−ω) > 0, three distinct layers for which similarity exists make up the region between the shock wave and the plate. The behaviour of the flow in these three layers is analysed.
Development of the boundary layer at a free surface from a uniform shear flow
Authors: Goren Simon L.
Published: March 2006

The development of the boundary layer accompanying the formation of a free surface at y′ = 0, from the two-dimensional uniform shear flow u′ = ωyω, is discussed. The analysis shows that the surface velocity and surface position vary as the cube root of the distance downstream, while the mass-transfer coefficient varies inversely as the cube root of this distance. It is shown how these may be applied to the formation of capillary jets.
An experiment on third-order resonant wave interactions
Authors: Longuet-Higgins M. S. , Smith N. D.
Published: March 2006

An experiment has been carried out to verify the existence of the resonant interaction between trains of gravity waves, predicted by Phillips (1960). As suggested by Longuet-Higgins (1962), two trains of waves in mutually perpendicular directions were generated in a rectangular wave tank. The ratio σ1/σ2of the wave frequencies was varied (1·4 < σ1/σ2< 2·1). When σ1/σ2[eDot ] 1·7357 it was expected that a resonant interaction would take place, generating a wave of frequency (2σ1−σ2). The amplitude of the third wave was expected to increase almost linearly in the direction of wave propagation. The shape of the response curve as a function of σ1/σ2was also predicted.

In the present experiments rather large wave amplitudes had to be used, and the theoretical shape of the response curve was distorted by non-linear detuning. Nevertheless the peak amplitude of the resonant wave was found to increase with distance in very nearly the manner predicted.

These experiments were carried out in 1961 but publication was deferred pending a similar but more accurate investigation by McGoldrick, Phillips, Huang & Hodgson (1966). Much of the theoretical discussion given in the present paper is relevant to their work.
On the theory of asymmetric shear flows past flat plates
Authors: Mark Richard M.
Published: March 2006

When a semi-infinite flat plate is immersed parallel to an unbounded, plane, steady, asymmetric, constant shear flow of an incompressible viscous fluid, an interaction occurs between the surface-generated vorticity and the external vorticity. A physical assumption was made in a previous paper (Mark 1962) concerning this problem that the pressure field in a thin layer adjacent to the top-side of the plate may be accurately approximated by the undisturbed constant-pressure field—that which exists before the insertion of the plate into the flow. This means that the vorticity interaction is assumed to have no effect on the undisturbed pressure field. That this is a valid first approximation far downstream along the plate where the interaction is intense is given rigorous support in this paper.

The flow below the plate is examined on a heuristic basis. It is found that there is a strong possibility for the flow to separate from the lower surface near the leading edge of the plate. However, far downstream the flow settles down to a Stokes-type flow near the plate.
Exploratory measurements in spiral turbulence
Authors: Atta Charles Van
Published: March 2006

The present experiments lay a foundation for a detailed study of interface propagation in a mixed laminar–turbulent flow between counter-rotating concentric cylinders. Such mixed flows, including one particularly well-organized pattern called spiral turbulence, are found to be a dominant feature of transition in Couette flow. In spiral turbulence, the laminar and turbulent regions of the flow form an alternating pattern of helical stripes, rotating with approximately the mean angular velocity of the two cylinders. Stable right-handed or left-handed spirals occur with equal probability when the flow is established from rest. Hot-wire measurements have been made of the mean cross-sectional shape of the interfaces in the axial mid-plane for a spiral-turbulent flow having low dispersion in the interface position. A nose of turbulence associated with the leading interface projects into the laminar region near the outer cylinder, while a corresponding tail is associated with the trailing interface near the inner cylinder. Fluctuations in interface position and in apparent length of the turbulent region are closely Gaussian, and the fluctuations are rapid compared with the period of rotation of either cylinder.
Steady three-dimensional vortex flow
Authors: Granger Robert
Published: March 2006

A theory is developed for an incompressible fluid in a steady three-dimensional rotational flow. Solutions are obtained subject to the restriction of small perturbations and are determinant provided that the vorticity distribution along the axis of rotation is known. Effects of viscosity are included. Closed-form expressions for the zeroth-order circulation and stream function and first-order circulation are given, with other higher-order expressions requiring high-speed computers. Experimental results of radial variation of axial velocity in the core show a distribution more elaborate than Gaussian.
On the entry problem for a compressible liquid
Authors: Pinsent H. G.
Published: March 2006

The problem considered is the entry of a thin symmetric wedge impinging normally on the free surface of a compressible inviscid liquid, gravitational effects being neglected. Since the body is thin, the problem is a linear one, and its solution is possible for the whole range of Mach numbers of the body's motion in the liquid. It is shown that the free-surface elevations are lowered considerably as the Mach number increases, and that the presence of the free surface acts so as to lower the pressure differences arising from compressibility.
Stability of the laminar mixing of two parallel streams with respect to supersonic disturbances
Authors: Lessen M. , Fox J. A. , Zien H. M.
Published: March 2006

The stability with respect to ‘supersonic’ disturbances of the laminar mixing of two parallel streams of a compressible fluid is studied. For locally supersonic disturbances there will be waves propagating outward from the mixing layer. The numerical results show that the flow is generally unstable with respect to supersonic disturbances, although the amplification rate is smaller than that for subsonic disturbances. The flow is more unstable at lower Mach number, and the increase of the angle between the disturbance wave-number vector and the principal flow direction tends to increase the instability.
The effect of longitudinal viscosity on the flow at a nozzle throat
Authors: Sichel M.
Published: March 2006

An inviscid transonic theory appears to be inadequate to describe the flow near the throat of a converging–diverging nozzle during the transition from the symmetrical Taylor (1930) type of flow to the subsonic–supersonic Meyer (1908) flow. A viscous transonic equation taking account of heat conduction and longitudinal viscosity has been developed previously (Cole 1949; Sichel 1963; Szaniawski 1963). An exact, nozzle-type of similarity solution of the viscous transonic equation, similar to the inviscid solution of Tomotika & Tamada (1950), has been found. This solution does provide a description of the gradual transition from the Taylor to the Meyer flow and shows the initial stages in the development of a shock wave downstream of the nozzle throat. The solution provides a viscous, shock-like transition from an inviscid, supersonic, accelerating flow to an inviscid, subsonic, decelerating flow.
The directional spectrum of ocean waves: an experimental investigation of certain predictions of the Miles–Phillips theory of wave generation
Authors: Gilchrist A. W. R.
Published: March 2006

The directional spectrum of wind-driven surface waves has been measured under conditions of limited fetch, in order to check the predictions of the Phillips–Miles theory of wave generation (Miles 1960). The expression obtained for the directional spectrum in this theory involves the spectrum of the atmospheric pressure fluctuations, but it is possible to obtain theoretical estimates of the major features of the directional spectrum without knowledge of the pressures. Specifically, it is possible to predict the frequency at which the power spectrum should peak, and, for the higher frequencies, the range of azimuth over which high spectral values should be observed; for the lower frequencies the theory indicates a bimodal distribution in azimuth (Phillips's resonance waves), and gives the angle of travel relative to the wind as a function of frequency.

The results of the measurements are in fairly good agreement with the theoretical predictions for the higher frequencies. The asymmetry of the fetch results in the prediction that the waves will travel at an angle to the wind which varies with frequency, and this was observed. The range of azimuth over which the spectral density is high is also close to the theoretical prediction. For the low frequencies the bimodal distribution was not observed: the waves were found to have a single predominant direction of travel at each frequency. However, this direction conformed closely to that of one of the two wave trains predicted by Phillips, and its variation with frequency was also that given by the theory. There is reason to suppose that the peculiarities of the experimental site may be responsible for the absence of the second wave train, especially as it would be difficult to account for the observed effects on any basis other than that of Phillips's theory.
Shock-tube studies of vibrational relaxation in nitrous oxide
Authors: Bhangu J. K.
Published: March 2006

Results of experimental investigations of vibrational relaxation regions of shock waves in nitrous oxide are reported in this paper. The Mach-number range covered was from 1·5 to 7·5 and the photographs of the shocks were made using a Mach-Zehnder interferometer and a spark source. The experimental and calculated values of the over-all density ratio were found to be in good agreement, and the values of the relaxation frequencies were consistent with the data of other workers.
Unsteady flow of a second-order fluid near a stagnation point
Authors: Srivastava A. C.
Published: March 2006

Two-dimensional flow of a second-order fluid near a stagnation point occurring on a flat plate which is performing harmonic oscillations in its own plane is considered. The equations have been integrated by the Kármán-Pohlhausen method for small values of ω, the frequency of the oscillation of the plate, and the W.B.K. method is applied to solve the equations for high values of ω. The velocity profile within the boundary-layer region and the shearing stress on the plate have been obtained in both the cases. The oscillation of the shearing stress has a phase lead over the oscillation of the plate. This phase lead decreases with increase of the second-order effect for small values of ω.
A theoretical study of non-equilibrium blunt-body flows
Authors: Conti Raul J.
Published: March 2006

Non-equilibrium inviscid flows behind a spherical-segment shock wave are investigated with the method of series truncation. This semi-analytical technique developed at Stanford is based on a systematic co-ordinate-perturbation scheme. The flow variables are expanded in series in powers of the longitudinal curvilinear co-ordinate leading away from the stagnation point. The problem is thus reduced to one of numerical integration of ordinary differential equations for functions of the normal co-ordinate. Unlike the similar situation of the Blasius series in boundary-layer theory, the present scheme–having to deal with elliptic equations–must resort to series truncation. As a consequence, a truncation error is introduced. The present paper shows a simple way of reducing this error.

The simplified air chemistry adopted is based on non-equilibrium dissociation and recombination of oxygen diluted in inert nitrogen. A wide spectrum of non-equilibrium régimes is investigated for a fixed set of flight conditions. In particular, near-frozen flows are followed to the vicinity of the stagnation point through a region of large temperature and concentration gradients located near the body. This equilibrium-drive region, arising from the singular nature of the frozen limit, is studied in some detail.
An experimental examination of the large-eddy equilibrium hypothesis
Authors: Gartshore Ian S.
Published: March 2006

The large-eddy energy equilibrium hypothesis states that the largest eddies of a turbulent shear flow are in approximate energy equilibrium throughout a significant part of their lives. This hypothesis leads to a relationship between the mean rate of shear strain and the Reynolds shear stress which involves the scale of the large eddies. By assuming that the large-eddy scale is proportional to the standard deviation of the free turbulent boundary, or laminar superlayer, the validity of this hypothesis may be checked experimentally. Intermittency and mean velocity measurements made in five different two-dimensional shear flows are presented and these results, together with values calculated from Townsend's measurements in a two-dimensional wake, support the form of relationship suggested by the energy equilibrium hypothesis.
Analytical and numerical studies of the structure of steady separated flows
Authors: Burggraf Odus R.
Published: March 2006

The viscous structure of a separated eddy is investigated for two cases of simplified geometry. In § 1, an analytical solution, based on a linearized model, is obtained for an eddy bounded by a circular streamline. This solution reveals the flow development from a completely viscous eddy at low Reynolds number to an inviscid rotational core at high Reynolds number, in the manner envisaged by Batchelor. Quantitatively, the solution shows that a significant inviscid core exists for a Reynolds number greater than 100. At low Reynolds number the vortex centre shifts in the direction of the boundary velocity until the inviscid core develops; at large Reynolds number, the inviscid vortex core is symmetric about the centre of the circle, except for the effect of the boundary-layer displacement-thickness. Special results are obtained for velocity profiles, skin-friction distribution, and total power dissipation in the eddy. In addition, results of the method of inner and outer expansions are compared with the complete solution, indicating that expansions of this type give valid results for separated eddies at Reynolds numbers greater than about 25 to 50. The validity of the linear analysis as a description of separated eddies is confirmed to a surprising degree by numerical solutions of the full Navier–Stokes equations for an eddy in a square cavity driven by a moving boundary at the top. These solutions were carried out by a relaxation procedure on a high-speed digital computer, and are described in § 2. Results are presented for Reynolds numbers from 0 to 400 in the form of contour plots of stream function, vorticity, and total pressure. At the higher values of Reynolds number, an inviscid core develops, but secondary eddies are present in the bottom corners of the square at all Reynolds numbers. Solutions of the energy equation were obtained also, and isotherms and wall heat-flux distributions are presented graphically.
On the analogy between thermal and rotational hydrodynamic stability
Authors: Debler Walter R.
Published: March 2006

The correspondence between the eigenvalues for the problem of the onset of convection in a fluid confined between two horizontal plates and for the stability of viscous flow between two cylinders rotating at almost the same angular velocity has been known for some time. The recent work of Chandrasekhar (1961) has prompted the extension of the analogy to a larger group of rotating cylinder problems and their associated convection cases in which the primary temperature distribution is parabolic. This paper shows the analogy between these two problems and presents data which give the corresponding temperature distribution for a given ratio of angular velocities between the two cylinders. The equivalent Rayleigh numbers are listed for the Taylor numbers given by Chandrasekhar (1954). The eigenfunctions for several of the parabolic temperature profiles are determined. These results show that the single vortex convection pattern becomes a double vortex for certain initial temperature distributions. The critical Rayleigh numbers for the stability of a layer of water which is near 4 °C is also found by analogy.
The steady state exothermal hydromagnetic discontinuity for an arbitrarily orientated magnetic field
Authors: Kennedy Lawrence A.
Published: March 2006

An exothermal hydromagnetic discontinuity in a perfectly conducting gas is studied for the case of an arbitrarily orientated magnetic field. The evolutionary modes and the manner of variation of the physical properties for such phenomena are determined. The Hugoniot adiabatic is obtained and analysed.
Pressure distribution and mass injection effects in the transitional separated flow over a spiked body at supersonic speed
Authors: Hahn Mansop
Published: March 2006

Pressure distribution and the effect of air injection in the separated flow over a spiked-hemisphere were investigated at a Mach number of 3·3, and Reynolds number around the transitional value. Pressure distribution along the spike as well as over the body was measured in the absence of injection. Air was injected into the separated flow at the spike tip and base and reattachment region through one or more orifices drilled normal to the surface, and the resulting flow patterns were observed using the schlieren technique. The results show that (i) the pressure variation along the spike is similar to a two-dimensional separated flow in the transition régime; and (ii) the mass injection at the spike tip has a strong destabilizing effect regardless of injection rate, while the injection from spike base and reattachment region can be either slightly stabilizing or destabilizing depending on the flow condition.
The effects of pressure gradients on turbulent flow near a smooth wall
Authors: Mellor George L.
Published: March 2006

A dimensional argument is presented leading to a functional form for the effective viscosity which embraces the hypothesis of a previous paper (Mellor & Gibson 1966; hereafter referred to as paper A) in the defect portion of a turbulent boundary layer. The new argument also suggests a way of determining the effective viscosity in the viscous sublayer when the flow is subjected to mainstream pressure gradients.

It will be shown that the large wall-velocity profiles and the defect-velocity profiles automatically overlap, even in the absence of a logarithmic portion. It will be shown further that equilibrium flows are uniquely determined by β andR.
Torsional oscillations of a fluid sphere with a rigid boundary in a uniform magnetic field
Authors: Wentzell R. A.
Published: March 2006

Plumpton & Ferraro (1955) considered the torsional oscillations of an infinitely conducting sphere in a uniform magnetic field. They showed that if the fluid and magnetic viscosity were assumed to be zero in the governing differential equations, then a continuous spectrum of eigenvalues could be obtained. This novel feature was clarified by Stewartson (1957) when he obtained the exact solution and showed that in the correct limit of a perfect conductor the eigen-values are discrete. Furthermore, in the limit of infinite conductivity the oscillations occur only on the axis of symmetry (figure 1).
Interfacial circulation due to surface-active agents in steady two-phase flows
Authors: Kenning D. B. R. , Cooper M. G.
Published: March 2006

Steady circulatory motions at the surface of tap-water flowing in an open channel and past a hemispherical air bubble on a channel wall are described and explained by the presence of a film of surface-active material. Boundary conditions for the liquid phase are derived by assuming that the surface film is insoluble and incompressible. Good agreement is obtained between the theoretical and measured velocity fields in the open-channel flow.
The stability of elastico-viscous flow between rotating cylinders Part 3. Overstability in viscous and Maxwell fluids
Authors: Beard D. W. , Davies M. H. , Walters K.
Published: March 2006

Consideration is given to the possibility of overstability in the Couette flow of viscous and elastico-viscous liquids. The relevant linear perturbation equations are solved numerically using an initial-value technique. It is shown that over-stability is not possible in the case of Newtonian liquids for the cases considered. In contrast, overstability is to be expected in the case of moderately-elastic Maxwell liquids. The Taylor number associated with the overstable mode decreases steadily as the amount of elasticity in the liquid increases, and it is concluded that highly elastic Maxwell liquids can be very unstable indeed.
A model of the undular bore on a viscous fluid
Authors: Chester W.
Published: March 2006

A solution for the weak bore is found in which the mean profile is dominated by viscosity, so that the velocity variation is given essentially by a quasi-uniform Poiseuille flow. It is found that such a transition between flows of different depths is possible provided the Froude number is less than 1·58. The possibility of superposing an inviscid perturbation on such a flow is then investigated. Under favourable circumstances the effect of this perturbation is to add to the profile of the free surface a term which decays exponentially in front of the bore, but is oscillatory behind it.
Determination of mean and dynamic skin friction, separation and transition in low-speed flow with a thin-film heated element
Authors: Bellhouse B. J. , Schultz D. L.
Published: March 2006

The application of a heated thin metallic film to the measurement of mean skin friction in laminar and turbulent flow on a flat plate, circular cylinder and in an annular tunnel is described. The manner in which transition and separation are detected with this instrument is illustrated by reference to tests on a circular cylinder. The influence of the ambient air temperature and the gauge temperature on the behaviour of the instrument is analysed and it is shown that a reliable element can be constructed, capable of being moved from one location to another, while retaining its calibration. An element, calibrated on an oscillating flat plate, is used to obtain the spectral density of skin friction in a turbulent boundary layer.
The effect of initial conditions on the development of a free shear layer
Authors: Bradshaw P.
Published: March 2006

The distance between the separation point and the final approach to a fully developed turbulent mixing layer is found to be of the order of a thousand times the momentum-deficit thickness of the initial boundary layer, whether the latter be laminar or turbulent. There are correspondingly large shifts in the virtual origin of the mixing layer, resulting in spurious Reynolds-number effects which cause considerable difficulties in tests of model jets or blunt-based bodies, and which are probably responsible for the disagreements over the influence of Mach number on the development of free shear layers. These effects are explained.
The flow in a turbulent boundary layer after a change in surface roughness
Authors: Townsend A. A.
Published: March 2006

The changes of surface stress in a deep boundary layer passing from a surface of one roughness to another of different roughness are described fairly accurately by theories that assume self-preserving development of the flow modifications. It has been shown that the dynamical conditions for self-preserving flow can be satisfied if the change in friction velocity is small and if log l0/z0 is large (l0 is the depth of the modified flow and z0 is the roughness length of the surface). In this paper it is shown that, if the change of friction velocity is not small, the dynamical conditions can be satisfied to a good approximation over considerable fetches if log l0/z0 is large. The flow modification is then locally self-preserving, that is, the fields of mean velocity and turbulence are in a moving equilibrium but one which changes very slowly with fetch and depends on the ratio of the initial to the current friction velocity. In the limit of a very large increase in friction velocity, the moving equilibrium is essentially that of a boundary layer developing in a non-turbulent free stream. Equations describing the flow development are derived for all changes of friction velocity, and the form of the velocity changes is discussed. For large increases of friction velocity, the depth of the modified layer is substantially less than would be expected from the theories of Elliott and of Panofsky & Townsend.
Thin-flame theory for a fuel droplet in slow viscous flow
Authors: Fendell Francis E. , Sprankle Maureen L. , Dodson David S.
Published: March 2006

The equilibrium burning of a spherical drop of pure non-gaseous fuel in a slow convective flow of hot oxidant is examined for Lewis number unity. A Stokes or Oseen flow with modified boundary conditions to permit mass transfer at the drop surface describes the velocity field. The method of inner and outer expansions is then adopted to describe the thermal and mass-fraction profiles under the model of a direct one-step irreversible indefinitely fast chemical reaction. The thin-flame position and surface mass-transfer rate, both functions of polar angle as well as radial position when convection is added to the conventional diffusive transport, are furnished in terms of the Peclet number. It is found that the interaction of the perturbational free-streaming with the asymmetric vaporization it induces can lead to drag coefficients in excess of the Stokes value.
The structure of the wave front in spinning detonation
Authors: Edwards D. H. , Parry D. J. , Jones A. T.
Published: March 2006

The structure and mode of propagation of spinning detonation waves in stoichiometric oxyhydrogen, at initial pressures of 20–30 mm, have been investigated. The waves were generated in a square-section tube and observations have been made by the smoked-film technique, spark schlieren photography and pressure gauges. At the front of the self-sustaining detonation waves obtained at these pressures, two Mach interactions exist, the trajectories of which are derived from the imprints made on the smoked foil. As the triple point traverses the tube section, its direction of motion is found to vary between 50° and 70° with the tube diameter. An analysis of a Mach triple point for these conditions predicts the absence of chemical reaction behind the Mach stem in the immediate neighbourhood of the triple point. Experimentally determined pressures and triple shock angles confirm, to within experimental error, the postulated theoretical configuration.
A technique for the precise measurement of small fluid velocities
Authors: Baker D. James
Published: March 2006

A technique for the quantitative measurement of fluid velocities in the range 0–5 cm/sec is described. The technique uses a pH indicator, is applicable in aqueous solutions and permits visualization and measurement of three-dimensional flow fields.
Evaluation of the momentum equation for a turbulent wall jet
Authors: Chao J. L. , Sandborn V. A.
Published: March 2006

Experimental evaluation of the radial momentum equation near the surface for an axisymmetrie turbulent wall jet is reported. The equation for flow contains six terms of magnitudes which cannot be neglected. The pressure gradient across the flow as well as along the flow is found to be of major importance. Thus, for a wall jet flow it is impossible to treat the radial and vertical momentum equations as independent of one another.
Velocity and temperature profiles in adverse pressure gradient turbulent boundary layers
Authors: Perry A. E. , Bell J. B. , Joubert P. N.
Published: March 2006

A correlation scheme for velocity and temperature profiles is derived for turbulent boundary layers in adverse pressure gradients. The resulting analytical expressions are obtained by what could be referred to as ‘regional similarity’ arguments. This avoids the need to make use of the Reynolds analogy (explicitly, at least) or the usual local gradient-type diffusion expressions for momentum and thermal transport (‘the local similarity’ and Boussinesq concept). The expressions agree well with experimental data for the velocity profiles and encouraging correlation is shown for the temperature profiles. The expressions cover a wider part of the profile than given by the logarithmic law of the wall. Surface roughness and Prandtl-number effects are included in the analysis.
The constraints imposed on tornado-like vortices by the top and bottom boundary conditions
Authors: Turner J. S.
Published: March 2006

A laboratory model of a tornado vortex has been produced, incorporating two features which are believed to be important to the understanding of the atmospheric phenomenon, but which have been largely ignored in previous studies. First, it has been shown that a vortex can be driven fromaboveby a mechanism analogous to convection in a cloud, and that density differences within the funnel itself are not essential. Associated with this mechanism of formation is a circulation in the vertical, with an upflow in the centre surrounded by a compensating annular downflow. Secondly, the bottom boundary is seen to have a strong influence on the vortex, since the down and up flows are linked there by a rapid radial inflow in a thin boundary layer.

In the present paper an approximate theoretical description of such a vortex is proposed. The interior and boundary layer flows are first examined separately, and then a condition is sought which makes the two solutions consistent. The starting-point of the theory is the assumption of a form of stream function which describes a circulation in the vertical having the essential features of that observed. The result of the matching procedure is to fix both the form of the tangential velocity profile, and the relative magnitudes of the three components of velocity. These deductions are not critically dependent on the assumed form of the motion in the vertical, and are in good agreement with the first measurements in the laboratory vortices, though the quantitative experimental results are not emphasized here.
Two supercavitating hydrofoils near a free surface
Authors: Green T. , Street R. L.
Published: March 2006

A two-dimensional, incompressible, irrotational, linearized flow model is employed in this analysis of two supercavitating, flat-plate hydrofoils in the presence of a free surface. The cavities are taken to have finite lengths, and gravity is neglected. The ensuing boundary-value problem is converted, by means of conformal mapping, to a mixed-boundary-value problem for the complex velocity in the upper half-plane. This altered problem is solved by use of the methods of thin-aerofoil theory and the solution involves digital-computer evaluation of a large number of incomplete elliptic integrals of the first and third kinds. Typical results are presented in graphs, and the results of the present work are compared with Yim's (1964) theory for a single supercavitating body near a free surface.
Heat transfer from turbulent separated flows
Authors: Spalding D. B.
Published: March 2006

A power-law relation is derived between the Stanton number and the Reynolds number, expressing the law of heat transfer for a wall adjacent to a region of turbulent separated flow. The derivation is based on Prandtl's (1945) proposal for the laws of dissipation, diffusion and generation of turbulent kinetic energy. The constants appearing in these laws are determined by reference to experimental data for the hydrodynamic properties of the constant-stress and the linear-stress layers.

The agreement between the resulting predictions and the experimental data of other workers is sufficiently good to suggest that the actual mechanism of heat transfer from separated flows has much in common with that which is postulated. Closer agreement can be expected only after the present one-dimensional analysis has been superseded by a two-dimensional one.
Dual solutions of the magnetogasdynamic boundary-layer equations
Authors: Ingham D. B.
Published: March 2006

This paper extends the work of Wilson (1964) to include the effect of compressibility in the recurrence of dual solutions in the flow in the boundary layer on a semi-infinite, thermally insulated, flat plate placed at zero incidence to a uniform stream of electrically-conducting gas with an aligned magnetic field at large distances from the plate. Numerical integration of the boundary-layer equations has been performed for several values of the ratio, β, of the square of the Alfvén speed to the fluid speed in the undisturbed fluid, the conductivity parameter ε = 0·1 and ∞ and the square of the Mach number M2 = 0, 1/2, 1, 2, 2·5, 4 and 5. The effect of compressibility is to increase the value of β for which a solution can exist such that the skin friction at the plate is greater than zero. Dual solutions are seen to occur for non-zero Mach number and all values of ε but no attempt here has been made to explain this phenomenon. An analytic argument indicates that no solutions of the equations exist if the skin friction at the plate is greater than zero and if the vorticity and current decay exponentially, the condition for which is
\[
M^2 < 1,\quad \beta > 1/(1-M^2).
\]
Nothing specific has been proved if this condition is not satisfied.
Aerodynamics of oscillating disks and a right-circular cylinder
Authors: Willmarth W. W. , Hawk N. E. , Galloway A. J. , Roos F. W.
Published: March 2006

Detailed studies are reported of the free and forced oscillation of disks and a right-circular cylinder constrained to rotate about a fixed diametrical axis passing through the centre of the body and normal to the free-stream direction. When a disk is free to rotate, it oscillates at a definite frequency with slowly varying amplitude and phase. A right-circular cylinder also oscillates at a definite frequency but with rapidly increasing amplitude. When the amplitude becomes large, after a few cycles of oscillation, the cylinder rotates steadily in one direction.

Analogue computer elements, position sensors and a dynamic moment balance were used to study the static restoring moment, dynamic restoring moment, average damping moment, statistical properties of the disk motion and power spectrum of the turbulent moment. The behaviour of the disk and cylinder are explained using the measurements and the theory for random excitation of a linear system. The turbulent exciting moment is caused by the unsteady flow in the wake and can be changed by placing disks and splitter plates in the wake. A model is proposed for the unsteady flow field in the wake behind the disk. The model relates the turbulent moment to the vortex shedding process in the wake.
Jet diffusion in the region of flow establishment
Authors: Sami Sedat , Carmody Thomas , Rouse Hunter
Published: March 2006

In the flow-establishment region of an air jet issuing with an efflux velocity of about 35 ft./sec from a 1.0 ft. diameter nozzle into still air, measurements were made of mean axial and radial velocities, mean static pressure, turbulence intensities, turbulent shear, and pressure fluctuation. For the measurement of the latter a pressure probe using a ceramic piezo-electric tube was developed. Also included in the measurements were the temporal mean gradient and autocorrelation of the axial-velocity fluctuation and the intermittency factor. The fluctuating-pressure and turbulence-intensity fields were observed to be closely similar in form. Through use of the measured distributions of mean-flow and turbulence characteristics, all terms of the integral and differential forms of the momentum and mean-energy equations were evaluated throughout the region. The results are presented herein by curves of variation of each of the terms as they appear in the corresponding equations.
Shock-wave strengthening by area convergence
Authors: Russell David A.
Published: March 2006

A 17 in. diameter shock tube was coupled to a 1 in. tube by a 10° half-angle conical convergence. Timing measurements showed that the shock waves emerged from the convergence at 2–3 times their entrance speeds, and then decelerated downstream. After the application of a viscous correction, the shock speeds at the convergence exit agreed to within 5% with equilibrium real-gas calculations of the model of Chester (1954), Chisnell (1957) and Whitham (1958). The downstream deceleration, due to viscosity and to higher-order interactions not included in the theory, was also briefly studied.
The formation of elliptical wakes
Authors: Kuo Yung-Huang , Baldwin Lionel V.
Published: March 2006

The wakes formed behind sharp-edged, bluff, elliptical bodies have elliptical cross-sections, but the major axis of the wake is aligned with the minor axis of the body. This effect was observed in both mean velocity and turbulent intensity data in wakes throughout the range of the experiment, from several body diameters to distances of 250 diameters downstream of the body. The turbulent energy in the wake flow near the body displayed a periodicity which was correlated using a Strouhal number. Over the Reynolds-number range from 8 × 103to 7 × 104, the Strouhal number depended only on the body eccentricity.
The effect of the variation of surface tension with temperature on the motion of bubbles and drops
Authors: Harper J. F. , Moore D. W. , Pearson J. R. A.
Published: March 2006

The boundary conditions at the surface of a small bubble rising in a liquid are examined theoretically, and it is shown by order-of-magnitude arguments, which are confirmed by detailed calculation in a special case, that although surfacetension gradients must always exist around the bubble, they are too small to affect the motion appreciably unless surface-active substances are present. This is because gradients of surface tension imply gradients of temperature in a pure liquid, and these turn out to be always small near the bubble if they tend to zero at large distances from it. The same is true for drops of one fluid in another.
The disintegration of wave trains on deep water Part 1. Theory
Authors: Benjamin T. Brooke , Feir J. E.
Published: March 2006

The phenomenon in question arises when a periodic progressive wave train with fundamental frequency ω is formed on deep water—say by radiation from an oscillating paddle—and there are also present residual wave motions at adjacent side-band frequencies ω(1 ± δ), such as would be generated if the movement of the paddle suffered a slight modulation at low frequency. In consequence of coupling through the non-linear boundary conditions at the free surface, energy is then transferred from the primary motion to the side bands at a rate that, as will be shown herein, can increase exponentially as the interaction proceeds. The result is that the wave train becomes highly irregular far from its origin, even when the departures from periodicity are scarcely detectable at the start.

In this paper a theoretical investigation is made into the stability of periodic wave trains to small disturbances in the form of a pair of side-band modes, and Part 2 which will follow is an account of some experimental observations in accord with the present predictions. The main conclusion of the theory is that infinitesimal disturbances of the type considered will undergo unbounded magnification if
\[
0 < \delta \leqslant (\sqrt{2})ka,
\]
where k and a are the fundamental wave-number and amplitude of the perturbed wave train. The asymptotic rate of growth is a maximum for δ = ka.
Viscoelastic flow past a wedge with a soluble coating
Authors: Hsu Chen-Chi
Published: March 2006

The steady, two dimensional, incompressible flow of a viscoelastic fluid past a wedge of 90 degrees coated with the viscoelastic material is studied theoretically using constitutive equations proposed by Oldroyd in 1958. The effect of diffusion of the coating as well as its material properties (viscosity, relaxation time, retardation time, etc.) on the frictional force is investigated.

A boundary-layer analysis is performed on the constitutive equations as well as on the momentum equations. A similarity transformation is found for the set of boundary-layer equations. Series expansion and Laplace's method are employed to obtain the solution in the asymptotic series of gamma functions.

The results obtained show that:

The thinner displacement thickness does not necessarily imply a large frictional force for the viscoelastic flow.

For a homogeneous viscoelastic flow, the frictional force increases as the degree of dilatancy of the material increases, and decreases with increasing degree of pseudo-plasticity of the material.

For a non-homogeneous viscoelastic flow with given material constants, depending on whether the material is pseudoplastic or dilatant and on the ratio of the material concentration of outer flow and the concentration at the body, the frictional coefficient will decrease or increase from that of the homogeneous flow with the concentration at the body as the Schmidt number increases, and will approach a limit when the Schmidt number becomes very large. This limit is the frictional coefficient of the homogeneous flow with the concentration of the outer flow.
Temperature measurements in a hypersonic gun tunnel using heat-transfer methods
Authors: Edney B. E.
Published: March 2006

The theory of Fay & Riddell (1958) is used to calculate stagnation temperatures from stagnation-point heat-transfer rates measured in the working section of a hypersonic gun tunnel at a Mach number of 9·8. Measurements using both thin-film gauges and calorimeters are described. The temperatures measured using this technique are found to be lower than predicted by Lemcke (1962) from measurements of shock strengths and final pressures in the gun barrel. This discrepancy is attributed to heat losses in the barrel during the initial shock compression cycle. A simple theory is developed to take into account these losses. There is good agreement between this theory and the experimental results.