bluuebunny/crossref_metadata_2025 huggingface dataset:
Calculations of the development of an undular bore
Authors: Peregrine D. H.
Published: March 2006

If a long wave of elevation travels in shallow water it steepens and forms a bore. The bore is undular if the change in surface elevation of the wave is less than 0·28 of the original depth of water. This paper describes the growth of an undular bore from a long wave which forms a gentle transition between a uniform flow and still water. A physical account of its development is followed by the results of numerical calculations. These use finite-difference approximations to the partial differential equations of motion. The equations of motion are of the same order of approximation as is necessary to derive the solitary wave. The results are in general agreement with the available experimental measurements.
Note on the use of plaster of paris in flow visualization, and some geological applications
Authors: Allen J. R. L.
Published: March 2006

The pattern of motion on the surface of a model shaped in plaster of paris and immersed in a water stream, can be made visible by reason of the marks caused when small discontinuities in the surface excite local fluctuations of velocity which lead to differential solution of the plaster and to small features of relief. This technique, which has so far been applied in geological studies, is illustrated by reference to motions about a cylinder on a flat plate and over symmetrical skewed steps. Current crescents and sand waves are briefly discussed in the light of these motions.
The entrainment function in turbulent boundary-layer and wall-jet calculations
Authors: Escudier M. P. , Nicoll W. B.
Published: March 2006

Some of the proposals made by Spalding (1964a) in his ‘Unified theory of friction, heat transfer, and mass transfer’ are examined. The two-component velocity-profile family proposed by Spalding is compared with measured boundary-layer and wall-jet velocity profiles and is shown to be adequate for flows with moderate wake components. The drag law implicit in the velocity-profile family is shown to be in good agreement with experimental data.

Recommendations are provided for entrainment functions for both boundary layers and wall jets.

Predictions of boundary-layer and wall-jet development, based on the recommended entrainment functions, are presented and compared with experiment. The predictions are in good agreement with experiment except in the vicinity of separation.
Submerged jets in short cylindrical flow vessels
Authors: Mcnaughton K. J. , Sinclair C. G.
Published: March 2006

Liquid-into-liquid jets in short cylindrical vessels have been investigated under conditions of uniform flow by using an aqueous blue tracer solution in conjunction with tránsparent cylindrical tanks. The vessels had diameters D of 3, 6, 12 and 24in., length-to-diameter ratios L/D of 1, 2 and 3 and inlet diameters d between ¼ and 1 in. Reynolds numbers in the inlet tube, Rei, ranged between 100 and 28,000. Four main types of jet were observed:
\[
\begin{array}{@{}l@{\qquad}l@{\quad}l@{}}
& \hbox{dissipated-laminar jets} & (Re_i < 300\;\hbox{approx}.);\\
& \hbox{fully laminar jets} & (300 < Re_i < 1000\;\hbox{approx}.);\\
& \hbox{semi-turbulent jets} & (1000 < Re_i < 3000\;\hbox{approx}.);\\
\hbox{and} & \hbox{fully turbulent jets} & (Re_i > 3000).
\end{array}
\]

The laminar length a of sub-turbulent jets was investigated and correlated with Rei and the geometric parameters by the equation
\[
a/d = 9.97 \times 10^7 Re_i^{-2.46}(D/d)^{-0.48} (L/d)^{0.74}.
\]
The mechanics of the formation region of vortices behind bluff bodies
Authors: Gerrard J. H.
Published: March 2006

The characteristic lengths of the oscillating wakes of bluff bodies is discussed; in particular, those used in the universal non-dimensional frequencies proposed by Roshko (1954b) and Goldburg, Washburn & Florsheim (1965). It is concluded that these are equivalent at high Reynolds number. A closer examination leads to the conclusion that there are two simultaneous characteristic lengths; the scale of the formation region, and the width to which the free shear layers diffuse. Discussion of the mechanics of the formation region results in a physical basis for the determination of the frequency by these two characteristic lengths. The ideas developed are applied to the effects of splitter plates in the wake. The possibility of a high-Reynolds-number symmetrical formation region is suggested as an explanation of the very small lift values observed in the absence of free-stream disturbances.
Steady free convection in a porous medium heated from below
Authors: Elder J. W.
Published: March 2006

This is an experimental and numerical study of steady free convection in a porous medium, a system dominated by a single non-linear process, the advection of heat. The paper presents results on three topics: (1) a system uniformly heated from below, for which the flow is cellular, as in the analogous Bénard-Rayleigh flows, (ii) the role of end-effects, and (iii) the role of mass discharge. Measurements of heat transfer are used to establish further the validity of the numerical scheme proposed by the author (1966a), while the other flows allow a more extensive study of the numerical scheme under various boundary conditions. The results are very satisfactory even though only moderately non-linear problems can be treated at present.

The main new results are as follows. For the Rayleigh-type flow, above a critical Rayleigh number of about 40, the heat transferred across the layer is proportional to the square of the temperature difference across the layer and is independent of the thermal conductivity of the medium or the depth of the layer. This result is modified when the boundary-layer thickness is comparable to the grain size of the medium. The investigation of end-effects reveals variations in horizontal wave-number and a pronounced hysteresis and suggests an alternative explanation of some observations by Malkus (1954).
On the breakdown of characteristics solutions in flows with vibrational relaxation
Authors: Rarity B. S. H.
Published: March 2006

The breakdown of the characteristics solution in the neighbourhood of the leading frozen characteristic is investigated for the flow induced by a piston advancing with finite acceleration into a relaxing gas and for the steady supersonic flow of a relaxing gas into a smooth compressive corner. It is found that the point of breakdown moves outwards along the leading characteristic as the relaxation time decreases and that there is no breakdown of the solution on the leading characteristic if the gas has a sufficiently small, but non-zero, relaxation time. A precise measure of this relaxation time is derived. The paper deals only with points of breakdown determined by initial derivatives of the piston path or wall shape. In the steady-flow case, the Mach number based on the frozen speed of sound must be greater than unity.
Twisting of liquid crystals
Authors: Ericksen J. L.
Published: March 2006

We discuss a one-parameter family of general solutions of the hydrostatic equations for liquid crystals. For certain values of the parameter, the energy may take on extremal values. We discuss special features of such solutions. Configurations similar to those considered naturally occur in liquid crystals of cholesteric type, suggesting that some such state has a relatively low energy.
Hydromagnetic stability of dissipative flow between rotating permeable cylinders
Authors: Chang Tien Sun , Sartory Walter K.
Published: March 2006

The theory of stability of the flow of a viscous, electrically conducting fluid between rotating cylinders in the presence of an axial magnetic field is extended to the case where the cylinders are permeable and the primary flow includes a radial component. Numerical results pertaining to the stationary axially symmetric modes are presented, and the asymptotic stability behaviour for large values of the radial Reynolds number is derived.
Measurement of the growth of a turbulent mercury jet in a coaxial magnetic field
Authors: Sajben Miklos , Fay James A.
Published: March 2006

Using a hot-wire system developed for this purpose, measurements of the velocity were made in a circular liquid-mercury jet issuing into a low-speed secondary flow and subject to a uniform axial magnetic field. The Reynolds number of the jet was about 10,000 while the magnetic interaction parameter varied from zero to slightly over one. The jet was strongly turbulent under all conditions investigated. The radial distribution of the mean and fluctuating component of the meridional velocity was measured at four axial stations located between 2 and 34 diameters from the nozzle exit. The results indicate that the rate of spreading of the jet is decreased, that the shape of the velocity profile changes and that the turbulent intensity decreases with increasing magnetic-field strength. The high-frequency components of the fluctuations in the second flow seem to be damped more strongly than fluctuations at low frequencies, while the reverse is observed within the core of the jet.
Step-induced separation of a turbulent boundary layer in incompressible flow
Authors: Bradshaw P. , Galea P. V.
Published: March 2006

Measurements of the low-speed flow up a step of height equal to 1·75 times the initial boundary-layer thickness show that the flow satisfies Stratford's (1959) condition for rapid separation, the extra stress gradients being confined to the first one-eighth of the boundary-layer thickness. The increase in turbulence intensity up to separation is small, and attributable to low-frequency fluctuations in separation position. Townsend's (1962) criterion predicts the separation point fairly accurately. A simple expression is found for the additional pressure rise that can be withstood by a boundary layer already fairly near separation, which gives tolerable results at any point in the flow up a step.
The maintenance of Reynolds stress in turbulent shear flow
Authors: Phillips O. M.
Published: March 2006

A mechanism is proposed for the manner in which the turbulent components support Reynolds stress in turbulent shear flow. This involves a generalization of Miles's mechanism in which each of the turbulent components interacts with the mean flow to produce an increment of Reynolds stress at the ‘matched layer’ of that particular component. The summation over all the turbulent components leads to an expression for the gradient of the Reynolds stress τ(z) in the turbulence\[ \frac{d\tau}{dz} = {\cal A}\Theta\overline{w^2}\frac{d^2U}{dz^2}, \]where${\cal A}$is a number, Θ the convected integral time scale of thew-velocity fluctuations andU(z) the mean velocity profile. This is consistent with a number of experimental results, and measurements on the mixing layer of a jet indicate thatA= 0·24 in this case. In other flows, it would be expected to be of the same order, though its precise value may vary somewhat from one to another.
Vortex decay above a stationary boundary
Authors: Barcilon Albert I.
Published: March 2006

An attempt is made to understand the decay of a free vortex normal to a stationary, infinite boundary. For rapidly swirling flows in fluids of small viscosity, thin boundary layers develop along the rigid boundary and along the axis, the axial boundary layer being strongly influenced by the behaviour of the plate boundary. An over-all picture of the flow is sought, with only moderate success in the region far from the origin. Near the origin, the eruption of the plate boundary layer into the axial boundary layer is studied.
Irrotational fluctuations near a turbulent boundary layer
Authors: Bradshaw P.
Published: March 2006

A verification of some of the predictions of the theory of Phillips (1955) is presented, and the relation between one-dimensional and two-dimensional wavenumber spectra is discussed. The convection velocity of the irrotational field deduced from measurements of the frequency spectrum alone appears to be about 0.9U1in the frequency range carrying most of the energy. It follows that the pressure-fluctuation spectrum is proportional to the velocity-fluctuation spectrum and varies as ω2at low frequency. The discrepancy between this result and measurements of wall-pressure spectra is plausibly attributed to extraneous sound.
Experiments on the low-speed flow past cones
Authors: Calvert J. R.
Published: March 2006

The wake behind a cone in incompressible flow has the form of a closed bubble. Measurements of velocity, turbulence and static pressure for various cone angles show that the wakes are all essentially similar. A wake Strouhal number may be defined, which is the same for all the models. A disk may be treated as a cone of 180° vertex angle.
A simple laboratory model for the oceanic circulation
Authors: Pedlosky J. , Greenspan H. P.
Published: March 2006

A linear theory is developed for the motion of a viscous, incompressible fluid in a rotating cylinder with a sloping bottom.

An analysis of the normal modes of oscillation reveals that the presence of the bottom slope introduces a new set of low frequency inertial oscillations to replace the purely geostrophic modes which are not allowed in this geometry. The new waves possess mean circulation and are the mechanism by which the fluid adjusts to changes in the rotation rate of the container, a process discussed in detail.

The steady motion produced in the cylinder when the cylinder's upper surface rotates at a different rate than the bottom surface is studied. It is shown that the presence of the bottom slope inhibits the steady fluid motion in the body of the cylinder and introduces a non-symmetric, high velocity side wall boundary layer.

Experimental evidence, presented to validate the theory, reproduces certain important features of the oceanic circulation.
Inviscid hypersonic flow over plane power-law bodies
Authors: Hornung H. G.
Published: March 2006

Theoretical solutions based on the expansion scheme for largexand largeM∞, as proposed by Freeman (1962), are obtained for the asymptotic inviscid flow over plane bodies of the shapey/d= (x/d)min the range$\frac{2}{3}/\gamma < m < \frac{2}{3}$where blast wave theory applies as a first approximation. In particular, the second-order terms, which are necessary to satisfy the body boundary conditions for the normal velocity are computed. The magnitude of the second-order terms is found to increase from zero at$m=\frac{2}{3}/\gamma $to infinity at$m = \frac{2}{3}.$

As a comparison with theory, experiments atM∞= 8·2 were made with two plane power-law bodies in the range$\frac{2}{3}/\gamma < m < \frac{2}{3} $and on a plane parabola with a tangent wedge nose. These consisted of the determination of shock-wave shapes, surface pressure distributions and detailed investigations of the distribution of pitot and static pressure across the shock layer.

The experimental results are in good agreement with the theory in the case m =1/2, where the second-order effects are small. At m = 5/8 the region of validity of the theory is limited to much larger distances from the nose of the body and larger Mach numbers. Accordingly, the prediction for the deviation from firstorder theory, although being correct in sign, is too small. Shock-wave shapes on bodies of the same power but of different size are correlated by the similarity theory when scaled with respect to the dimensiond.

The experimental results obtained with the wedge-parabola are in very good agreement with a characteristics solution by C. H. Lewis (1965, unpublished).
Instability due to viscosity stratification
Authors: Yih Chia-Shun
Published: March 2006

The principal aim of this paper is to show that the variation of viscosity in a fluid can cause instability. Plane Couette-Poiseuille flow of two superposed layers of fluids of different viscosities between two horizontal plates is considered, and it is found that both plane Poiseuille flow and plane Couette flow can be unstable, however small the Reynolds number is. The unstable modes are in the neighbourhood of a hidden neutral mode for the case of a single fluid, which is entirely ignored in the usual theory of hydrodynamic stability, and are brought out by the viscosity stratification.
A note on the existence of wakes behind large, rising bubbles
Authors: Maxworthy T.
Published: March 2006

Using simple flow-visualization techniques, it has been shown that as a large volume of air rises through a quiescent liquid it produces a well-defined wake and that the drag on the bubble appears as a momentum defect within this wake.
Three-dimensional boundary layers: a report on Euromech 2
Authors: Horlock J. H. , Norbury J. F. , Cooke J. C.
Published: March 2006

The second European Mechanics Colloquium, on the subject of three-dimensional boundary layers, was held at Liverpool University from 4 to 7 January 1966 and was attended by thirty-eight people closely associated with current work in this field.

The meeting was opened by an introductory review by J. C. Cooke, who successfully sought to provoke discussion by emphasizing areas of apparent agreement and disagreement. The discussions which followed were based on a series of contributions by participants in the Colloquium, and covered the following topics:

Laminar boundary layers.

Three-dimensional perturbations of two-dimensional turbulent boundary layers.

Corner and secondary flows.

Boundary layers associated with flow past obstacles.

Flow over delta wings.

Separation.

Flow over rotating surfaces.

Heat and mass transfer.

Miscellaneous topics.

In all these cases, the emphasis was on the three-dimensional nature of the flow, and in this report the discussions are summarized under these headings.
The spread of a turbulent plane jet issuing into a parallel moving airstream
Authors: Bradbury L. J. S. , Riley J.
Published: March 2006

The results of an experimental investigation into the development of a turbulent plane jet issuing into a parallel moving airstream are described. On the basis of a simple dimensional argument, it is shown that the results for the spread of jets with different ratios of jet nozzle to free-stream velocity can be collapsed into a single universal curve provided the effective origins of the various sets of data can be shifted. Evidence is found of a change in structure of the jet from a self-preserving plane jet flow near the origin of the flow towards a selfpreserving wake type of flow far downstream from the origin. This change of structure is compared with a prediction based on a simple application of Town-send's large-eddy hypothesis. It is shown that the hypothesis does not account for the way in which the jet structure changes and possible reasons for this are briefly discussed. Finally, some comments are made on the usefulness of the various theories of jet spreading.
A variational principle for a fluid with a free surface
Authors: Luke J. C.
Published: March 2006

The full set of equations of motion for the classical water wave problem in Eulerian co-ordinates is obtained from a Lagrangian function which equals the pressure. This Lagrangian is compared with the more usual expression formed from kinetic minus potential energy.
Non-linear dispersion of water waves
Authors: Whitham G. B.
Published: March 2006

The slow dispersion of non-linear water waves is studied by the general theory developed in an earlier paper (Whitham 1965b). The average Lagrangian is calculated from the Stokes expansion for periodic wave trains in water of arbitrary depth. This Lagrangian can be used for the various applications described in the above reference. In this paper, the crucial question of the ‘type’ of the differential equations for the wave-train parameters (local amplitude, wave-number, etc.) is established. The equations are hyperbolic or elliptic according to whetherkh0is less than or greater than 1.36, wherekis the wave-number per 2π andh0is the undisturbed depth. In the hyperbolic case, changes in the wave train propagate and the characteristic velocities give generalizations of the linear group velocity. In the elliptic case, modulations in the wave train grow exponentially and a periodic wave train will be unstable in this sense; thus, periodic wave trains on water will be unstable ifkh0> 1·36, The instability of deep-water waves,kh0> 1·36, was discovered in a different way by Benjamin (1966). The relation between the two approaches is explained.
The two-dimensional laminar jet in parallel streaming flow
Authors: Wygnanski I.
Published: March 2006

Solutions to the problem of a two-dimensional, laminar jet of incompressible fluid issuing into a uniform stream in the direction of the main flow are considered. Two co-ordinate-type expansions are developed. A direct expansion, when suitably transformed, predicts approximately the velocity along the plane of symmetry of the jet for all values of the abscissa, with a maximum error of 7·6% far downstream from the origin. This error is established by comparison with a second, asymptotic expansion valid only at large values of the abscissa. The two expansions are subsequently joined, permitting an approximate determination of a constant which multiplies a third-order term in the asymptotic series and which initially remained unknown even after satisfying all boundary conditions imposed on these series.

The decay of velocity excess along the plane of symmetry of the jet is accelerated by the presence of the external stream.
Finite-amplitude instability of parallel shear flows
Authors: Reynolds W. C. , Potter Merle C.
Published: March 2006

A formal expansion method for analysis of the non-linear development of an oblique wave in a parallel flow is presented. The present approach constitutes an extension and modification of the method of Stuart and Watson. Results are obtained for plane Poiseuille flow, and for a combination of plane Poiseuille and plane Couette flow. The Poiseuille flow exhibits finite-amplitude subcritical instability, and relatively weak but finite disturbances markedly reduce the critical Reynolds number. The combined flow, which becomes stable to infinitesimal disturbances at all Reynolds numbers when the Couette component is sufficiently great, remains unstable to finite disturbances.
Temperature measurements in a hypersonic gun tunnel using a modified line-reversal method
Authors: Brown-Edwards E. G.
Published: March 2006

Temperature measurements in the test section of a hypersonic gun tunnel using a modified line-reversal two-beam optical pyrometer have been performed. Measurements were made in the shock layer at the front of an ‘end-on’ flat-faced cylinder using argon or air as the driven gas. The measured temperatures were greater than the calculated isentropic temperatures but much less than the originally predicted shock-heated values. The experimental values agreed reasonably well with the theoretical temperatures for shock-heated air corrected for boundary-layer and heat-loss effects in the gun barrel and also with previously reported experimental values found using heat-transfer methods. Preliminary studies of the vibrational relaxation of nitrogen and air in the test section have been carried out using a flat-sided ‘relaxation’ tube (a Pitot tube with glass windows). They demonstrated the feasibility of this approach.
On the motion due to sources and sinks distributed along the vertical boundary of a rotating fluid
Authors: Barcilon Victor
Published: March 2006

The motion induced by sources and sinks distributed along the vertical side wall of a cylinder filled with fluid and rotating about a vertical axis is considered. Vertical motion, and hence vertical transport, is confined to a vertical boundary layer of thicknessE1/3, whereEis the Ekman number. The horizontal transport occurs through the interior of the fluid. The Ekman layers do not play any active role in the transport process. The results of a very simple experiment confirm these conclusions.
The interaction of a fibre tangle with an airflow
Authors: Taub Paul A.
Published: March 2006

An analytical model of the interaction of a fibre tangle with an airflow is proposed. This model replaces the discrete fibres by a continuum medium with a non-linear stress-strain law. The governing equations have been examined for one-dimensional unsteady flow configurations and have been found to possess five characteristic directions.

A numerical-solution procedure, based upon the method of characteristics, has been outlined and applied to the flow within a dilation chamber. A fibre sample is located at the centre of the chamber, which is alternately pressurized and depressurized.
Transient convection in a porous medium
Authors: Elder J. W.
Published: March 2006

Laboratory and numerical experiments on non-steady convective flows in a porous medium are reported. The main objective is to note the detailed comparison found between the time-dependent solutions and the time-like development of the iterative solutions of the steady equations originally pointed out by Garabedian (1956) and others.

Two flows are chosen for study. The first is the flow which develops when a blob of hot fluid is released at the base of a porous slab. The second is the flow which develops when a portion of the base of a porous slab is suddenly heated. The former flow is very simple and ideally suited for establishing the numerical scheme. The latter flow, however, produces several unexpected features. The gross features of the time development, when the motion is strongly non-linear, show an alternation between periods of slow gradual adjustment and periods of rapid change.
On the oscillatory instability of a differentially heated fluid loop
Authors: Welander Pierre
Published: March 2006

A theoretical discussion is given of the motion of a fluid contained in a tube forming a closed loop that is heated from below and cooled from above. The fluid is assumed to have uniform temperature over each cross-section, and the heat transfer is assumed proportional to the difference between the local temperatures of the fluid and the tube. The latter temperature is prescribed. The system has one steady solution with warm fluid rising in one branch and cold fluid sinking in the other. This solution may, however, become unstable in an oscillatory manner. A weak instability takes the form of pulsations, the motion being always of one sign, while a strong instability takes the form of oscillations with zero mean motion. These oscillations are irregular and do not repeat themselves even over very long times.

These unstable motions are associated with thermal anomalies in the fluid that are advected materially around the loop. The anomalies amplify through the correlated variations in flow rate. A warm pocket of fluid creates maximum flow rate going through the upper part and minimum flow rate going through the lower part of the loop. Accordingly it passes quicker through the heat sink than through the heat source, and the latter becomes more effective. Similarly, the heat sink acts more effectively on a cold pocket of fluid.

The curve of neutral stability is worked out as a function of the two parameters of the problem, a non-dimensional gravity and a non-dimensional friction coefficient. The instability has also been studied by direct numerical time integration of the model equations.

It is suggested that the mechanism of instability found for this model operates also in more complicated systems, and can explain the pulsative type of motions observed recently in certain convection experiments.
Stability of plane Poiseuille flow to periodic disturbances of finite amplitude in the vicinity of the neutral curve
Authors: Pekeris Chaim L. , Shkoller Boris
Published: March 2006

Stuart (1960) has developed a theory of the stability of plane Poiseuille flow to periodic disturbances of finite amplitude which, in the neighbourhood of the neutral curve, leads to an equation of the Landau (1944) type for the amplitude A of the disturbance:
\[
d|A|^2/dt = k_1|A|^2 - k_2|A|^4.
\]
If k2 is positive in the supercritical region (R > RC) where k1 is positive, then, according to Stuart, there is a possibility of the existence of periodic solutions of finite amplitude which asymptotically approach a constant value of (k1/k2)½. We have evaluated the coefficient k2 and found that there indeed exists a zone in the (α, R)-plane where it is positive. This is the zone inside the dashed curve shown in figure 1, with the region of instability predicted by the linear theory included inside the ‘neutral curve’. Stuart's theory and Eckhaus's generalization thereof could apply in the overlapping zone just above the lower branch of the neutral curve.
Imploding shocks and detonations
Authors: Welsh Robert L.
Published: March 2006

The gasdynamic problem of collapsing shocks and detonation waves having spherical or cylindrical symmetry is considered near the point or axis of symmetry. The solution basic to this work is the self-similar flow of a collopsing symmetrical shock wave with counterpressure neglected. The focusing effect as the flow progresses causes the front to accelerate and its velocity is singular at the instant of collapse. In the present work the perturbations, due to counter-pressure and also to a uniform heat release, which give rise to essentially identical mathematical solutions, are evaluated. The basic self-similar solution is investigated in detail over a range of values of the specific heat ratio.
Transition in oscillating boundary layer flows
Authors: Obremski H. J. , Fejer A. A.
Published: March 2006

An experimental investigation of transition phenomena in non-steady boundary layers of sinusoidally oscillating flows was conducted, and the effect of various parameters on the transition process was observed.

The manner in which transition occurs appears to be related to a dimensionless grouping designated as the non-steady Reynolds number, (Re)NS= LΔU/2πvν. When this number exceeds a certain critical value, transition begins with turbulent bursts appearing periodically at the frequency of the free stream oscillation; these are preceded by instability waves having the appearance of a Tollmien-Schlichting instability. The transition Reynolds number depends, in this case, only on the amplitude of the free stream oscillations and not on their frequency, at least to the first order. Below a critical value of this parameter, transition occurs at a relatively constant Reynolds number which appears independent of the amplitude and frequency of the oscillation, at least over the range tested.

When the bursts appear periodically, their development appears to occur in two succeeding phases: an initial or ‘creative’ phase marked by a sequential appearance of turbulence upstream and rapid development and a latter or ‘convective’ phase marked by turbulent spots having relatively constant leading and trailing edge velocities.

The dimensionless amplitude, ΔU/U∞, of the imposed oscillations was varied from 0.014 to 0.29 while the oscillation frequencies extended from 4.5 to 62c/s.Pressure gradients imposed on the flat plate model during the course of the study are given bydCp/dx = − 0.004/ft., −0.081/ft. and 0.045/ft. whereCp= 2p/ρU2∞and x is the distance (ft.) along the plate.
The scalar spectrum in the viscous-convective subrange
Authors: Nye James O. , Brodkey Robert S.
Published: March 2006

A modified design of a fibre optic light probe was used for the measurement of turbulent concentration fluctuations and the spectra associated with these. The main object was to establish experimentally the nature of the scalar spectrum in the viscous-convective subrange. The existence of a spectral region with a (-1)-power law form supports the uniform straining model proposed by Batchelor (1959) for Schmidt numbers (v/D) much greater than unity. For this range, the data do not agree with the cascading process suggested by Pao (1965).

An additional object was to study further the decay of the concentration fluctuations in terms of a measure of the turbulent mixing. More specifically, the limitations of applying the isotropic stationary mixing theory of Corrsin (1957, 1964a) to a shear pipe flow situation and the validity of the earlier data for this case (Lee & Brodkey 1964; Brodkey 1966a, b; and Gegner & Brodkey 1966) were investigated.
Shear layers in a rotating fluid
Authors: Baker D. James
Published: March 2006

A homogeneous fluid of viscosityvis confined between two co-axial disks (vertical separationH) which rotate relative to a rotating system (angular velocity Ω). The resulting velocity field is studied for values of the parameterv/2ΩH2in the range 1·6 × 10−2to 1·8 × 10−3. The Rossby number, defined as the ratio of the relative angular velocity of the disks to the angular velocity of the system, ranged from 0·038 to 0·0041. The dependence of the resulting velocity field (interior and boundary-layer flow) on geometrical parameters, imposed surface and bottom velocities, and Ω, is in good agreement with the calculations of Stewartson and Carrier. In particular, when the two disks rotate with the same angular velocity, the width of the vertical shear layer at the edge of the disks is found to be proportional to Ω−0·25±0·02. When the disks rotate in opposite senses, a shear layer in the vertical velocity is observed which transports fluid from one disk to the other and whose width is proportional to Ω−0·40±0·10. The magnitude and shape of the observed vertical velocity is in fair agreement with a numerical integration of the theoretical results.
Effect of longitudinal surface curvature on boundary layers
Authors: Narasimha Roddam , Ojha S. K.
Published: March 2006

We consider here the higher order effect of moderate longitudinal surface curvature on steady, two-dimensional, incompressible laminar boundary layers. The basic partial differential equations for the problem, derived by the method of matched asymptotic expansions, are found to possess similarity solutions for a family of surface curvatures and pressure gradients. The similarity equations obtained by this anaylsis have been solved numerically on a computer, and show a definite decrease in skin friction when the surface has convex curvature in all cases including zero pressure gradient. Typical velocity profiles and some relevant boundary-layer characteristics are tabulated, and a critical comparison with previous work is given.
Effect of viscosity on gravity waves and the upper boundary condition
Authors: Yanowitch Michael
Published: March 2006

The linearized problem of two-dimensional gravity waves in a viscous incompressible stratified fluid occupying the upper half-space z > 0 is investigated. It is assumed that the dynamic viscosity coefficient μ is constant and that the density distribution ρ(z) is exponential. This leads to a fourth-order differential equation in the z co-ordinate, the coefficients of which depend on ρ(z) and on a dimensionless parameter ε which is proportional to μ/σ, σ being the frequency of the oscillation. The problem is solved for small ε. It is found that there is a region in which the solutions behave like certain solutions of the inviscid problem (with ε = 0). However, when the solutions of the inviscid problem are wave-like in z, they do not satisfy the radiation condition. This is because the viscosity, in addition to damping the motion for large z, reflects waves. The appropriate solution of the inviscid problem consists, therefore, of an incident and a reflected wave. As μ → 0, the ratio of the amplitudes of the reflected and the incident wave approaches exp (− 2π2H/Λ), where Λ is the vertical wavelength, and H the density scale height. The solution, however, does not have a limit since the reflecting layer shifts, altering the phase of the reflected wave. The results of the analysis are supplemented by a number of numerically computed solutions, which are then used to discuss the validity of the linearization.
The determination of fluctuating velocity in air with heated thin film gauges
Authors: Bellhouse B. J. , Schultz D. L.
Published: March 2006

When attempts are made to use thin film anemometers in airflow to measure fluctuating velocity it is found that the dynamic sensitivity cannot be obtained from a steady-flow calibration. It is found that the dynamic sensitivity is considerably less than that predicted by static calibration and that the sensitivity is frequency-dependent. It is shown that thermal feedback from the substrate, on which the gauge is mounted, to the heated element is responsible for the variation of sensitivity with frequency, despite constant-temperature operation of the probe, and this variation is examined theoretically and experimentally.
The shape of a diffracting shock wave
Authors: Skews B. W.
Published: March 2006

This paper describes an experimental study of the shape of a shock diffracting around a corner made up of two plane walls, for corner angles from 15 to 165° (in 15° steps) and shock Mach numbers from M0 = 1·0 to 4·0. The results are compared with profiles determined from the diffraction theory of Whitham (1957, 1959). The agreement is shown to be good for an incident shock Mach number of 3·0, and fair in other cases. The behaviour is found to follow the trends established by Lighthill (1949) in a linearized theory. Results for the Mach number of the wall shock are also presented. The shock does not degenerate to a sound wave even for large corner angles and low Mach numbers.
A non-linear theory for a full cavitating hydrofoil in a transverse gravity field
Authors: Larock Bruce E. , Street Robert L.
Published: March 2006

An analysis is made of the effect of a transverse gravity field on a two-dimensional fully cavitating flow past a flat-plate hydrofoil. Under the assumption that the flow is both irrotational and incompressible, a non-linear method is developed by using conformal mapping and the solution to a mixed-boundary-value problem in an auxiliary half plane. A new cavity model, proposed by Tulin (1964a), is employed. The solution to the gravity-affected case was found by iteration; the non-gravity solution was used as the initial trial of a rapidly convergent process. The theory indicates that the lift and cavity size are reduced by the gravity field. Typical results are presented and compared to Parkin's (1957) linear theory.
Hypersonic weak-interaction similarity solutions for flow past a flat plate
Authors: Bush William B. , Cross Arthur K.
Published: March 2006

The hypersonic weak-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. The fluid is assumed to be a perfect gas having constant specific heats, a constant Prandtl number, σ, of order unity, and a viscosity coefficient varying as a power, ω, of the absolute temperature. Limiting forms of solutions are studied for the free-stream Mach number,M, the free-stream Reynolds number (based on the plate length),RL, and the reciprocal of the weak-interaction parameter, (ξ*)−1= [Fscr ](M,RL, ω, σ), greater than order unity.

By means of matched asymptotic expansions, it is shown that, for (1 − ω) > 0, the zone between the shock wave and the plate is composed of four distinct regions for which similarity exists. The behaviour of the flow in these four regions is analysed.
A theory of water-bells
Authors: Parlange Jean-Yves
Published: March 2006

A theory is developed to determine the shape of water-bells. The motion of the gas induced by the moving walls is taken into account in this analysis. A rapidly converging iterative procedure leads to a theoretical shape which agrees well with the experimental shape of the water-bell.
An underwater explosive shock gun
Authors: Coombs A. , Thornhill C. K.
Published: March 2006

A theoretical study is made of a simple design for an underwater shock gun, which consists of a chamber in the form of a hollow circular cone, with a spherical sector of explosive charge fitted into the apex. When the explosive is initiated at the apex, the resulting sector of a spherical blast wave will be diffracted by expansion waves moving inwards after the leading shock has emerged from the rim of the cone.

The progress of the expansion wave-fronts is calculated, and the results show a surprising inability of the diffraction process to ‘eat into’ the full-strength sector of spherical blast. It is found to be possible to design such a gun so that it is capable of projecting a high intensity shock-pressure beam over a considerable range, using only a very small explosive charge.
The formation of a dip on the surface of a liquid draining from a tank
Authors: Lubin Barry T. , Springer George S.
Published: March 2006

Experiments were performed studying the formation of a dip on the surface of an initially stationary liquid draining from a cylindrical tank through an axisym-metrically placed circular orifice. Based upon the information obtained from the experiments, a simple analytical expression was derived predicting the height of the liquid surface in the tank at which this dip forms. A comparison was made between the experimental data and the results of the analysis and good agreement was found between theory and data.
Laminar free convection in boundary layers near horizontal cylinders and vertical axisymmetric bodies
Authors: Saville D. A. , Churchill S. W.
Published: March 2006

In this article the problem of describing free convection near either horizontal cylinders or vertical axisymmetric bodies with fairly arbitrary body contours is studied. The solutions of two, coupled, partial differential equations, for the temperature and stream functions, are represented by series which are universal with respect to body contours within a specified class of body shapes (e.g. round-nosed cylinders). The series appear to converge rapidly so that a minimum of computational effort is required, even for classes of body shapes which do not admit the usual similarity transformations. For either horizontal, circular cylinders or spheres the series converge faster than expansions of the Blasius type and one-term approximations compare favourably with some of the existing experimental data.
A wave-guide model for turbulent shear flow
Authors: Landahl Marten T.
Published: March 2006

It is shown that for a dynamical system admitting wave propagation modes (i.e. a wave-guide) the cross-power spectral density for stationary random fluctuations in the system will be dominated by the waves if they are lightly damped, the reason being that these can correlate over large distances of the order the inverse of the damping ratio. For a turbulent shear flow the wave propagation constant is obtained approximately from the solution of the Orr-Sommerfeld problem for the mean flow. Numerical calculations for a flat-plate boundary layer produce results for the streamwise dependence of the cross-power spectral density for the surface pressure fluctuations in good qualitative and quantitative agreement with measurements. An exception is the convection velocity for which the theory predicts a value that is somewhat too low.
A note on the stability of an infinite fluid heated from below
Authors: Robinson J. L.
Published: March 2006

The problem of the stability of a fluid with time-dependent heating has been investigated by Morton (1957), Lick (1965) and Foster (1965). Morton and Lick assumed that the rate of change of the temperature profile is small compared with the growth rate of the disturbances (quasi-static assumption). This assumption is invalid near the onset of instability (as defined by ∂/∂t = 0), and Foster has therefore used an initial-value approach.

In this paper the range of validity of the quasi-static assumption is discussed, and results of a time-scaled analysis and calculations based on this are compared with the work of Foster; the agreement is found to be good. We restrict our attention to a semi-infinite fluid initially at a constant temperature; at time t = 0 a temperature difference ΔT is applied at the (lower) horizontal boundary (case (A) of Foster).
Effect of radiative heat loss on steady hypersonic flow past a blunt body
Authors: Bloor M. I. G.
Published: March 2006

Using the grey gas approximation, the effect of radiative heat loss on axially symmetric flows is studied. Using an expansion procedure about the axis of symmetry, a numerical solution for the stagnation region is found taking the shock to be spherical. The results of this calculation are compared with the results of Lighthill's non-radiative constant density solution.
Experiments on a turbulent cylindrical wall jet
Authors: Starr J. B. , Sparrow E. M.
Published: March 2006

The investigation described here is an experimental study directed toward determining flow field and surface friction characteristics of a cylindrical wall jet. The flow configuration is obtained by placing a cylindrical rod along the axis of a converging nozzle. The flow field thus produced consists of a developing turbulent boundary layer co-existing with an outer fluid layer that mixes freely with quiescent surroundings. Direct measurements of fluid friction at the rod surface, performed with a hot-film element, revealed a significant effect of transverse surface curvature on the local friction factor. Velocity profiles at various axial stations exhibited similarity in the outer mixing layer, but not in the boundary layer adjacent to the surface. Representations of the velocity field in terms of law of the wall variables and defect-law variables revealed significant transverse curvature effects. The measured wall-jet velocity profiles could be satisfactorily represented in terms of a law of the wake, wherein the wake function depends on a transverse curvature parameter. In the outer mixing layer, the eddy viscosity data correspond closely to those of free jets.
The thermohaline Rayleigh-Jeffreys problem
Authors: Nield D. A.
Published: March 2006

The onset of convection induced by thermal and solute concentration gradients, in a horizontal layer of a viscous fluid, is studied by means of linear stability analysis. A Fourier series method is used to obtain the eigenvalue equation, which involves a thermal Rayleigh numberRand an analogous solute Rayleigh numberS, for a general set of boundary conditions. Numerical solutions are obtained for selected cases. Both oscillatory and monotonic instability are considered, but only the latter is treated in detail. The former can occur when a strongly stabilizing solvent gradient is opposed by a destablizing thermal gradient. When the same boundary equations are required to be satisfied by the temperature and concentration perturbations, the monotonic stability boundary curve in the (R, S)-plane is a straight line. Otherwise this curve is concave towards the origin. For certain combinations of boundary conditions the critical value ofRdoes not depend onS(for some range ofS) or vice versa. This situation pertains when the critical horizontal wave-number is zero.

A general discussion of the possibility and significance of convection at ‘zero’ wave-number (single convection cell) is presented in an appendix.