bluuebunny/crossref_metadata_2025 huggingface dataset:
Electrical conductivity of low-pressure shock-ionized argon
Authors: Smy P. R. , Driver H. S.
Published: March 2006

The electrical conductivity of shock-ionized argon produced in an electromagnetic shock tube of low attenuation has been measured at shock speeds of March 10–33, with initial pressures of 0·01–2·0 mm Hg. These measurements extend considerably the range of previous measurements performed with pressure-driven shock tubes. With the higher initial pressures or at the highest Mach numbers the measured conductivity is in good agreement with the previous measurements and with the Spitzer–Harm (1953) formula for the conductivity of a fully ionized gas. With the lower initial pressures (which have not previously been investigated) and at the lower March numbers the conductivity falls to less than half of the Spitzer-Harm value. Order-of-magnitude calculations show that diffusion of atoms, and heat conduction by the plasma atoms from the plasma to the shock-tube walls, can cause appreciable plasma cooling (and hence a reduction of the electrical conductivity) with the lowest initial pressures. This mechanism in conjunction with non-attainment of equilibrium ionization appears to explain the observed diminution in conductivity at the lowest pressures, but not the reduced conductivity at the medium pressures.

Induced e.m.f. flow-velocity measurements indicate steady-flow conditions in the shock tube while photomultiplier measurements of the plasma radiation indicate that the column of shock-heated gas is 10–20 cm long; this latter figure is supported by the conductivity measurements. The fact that the length of the shock-heated gas column is not drastically shortened at low initial pressures in constrast to the work of Duff (1959), Roshko (1960) and Hooker (1961) is attributed to the fact that in this experiment both driver and driven gases are at high temperature.
Rough-wall boundary layers in adverse pressure gradients
Authors: Perry A. E. , Joubert P. N.
Published: March 2006

Smooth- and rough-wall boundary layers and fully developed pipe and duct flow investigations are reviewed. It is shown that the effect of roughness on the flow away from the wall can be accounted for by using an equivalent viscosity νe. This viscosity is thought to depend only on the variables at the wall, such as shear stress τ0, fluid density ρ, viscosity μ and the roughness size and geometry and that the relationship between these variables is the same for both boundary layers and duct flow. However, experiments to date have been confined to the ‘rough régime’ and to boundary layers with a zero pressure gradient.

Experiments were performed and the results show that the above finding can be extended to boundary layers with adverse pressure gradients in the rough régime.

A general method for measuring the local boundary-layer characteristics, with roughness and pressure gradients present, is developed.
Turbulent mixing at the top of stratocumulus clouds
Authors: Turner J. S. , Yang I. K.
Published: March 2006

The process of mixing at the top of a turbulent cloud layer contains a new feature which has not been considered in previous studies of mixing; evaporation of liquid water can cause density changes which may affect the dynamics. A model experiment has been devised to study this problem, using liquids whose density behaviour is non-linear to simulate evaporation.

The existence of a moist, stable, turbulent region above cloudtop can be explained using the laboratory results, which suggest that this region can be regarded dynamically as part of the cloud. Comparison of the rates of mixing in the model experiments with and without ‘evaporation’ suggests that evaporation could cause a small decrease in the mixing rate for a given density difference, but the change would be negligible in practice. This result also sheds some light on the mechanism of mixing, in both the linear and non-linear cases.
Magnetic eddies in an incompressible viscous fluid of high electrical conductivity
Authors: Moffatt H. K.
Published: March 2006

It is shown that in an incompressible fluid in which the magnetic diffusivity λ is much less than the kinematic viscosity ν, certain magnetic field distributions of limited spatial extent (conveniently described as magnetic eddies) can exist on a length scale such that the associated Reynolds number and magnetic Reynolds number are respectively small and large compared with unity. The Lorentz forces are in equilibrium with the dynamic forces associated with the fluid motion. The boundary condition imposed on this motion is that at a large distance from a magnetic eddy the velocity field should be a uniform axisymmetric irrotational straining motion. The eddies are steady in the limit λ → 0, but decay slowly in a fluid of finite conductivity. Two particular eddies are considered in detail: a disk-shaped eddy in a compressive straining motion, and a spherical eddy in an extensive straining motion. Possible applications to turbulence in interstellar gas clouds are qualitatively considered.
Observations of turbulence in a tidal current
Authors: Bowden K. F. , Howe M. R.
Published: March 2006

This is a study of the longitudinal and vertical turbulent velocities which were measured both near the surface and near the bottom of an estuarine tidal current. The turbulence spectra, representing mainly the energy-containing eddies of the flow, were derived, and it was also possible to determine values for the Reynolds stresses at different depths and to make an estimate of the scales of the turbulence. The results are compared with similar observations in the open sea and certain features are discussed which resemble those of measurements of turbulent flow in laboratory experiments and in the atmosphere.
A new method for treating supersonic flow past nearly plane wings
Authors: Lewin Myrna , Schmeltzer Robert A.
Published: March 2006

Function-theoretic techniques are used for determining the supersonic flow past a wing of infinite length having a straight leading edge. The problem is reduced to a set of dual integral equations which are solved by function - theoretic methods. This approach is shown to be useful for treating more general - type leading edges yielding closed - form solutions which heretofore have been unobtainable. The general solutions obtained here are shown to be in complete agreement with previous solutions for the flow at large distances downstream on the aerofoil. For a wing of infinite span, the solution reduces to the well - known perturbation potential for a distribution of sources in a horizontal plane.
Departures from the linear equation for vibrational relaxation in shock waves in oxygen and carbon dioxide
Authors: Zienkiewicz H. K. , Johannesen N. H.
Published: March 2006

The detailed structure of the relaxation region in shock waves in oxygen was investigated using Blackman's experimental results. Oxygen was found to display a behaviour similar in many ways to that found previously for carbon dioxide with the relaxation frequency, as defined by the simple relaxation equation, depending on the departure from equilibrium as well as on temperature. The previous results for carbon dioxide were further analysed by means of a separate relaxation equation for each mode.
Shock-expansion theory and simple wave perturbation
Authors: Jones J. G.
Published: March 2006

The calculation by shock-expansion theory of supersonic aerofoil flow fields with varying entropy is simplified by assuming the flow behind the curved attached shock to be a small perturbation of a simple wave. A characteristic perturbation method is used.
A linearized theory for rotational supercavitating flow
Authors: Street Robert L.
Published: March 2006

In this paper methods are given for establishing qualitative and quantitative measures of the effects of rotation in supercavitating flows past slender bodies. A linearized theory is developed for steady, two-dimensional flow under the assumption that the flow has a constant rotation throughout. The stream function of the rotational flow satisfies Poisson's equation. By using a particular solution of this equation, the rotational problem is reduced to a problem involving Laplace's equation and harmonic perturbation velocities. The resulting boundary-value problem is solved by use of conformal mapping and singularities from thinairfoil theory. The theory is then applied to asymmetric shear flow past wedges and hydrofoils and to symmetric shear flow past wedges. The presence of rotation is shown to create significant changes in the forces acting on the slender bodies and in the shape and size of the trailing cavities.
The effect of confining walls on the stability of the steady wake behind a circular cylinder
Authors: Shair* F. H. , Grove A. S. , Petersen E. E. , Acrivos A.
Published: March 2006

The results of an experimental investigation are presented to show that the stability of the steady laminar wake behind a circular cylinder is strongly influenced by the proximity of the walls of the confining experimental equipment.
Viscous and resistive eddies near a sharp corner
Authors: Moffatt H. K.
Published: March 2006

Some simple similarity solutions are presented for the flow of a viscous fluid near a sharp corner between two planes on which a variety of boundary conditions may be imposed. The general flow near a corner between plane boundaries at rest is then considered, and it is shown that when either or both of the boundaries is a rigid wall and when the angle between the planes is less than a certain critical angle, any flow sufficiently near the corner must consist of a sequence of eddies of decreasing size and rapidly decreasing intensity. The ratios of dimensions and intensities of successive eddies are determined for the full range of angles for which the eddies exist. The limiting case of zero angle corresponds to the flow at some distance from a two-dimensional disturbance in a fluid between parallel boundaries. The general flow near a corner between two plane free surfaces is also determined; eddies do not appear in this case. The asymptotic flow at a large distance from a corner due to an arbitrary disturbance near the corner is mathematically similar to the above, and has comparable properties. When the fluid is electrically conducting, similarity solutions may be obtained when the only applied magnetic field is that due to a line current along the intersection of the two planes; it is shown that the effect of such a current is to widen the range of corner angles for which eddies must appear.
Resonant oscillations in closed tubes
Authors: Chester W.
Published: March 2006

An investigation is made of the disturbances produced in a closed, gas-filled tube by the oscillations of a piston at one end, when the piston oscillates at near resonant frequencies. Within a well-defined frequency band around each resonant frequency, shock waves appear in the solution; outside this interval the oscillations are continuous, but not purely sinusoidal.

The solution includes the effects of compressive viscosity, and of shear viscosity in the boundary layer at the walls of the tube. For typical laboratory conditions the effect of compressive viscosity is found to be quite small (giving a shock thickness of the order of 10−4in.). The boundary layer effect can be more significant, though the most important modification required of the usual acoustic theory is found to arise from the non-linear terms.
A wake model for free-streamline flow theory Part 2. Cavity flows past obstacles of arbitrary profile
Authors: Wu T. Yao-Tsu Wu , Wang D. P.
Published: March 2006

In Part 1 of this paper a free-streamline wake model was introduced to treat the fully and partially developed wake flow or cavity flow past an oblique flat plate. This theory is generalized here to investigate the cavity flow past an obstacle of arbitrary profile at an arbitrary cavitation number. Consideration is first given to the cavity flow past a polygonal obstacle whose wetted sides may be concave towards the flow and may also possess some gentle convex corners. The general case of curved walls is then obtained by a limiting process. The analysis in this general case leads to a set of two functional equations for which several methods of solution are developed and discussed.

As a few typical examples the analysis is carried out in detail for the specific cases of wedges, two-step wedges, flapped hydrofoils, and inclined circular are plates. For these cases the present theory is found to be in good agreement with the experimental results available.
Correlation measurements in a non-frozen pattern of turbulence
Authors: Fisher M. J. , Davies P. O. A. L.
Published: March 2006

The properties of a turbulent flow are often described in terms of velocity correlations in space, in time, and in space-time. In this paper the interpretation of velocity correlation measurements which are made in a region of highintensity turbulence is considered in some detail. Under these conditions it is shown that some account must be taken of the effects of both mean and fluctuating shear stresses which are continuously modifying the turbulent structure. For an almost frozen pattern, for example, in the turbulence behind a grid, the turbulent convection velocity is amost equal to the mean flow velocity, while the space correlation and auto-correlation of the velocity fluctuations are simply related through this velocity. In contrast to this, when the intensity is high, the convection velocity may differ considerably from the mean velocity, while it is shown that different turbulent spectral components appear to travel at different speeds. This means that the turbulent spectrum and the turbulent space scales are no longer simply related. For example, the high-frequency spectral components may be ascribed to both the high-velocity eddies and the small wave-number components acting together.

Experimental results are presented which indicate the conditions under which the assumption of a frozen pattern leads to uncertainties in the subsequent interpretation of the measurements. The measurements also show that the observed difference between the mean and the convection velocity may be qualitatively explained in terms of the skewness of the velocity signals.
The drag of a compressible turbulent boundary layer on a smooth flat plate with and without heat transfer
Authors: Spalding D. B. , Chi S. W.
Published: March 2006

The theoretical treatments given by earlier authors are classified, reviewed and where necessary extended; then the predictions of twenty of these theories are evaluated and compared with all available experimental data, the root-meansquare error being computed for each theory. The theory of van Driest-II gives the lowest root-mean-square error (11.0%).

A new calculation procedure is developed from the postulate that a unique relation exists betweencfFcandRFRwherecfis the drag coefficient,Ris the Reynolds number, andFcandFRare functions of Mach number and temperature ratio alone. The experimental data are found to be too scanty for bothFcandFRto be deduced empirically, soFcis calculated by means of mixing-length theory andFRis found semi-empirically. Tables and charts of values ofFcandFRare presented for a wide range ofMGandTS/TG. When compared with all experimental data, the predictions of the new procedure give a root-mean-square error of 9.9%.
Effect of finite boundaries on the Stokes resistance of an arbitrary particle Part 2. Asymmetrical orientations
Authors: Brenner Howard
Published: March 2006

A general treatment is given of the first-order effects of wall proximity on the increased resistance to translational motions of a rigid particle of arbitrary shape settling in the Stokes régime. The analysis generalizes a previous treatment (Brenner 1962) to the case where the principal axes of resistance of the particle may have any orientation relative to the principal axes of the bounding walls. It is shown that, to the first order in the ratio of particle-to-boundary dimensions, the increased resistance of the particle can be represented by a symmetric, second-rank tensor (dyadic) whose value is independent of particle shape and orientation.
On the cellular patterns in thermal convection
Authors: Stuart J. T.
Published: March 2006

In the theory of thermal convective instability between two horizontal planes there are many solutions that are periodic in the horizontal co-ordinates, while in experiment convection is observed to take place in cellular patterns. It is often assumed, or decided after insufficient argument, that the periodic solutions of the mathematical model ‘explain’ or correspond to these patterns, but a completely satisfactory discussion of this correspondence has not been given. Indeed, with certain mathematical solutions ambiguities arise as to what cell centres and cellular boundaries are. A detailed discussion has recently become especially necessary because attempts are being made to predict which particular cellular pattern will occur in given experimental conditions.

In this paper the topic is studied afresh and the question is asked: what features, in the mathematical model, correspond to what an experimentalist observes in cellular convective motion? In answer a definition of a cell is formulated which relates certain surfaces in the flow field of the mathematical model to steady vertical cellular boundaries that are observed in experiment, and which shows where the cell centres lie. In particular the classical hexagonal cellular pattern, of the mathematical model, is shown to be the prototype pattern of what is experimentally observed. On the other hand the square and so called ‘rectangular’ cases of linearized theory are shown not to correspond truly to square and rectangular cells at all. The new formulation is especially relevant to theoretical work on the prediction of cell shape and direction of flow in cells, since precise knowledge of the shapes of the cellular boundaries and locations of cell centres is essential if predictions are to be compared with observation.
Thermal instability in a horizontal fluid layer: effect of boundary conditions and non-linear temperature profile
Authors: Sparrow E. M. , Goldstein R. J. , Jonsson V. K.
Published: March 2006

An investigation is carried out to determine the conditions marking the onset of convective motion in a horizontal fluid layer in which a negative temperature gradient occurs somewhere within the layer. In such cases, fluid of greater density is situated above fluid of lesser density. Consideration is given to a variety of thermal and hydrodynamic boundary conditions at the surfaces which bound the fluid layer. The thermal conditions include fixed temperature and fixed heat flux at the lower bounding surface, and a general convective-radiative exchange at the upper surface which includes fixed temperature and fixed heat flux as special cases. The hydrodynamic boundary conditions include both rigid and free upper surfaces with a rigid lower bounding surface. It is found that the Rayleigh number marking the onset of motion is greatest for the boundary condition of fixed temperature and decreases monotonically as the condition of fixed heat flux is approached. Non-linear temperature distributions in the fluid layer may result from internal heat generation. With increasing departures from the linear temperature profile, it is found that the fluid layer becomes more prone to instability, that is, the critical Rayleigh number decreases.
The flow in the mixing region of a jet
Authors: Kolpin Marc A.
Published: March 2006

The object of this work was to investigate experimentally the structure of the early shear layer of high-speed jets and its relation to the mechanism of noise generation. Of special interest was the question of the existence of periodic fluctuations in the velocity field. The experimental investigation is divided in three parts.

Optical observation of the jet flow by means of the shadowgraph technique.

Measurement of mean Mach number and temperature profiles.

Survey by means of hot-wire of the component of the fluctuating velocity field in the mean flow direction.

The shadowgraphs show very interesting features of the breakdown process of free shear layers, but fail to show any propagation of strong acoustic disturbances in the near pressure-field.

Mean profile measurements show that the flow field in the range 1 [les ]x/d[les ] 4 develops in a conical fashion, i.e. the mean profiles in Mach number and temperature can be expressed in terms of a single conical variable η = (2r–d)/2x. The fluctuating velocity field is described in terms of the intensity of turbulence, its spectral distribution, and two-point space-time correlation functions. Similarity laws are given for the power spectra and the space-time correlation functions. On the cylinderr= ½d, the convection speed of the turbulent field is different for the different eddy sizes, varying from the local mean speed for small eddies to ½Uexitfor the large eddies. Measurements of the angular correlation function are reported which show no correlation of the fluctuations across the jet diameter.
Magnetohydrodynamic free convection
Authors: Riley N.
Published: March 2006

The flow of an electrically conducting fluid up a hot vertical plate in the presence of a strong magnetic field normal to the plate is considered. A solution is developed based on the idea of matching ‘outer’ and ‘inner’ solutions in the moving layer of fluid. An approximate Pohlhausen method of solution is also given which yields results in fairly good agreement with the exact analysis.
Flow of an inviscid fluid past a sphere in a pipe
Authors: Lai Wei
Published: March 2006

The problem of flow of an inviscid, incompressible fluid inside a circular pipe, with a sphere on the axis of the pipe, has been studied by Lamb (1936) (irrotational flow), Long (1953) and Fraenkel (1956) (swirling flow). Because of the difficulty of satisfying all the boundary conditions in the problem, only approximate solutions, valid for spheres of small diameter (compared with that of the pipe) have been obtained. In this paper, it is found that by introducing a vortex sheet over a segment of the diameter of the sphere, flow patterns can be obtained by an inverse method for the case of large spheres. Four different types of flow are considered: (1) irrotational flow, (2) swirling flow with constant axial and angular velocities far upstream, without lee waves, (3) swirling flow with constant axial and angular velocities far upstream, with lee waves, and (4) rotational flow with a paraboloidal velocity distribution far upstream.
A slender-body theory for ship oscillations in waves
Authors: Newman J. N.
Published: March 2006

A linearized theory is developed for the oscillations of a slender body which is floating on the free surface of an ideal fluid, in the presence of incident plane progressive waves. Green's theorem is used to represent the velocity potential and the first-order slender-body potential is developed from asymptotic approximation. The general theory is valid for arbitrary slender bodies in oblique waves, and detailed results are presented for a body of revolution.
Some methods for flows past blunt slender bodies
Authors: Tuck E. O.
Published: March 2006

It is suggested that the use of prolate spheroidal co-ordinates in certain problems involving slender bodies may lead to results which not only are more likely to be uniformly valid for blunt bodies, but in many cases require less complicated analysis than results obtained by standard methods which use cylindrical co-ordinates. The method is developed for a simple problem in potential theory and is then applied also to a problem in Stokes flow, yielding a procedure for obtaining the Stokes drag on a slender body of arbitrary shape. For comparison purposes, consideration is also given to the use of both cylindrical and di-polar co-ordinates, and as a by-product of the comparison of results on cylindrical and spheroidal systems some new simple formulae involving Legendre polynomials are obtained heuristically, and then rigorously proved.
On the pressure induced by the boundary layer on a flat plate in shear flow
Authors: Toomre Alar , Rott Nicholas
Published: March 2006

The problem solved is that of the interaction between a laminar boundary layer on a semi-infinite flat plate and an oncoming shear flow of finite lateral dimensions bounded by uniform irrotational flow extending to infinity. The pressures along the plate and upstream of the same are deduced (to a linearized approximation) in the form of a Fourier integral based on the solution of a simpler periodic flow problem. It is found that while the assumption of an infinite, uniform shear flow gives asymptotically correct interaction pressure gradients on the plate near the leading edge, the pressure level even there (compared to upstream infinity) is strongly influenced by the boundedness of the external shear. At distances from the leading edge which are large compared to the lateral extent of the shear flow, the pressure gradients along the plate are shown to be vanishingly smaller than in the infinite shear case.
The interaction of transverse electromagnetic plane waves and a moving ionizing shock wave in the presence of a magnetic field
Authors: Hughes W. F. , Young F. J.
Published: March 2006

Propagation of a transverse electromagnetic wave along a d.c. magnetic field and interaction with a moving shock wave is investigated. The direction of propagation is normal to the shock front. Solutions to electromagnetic fields, gas velocities and Doppler shifts in frequency are found in both the ionized and un-ionized gases. A frequency is obtained at which electromagnetic reflexion from the shock front is minimized. In the ionized gas behind the shock front a fast and a slow electromagnetic wave result. By adjusting the shock velocity the frequency of the slow wave can be either raised or lowered. This frequency change, however, is not the Doppler shift and, consequently, can be made much larger than the Doppler shifts encountered at non-relativistic velocities. The slow wave attenuates much less than the ordinary fast wave, and applications to diagnostics and communications through plasmas and laser-beam frequency multiplication may be possible.
Experimental studies on the motion of a flexible hydrofoil
Authors: Kelly H. R. , Rentz A. W. , Siekmann J.
Published: March 2006

A thin, flexible hydrofoil has been used as a model to simulate the swimming of a two-dimensional fish in an ideal, incompressible fluid, as treated in recent theoretical papers. The apparatus is described in some detail and typical data are compared with the predictions of theory. An error analysis is given, showing that, within the expected errors and limits of validity of theory, experimental verification of theory is very good.
On magnetohydrodynamic flows with aligned magnetic fields
Authors: Glauert M. B.
Published: March 2006

The boundary layers due to finite viscosity and magnetic diffusivity are studied in relation to two models of the flow of a conducting fluid past a body in an aligned magnetic field. In each case it is deduced that the growth of the boundary layer may have substantial effects, such as to raise doubts about the validity of the assumed basic flow patterns.
An experimental investigation of the steady separated flow past a circular cylinder
Authors: Grove A. S. , Shair F. H. , Petersen E. E.
Published: March 2006

The steady separated flow past a circular cylinder was investigated experimentally. By artificially stabilizing the steady wake, this system was studied up to Reynolds numbers R considerably larger than any previously attained, thus providing a much clearer insight into the asymptotic character of such flows at high Reynolds numbers. Some of the experimental results were unexpected. It was found that the pressure coefficient at the rear of the cylinder remained unchanged for 25 [les ] R [les ] 177, that the circulation velocity within the wake approached a non-zero limit as the Reynolds number increased, and that the wake length increased in direct proportion to the Reynolds number.
On the near-equilibrium and near-frozen regions in an expansion wave in a relaxing gas
Authors: Jones J. G.
Published: March 2006

A weak expansion wave propagating in a relaxing gas is discussed with particular reference to the ‘near-equilibrium’ and ‘near-frozen’ regions. The concept of bulk viscosity is used in conjunction with Burger's equation in the near-equilibrium region. The asymptotic equilibrium simple wave is modified by diffusive regions in the neighbourhood of the first and last rays. It is shown that in the case of a weak expansion wave, Chu's asymptotic solution of the acoustic equation describes the wave-form for a finite time interval before convection effects become noticeable. In the near-frozen region a characteristic perturbation method is used to describe the flow near the wave-front.
On the theory of growing cavities behind hydrofoils
Authors: Woods L. C.
Published: March 2006

A general theory of unsteady cavitating flow past hydrofoils and other obstacles is given for the case of cavities of finite length L. If the circulation Γ, the cavity volume V and L are known as functions of time, the theory yields explicit formulae for the velocity over the wetted surface and for the cavitation number σ. The theory is based on the approximation that the cavity is bounded by stream-lines, and so is valid only for slow rates of change of L, V and Γ. The possibility of allowing for the presence of a vortex sheet behind the cavity is discussed. The theory is extended to the case of a cascade of hydrofoils behind which extend growing cavities.

Two examples of the theory are discussed, namely the unsteady flow past a symmetrical wedge, and the unsteady flow past a flat plate hydrofoil cavitating from the leading edge.
Note on the interpretation of two-dimensional theories of growing cavities
Authors: Benjamin T. Brooke
Published: March 2006

It is shown in general how a two-dimensional flow can be justified as a physical approximation, notwithstanding the logarithmic singularity in pressure that occurs at infinity when the cavity expands or contracts at a varying rate. The argument presented, which affords a more natural interpretation than alternatives previously suggested, refers to the approximate equivalence-to a determinable degree of accuracy-between the hypothetical plane flow and the inner region of some real three-dimensional flow with small spanwise variations. The main ideas are illustrated by the example of a long ellipsoidal body which changes in volume while also undergoing shape perturbations.
Higher approximations in boundary-layer theory Part 3. Parabola in uniform stream
Authors: Dyke Milton Van
Published: March 2006

The classical laminar boundary layer on a parabolic cylinder is calculated using the Blasius series, with modifications to improve convergence, and supplemented by an asymptotic expansion valid far downstream from the nose. The flow due to displacement thickness is thereby found with sufficient accuracy to permit evaluation of its second-order effect upon the boundary layer near the stagnation point. The skin friction and heat transfer are found to be reduced there by both displacement and curvature.
On cellular convection driven by surface-tension gradients: effects of mean surface tension and surface viscosity
Authors: Scriven L. E. , Sternling C. V.
Published: March 2006

The onset of steady, cellular convection driven by surface tension gradients on a thin layer of liquid is examined in an extension of Pearson's (1958) stability analysis. By accounting for the possibility of shape deformations of the free surface it is found that there is no critical Marangoni number for the onset of stationary instability and that the limiting case of ‘zero wave-number’ is always unstable. Surface viscosity of a Newtonian interface is found to inhibit stationary instability. A simple criterion is found for distinguishing visually the dominant force, buoyancy or surface tension, in cellular convection in liquid pools.
Contribution to the theory of cellular thermal convection
Authors: Palm Enok , Øiann Henry
Published: March 2006

In a previous paper on cellular thermal convection (Palm 1960) the importance of the effect caused by temperature variation of kinematic viscosity was pointed out. It was demonstrated that this effect would, owing to non-linear interactions, lead to a tendency towards hexagonal cells. For mathematical simplicity, only the interaction of two wave-components was taken into account.

Segel & Stuart (1962), working with the same equations, have examined the stability of the various equilibrium solutions. They arrive at the important conclusion that a necessary condition for the solution corresponding to hexagons to be stable is that the variation of viscosity with temperature be sufficiently great.

In the present paper the problem is discussed from a somewhat more general point of view. First it is shown that, when the variation of viscosity with temperature is sufficiently great, the solution corresponding to hexagons is the only stable one if only two wave-components are taken into account. To examine if this result is also true when the motion consists of an arbitrary number of wave-components, the case of three wave-components is studied. It turns out that in this case also the only possible mode is the pattern consisting of hexagons. The validity of this result is easily extended to a more general class of wave-components. It is shown that the solution corresponding to hexagons is stable for all small disturbances which can possibly occur. To prove this it is necessary to take into account non-linear disturbance theory.

A reasonable conclusion from the paper by Segel & Stuart and the present paper is that a hexagonal pattern is observed only when a condition of the form (6.9) is fulfilled. Experiments concerning this problem are, however, lacking.
The production and diffusion of vorticity in duct flow
Authors: Brundrett E. , Baines W. D.
Published: March 2006

Secondary flows in non-circular ducts are accompanied by a longitudinal component of vorticity. The equation of motion defining this component in a turbulent flow is composed of three terms giving the rates of production, diffusion and convection. Since the expression for production is the second derivative of Reynolds strees components, longitudinal vorticity cannot exist in laminar flow. For turbulent flow in a square duct the Reynolds stress tensor is examined in detail. Symmetry requirements alone provide relationships showing that the production is zero along all lines of symmetry. General characteristics of flow in circular pipes are sufficient to indicate where the production must be greatest. Experimental measurements verify this result and define the point density of production, diffusion and convection of vorticity. Data also indicate that the basic pattern of secondary flow is independent of Reynolds number, but that with increasing values of Reynolds number the flows penetrate the corners and approach the walls. A similar experimental investigation of a rectangular duct shows that the corner bisectors separate independent secondary flow circulation zones. Production of vorticity is again associated with the region near the bisector. However, there is some evidence that the secondary flow pattern is not so complex as inferred from the distortion of the main longitudinal flow.
The magnetohydrodynamic squeeze film
Authors: Kuzma Dennis C. , Maki E. Roland , Donnelly Russell J.
Published: March 2006

Magnetohydrodynamic squeeze films are investigated theoretically and experimentally. The theory of magnetohydrodynamic lubrication as applied to squeeze films is extended to include fluid-inertia effects and buoyant forces. Excellent agreement is obtained between theory and experiment.
Study of rarefied shear flow by the discrete velocity method
Authors: Broadwell James E.
Published: March 2006

The application of a simple discrete velocity model to low Mach number Couette and Rayleigh flow is investigated. In the model, the molecular velocities are restricted to a finite set and in this study only eight equal speed velocities are allowed. The Boltzmann equation is reduced by this approximation to a set of coupled differential equations which can be solved in closed form. The fluid velocity and shear stress in Couette flow are in approximate accord with those of Wang Chang & Uhlenbeck (1954) and of Lees (1959) over the complete range of Knudsen number. Similarly, the Rayleigh flow solution is remarkably like those found by other investigators using moment methods.
Steady flow past non-uniform wire grids
Authors: McCarthy J. H.
Published: March 2006

A solution is obtained for steady, moderately sheared, three-dimensional flow past a wire grid of arbitrary resistance distribution which is placed normal to the axis of a duct of arbitrary but constant cross-section. The formulation presented is an extension of those given by Owen & Zienkiewicz (1957) and Elder (1959) for weakly shared, two-dimensional flow past wire grids. Unlike these earlier formulations, however, in the present study the equations of motion are solved without placing restrictions on the magnitude of variation of resistance across the grid. The resulting solution, taking account of streamline deflexions, is verified experimentally for moderately sheared flow past three grids constructed to produce three widely differing velocity distributions in a water tunnel of circular cross-section.
A demonstration of Alfvén waves Part 1. Generation of standing waves
Authors: Jameson Antony
Published: March 2006

In this paper the equations for Alfvén waves are examined and conditions necessary for the occurrence of resonance are determined. An experiment using liquid sodium inside a torus is described. Waves were generated by means of alternating current supplied to a coil around the torus. A strong resonance was observed at the fundamental frequency, and a weak resonance at three times this frequency. At the fundamental resonance the alternating magnetic field attained magnitudes more than 9 times the magnitude of the field that would have been generated in free space by the exciting current. The results were in good agreement with prediction.
The stability of a viscous fluid between rotating cylinders with an axial flow
Authors: Krueger E. R. , Prima R. C. Di
Published: March 2006

The stability of viscous flow between rotating cylinders with an axial flow has been investigated theoretically by Goldstein (1937), Chandrasekhar (1960, 1962), and Di Prima (1960); and experimentally by Cornish (1933), Fage (1938), Kaye & Elgar (1957), Donnelly & Fultz (1960) and Snyder (1962a). As was pointed out by Di Prima (1960) there were a number of discrepancies in the early work of the 1930's which were clarified in part by the papers of the 1960's. In turn, there appear to be certain small detailed differences in the more recent papers. In part it is these differences with which the present paper is concerned. In addition, the results of the previous theoretical investigations which are limited to the case in which the cylinders rotate in the same direction, are extended to the case of counter rotation.
On the inviscid instability of the hyperbolictangent velocity profile
Authors: Michalke A.
Published: March 2006

The Rayleigh stability equation of inviscid linearized stability theory was integrated numerically for amplified disturbances of the hyperbolic-tangent velocity profile. The evaluation of the eigenvalues and eigenfunctions is followed by a discussion of the streamline pattern of the disturbed flow. Here no qualitative distinction is found between an amplified and the neutral disturbance. But considering the vorticity distribution of the disturbed flow it is shown that in the case of amplified disturbances two concentrations of vorticity occur within a disturbance wavelength, while in the neutral case only one maximum of vorticity exists. The results are discussed with respect to the instability mechanism of free boundary-layer flow.
Turbulence in the noise-producing region of a circular jet
Authors: Bradshaw P. , Ferriss D. H. , Johnson R. F.
Published: March 2006

The flow in the noise-producing region of a circular jet is found to be dominated by a group of large eddies, containing nearly a quarter of the turbulent shear stress in the quasi-plane region of the shear layer: their contribution to the shear stress decreases as the effects of axisymmetry become noticeable at more than about two diameters downstream of the nozzle. These large eddies appear to be almost entirely responsible for the irrotational fluctuations near the nozzle, which, for this and other reasons, are larger relative to the reference dynamic pressure than in other shear flows. As a consequence of this, the convection velocity near the high- and low-velocity edges of the flow is biased towards the mean velocity in the high-intensity region. The dominance of the large eddies therefore explains the measurements of near-field pressure fluctuations by Franklin & Foxwell (1958), and of convection velocity by Davies, Barratt & Fisher (1963) and the present authors. The strength of these large eddies, compared with those in the boundary layer or wake, is remarkable.

The large eddies appear to be mixing-jets similar to those found by Grant (1958) in the wake, but with their projection in the (y, z)-plane inclined at about 45° to the y (radial) axis instead of lying along the y-axis as in the wake.

It is suggested that the augmentation of these large eddies by artificial means could be used to increase the mixing rate and permit the reduction of jet noise by means of acceptably short ejector shrouds.

The medium-scale motion is found to be far from isotropic in scales, although the two scales associated with a given vorticity component are more nearly equal. This phenomenon is also noticeable in the wake.

It is found that the departure from self-preservation, which starts when the shear layer thickness is no longer small compared with the nozzle radius, does not grossly affect the region of high turbulence intensity and maximum noise production until this region itself is no longer small compared with the radius. The maximum shear stress seven diameters downstream of the exit is still 70% of its value near the exit, and the non-dimensional mean velocity gradient is practically unchanged.
Time-reversed flows
Authors: Slattery John C.
Published: March 2006

Under the assumption that the local acceleration and inertial terms are to be neglected in the equation of motion, a comparison is made between the unsteadystate movement of a suspension of particles and the same problem in reversed (or negative) time. The formalized discussion confirms Bretherton's (1962) conclusion that, if in a steady unidirectional shear flow at small Reynolds number a rotationally symmetric particle twice assumes a position with its axis of rotation in the plane perpendicular to the flow, its orbit must be periodic. The reversibility phenomena observed by S. G. Mason (1963) in dilute and concentrated suspensions are explained as well.
Drag on an axially symmetric body vibrating slowly along its axis in a viscous fluid
Authors: Kanwal R. P.
Published: March 2006

Let D0 be the Stokes drag on an axially symmetric body moving parallel to its axis with velocity U0 through an unbounded fluid. The drag D experienced by the same body oscillating with velocity U = U0eiσt along its axis in the unbounded fluid is given by the expression
$\frac{D}{D_0} = \left \{{1 +{\frac {d_0}{6 \surd{(2)} \pi \mu a U_0}}(1+i)M+O(M^2)}\right \}e^{i \sigma t},$
where a is any characteristic particle dimension and
$M^2 = a^2 \sigma \rho |\mu$
is a dimensionaless number. The part of this drag formula which gives the energy dissipation is calculated for bodies of various shapes.
On the swimming of a flexible plate of arbitrary finite thickness
Authors: Uldrick J. P. , Siekmann J.
Published: March 2006

This paper studies the effect of profile thickness on the propulsive forces generated by the swimming of a two-dimensional fish. Comparison of numerical calculations with reported experimental data shows good agreement and demonstrates a decrease of thrust with increasing thickness. Previous two-dimensional linearized theories on fish propulsion dealing with the motion of an infinitesimally thin hydrofoil are included in the present contribution as special cases.
Instability of the flow between rotating cylinders: the wide-gap problem
Authors: Sparrow E. M. , Munro W. D. , Jonsson V. K.
Published: March 2006

An analytical investigation is carried out to determine the conditions for instability in a viscous fluid contained between rotating coaxial cylinders of arbitrary radius ratio. A solution method is outlined and then applied to cylinders having radius ratios ranging from 0·95 to 0·1. Consideration is given to both cases wherein the cylinders are rotating in the same direction and in opposite directions. Results are reported for the Taylor numbers and wave-numbers which mark the onset of instability. The present results are also employed to delineate the range of applicability of the closed-form instability predictions of Taylor and of Meksyn, which were derived for narrow-gap conditions.
On the stability of viscous flow between rotating cylinders Part 1. Asymptotic analysis
Authors: Duty R. L. , Reid W. H.
Published: March 2006

The stability of Couette flow is discussed in the case in which the cylindes rotate in opposite directions by an asymptotic method in which the Taylor number is treated as a large parameter. On assuming the principle of exchange of stabilities to hold, the problem is then governed by a sixth-order differential equation with a simple turning point. It is shown how the solutions of this equation can be represented asymptotically in terms of the solutions of the comparison equation yvi = xy. The solutions of this comparison equation have recently been tabulated and we thus have an explicit representation of the solution of the stability problem in terms of tabulate functions. Detailed results for the critical Taylor number and wave-number at the onset of instability and the associated eigenfunctions are given for the limiting case μ → − ∞, where μ = Ω2/Ω1, and Ω1 and Ω2 are the angular velocities of the inner and outer cylinders respectively. In this limiting case it is found that there exists and infinite number of cells between the cylinders, but that the amplitude of the secondary motion in all but the innermost cell is small.
Instability of a viscous fluid of variable density in a magnetic field
Authors: Dunwoody N. T.
Published: March 2006

The instability to small two-dimensional disturbances of an electrically conducting fluid of variable density is investigated. The viscous fluid is bounded between two vertical parallel planes normal to which a magnetic field of constant intensity is applied. Significant parameters upon which the behaviour of the Rayleigh number at neutral stability depends are the Hartmann number M and the wave-number α which is associated with a periodic disturbance with periodicity in the unbounded horizontal direction.

The solution may be sought by considering basic disturbances which are either symmetric or antisymmetric about the median plane parallel to the boundary planes. It is found that for a given magnetic field strength the critical Rayleigh number governing stability is associated with an antisymmetric disturbance of zero wave-number. The least stable symmetric disturbance which arises when the wave-number is zero is less easily excited. This trend is seen again in the purely hydrodynamic case (M = 0) where, corresponding to a finite wave-numbe value, the more unstable mode at neutral stability is found to be an antisymmetric one.

The most unstable situation occurs when both the Hartmann number and the wave number zero. In this case the result of Wooding (1960) that the minimum critical Rayleigh number is zero and is associated with a symmetric disturbance is reobtained.