bluuebunny/crossref_metadata_2025_split huggingface dataset:
The influence of radiative transfer on cellular convection
Authors: Goody R. M. 
Published: March 2006

This paper presents an approximate solution of the problem of the onset of convection between plane-parallel plates heated from below when the fluid between them absorbs and emits thermal radiation. A complete solution to this problem would be extremely difficult, and the equation of radiative transfer is therefore developed in two approximate forms, one appropriate to an opaque medium, the other to a transparent medium. This equation is then combined with the dynamical equations of the problem.The initial static state is investigated by use of the Milne-Eddington approximation, and it is shown that there can be very large variations of temperature near to the boundaries.The conditions for marginal stability are investigated both for motions which are restricted to the temperature boundary layer, and for motions which take place in the body of the fluid. In the former case it is found that a complete solution is provided by the approximate form for a transparent medium, and in the latter case a reasonable interpolation has to be made between results for the two approximate forms in order to complete the solution.The effect of radiative transfer both on the initial static state and on the dynamical equations is such that the fluid is stabilized. This stabilization could probably be detected in the laboratory under certain conditions. In the earth's atmosphere the critical Rayleigh number for large scale motions may be increased by a factor 105, while at the surface of the solar photosphere the factor may be as large as 1012.
The almost-rigid rotation of viscous fluid between concentric spheres
Authors: Proudman Ian 
Published: March 2006

Two concentric spheres are supposed to rotate about the same axis with almost the same angular velocity, so that the viscous stresses over the surfaces of the spheres induce a flow which may be represented by a small perturbation superimposed upon a rigid body rotation of the fluid as a whole. The governing equations are therefore linearized in the magnitude of the perturbation, and it appears that the validity of this linearization is independent of the Reynolds number of the primary rotation. Attention is then restricted to the case in which the Reynolds number is large, the principal object of the note being to exemplify some of the properties of rotating systems at large Reynolds numbers in terms of a particularly simple mathematical model.It is found that the cylindrical surface that touches the inner sphere (the axis being the axis of rotation) is a singular surface in which velocity gradients are very large. Everywhere outside this cylinder, the fluid rotates as a rigid body with the same angular velocity as the outer sphere. Inside the cylinder, the velocity distribution in the central (inviscid) core of the motion is shown to be determined by the velocity distribution in the boundary layers over the spheres, and explicit solutions are obtained for all these velocity distributions. The mechanics of the cylindrical shear layer itself is also discussed, though no explicit solution is obtained in this case.
Buoyant plumes in a moist atmosphere
Authors: Morton B. R. 
Published: March 2006

This paper describes a simple model which can be used to investigate the transport of water vapour by thermal plumes in the atmosphere. For an approximate treatment of these plumes, it is assumed (as in a previous paper) that the vertical velocity, temperature and specific humidity are constant across the ascending column, and that the inflow velocity due to mixing at the edge of the plume is proportional to the vertical velocity within the plume. The behaviour of the rising air is then investigated by means of equations representing the conservation of mass, momentum, heat and water vapour, and numerical solutions are obtained for representative cases.It is shown that in a stably stratified atmosphere the plume air will become saturated if the source is sufficiently strong, and that the height of this saturation level can be determined in terms of dimensionless parameters representative of the source and the environment. Above the saturation level the analysis is continued by taking into account both vapour and liquid phases of water, and an approximate treatment is given for the behaviour of small plume clouds. It is found that there is a critical size for these; smaller clouds remain characteristic of the plume, but larger ones extend upwards to heights which do not depend on the previous parameters.
Diffusion from a fixed source at a height of a few hundred feet in the atmosphere
Authors: Hay J. S. , Pasquill F. 
Published: March 2006

The results of measurements of the vertical distribution of airborne particles, released usually at a height of 500 ft., and sampled for periods of about 30 minutes at downwind distances of 100, 300 and 500 metres, are presented and discussed.At all distances the frequency distributions of the particle elevation with respect to the site of release are closely similar in shape and size to the frequency distribution of wind inclination at the site of release. This is interpreted as showing that, despite the uncorrelated effects of small eddies, high correlation was maintained in the motion of a particle, for periods of 1 minute or more, by the dominant action of persistent eddies which contributed heavily to the turbulent energy. In contrast to this result, the wind observations showed that the Eulerian auto-correlation coefficient (Rr) fell to about 0.2 in 10 seconds.
The effect of a magnetic field on Stokes flow in a conducting fluid
Authors: Chester W. 
Published: March 2006

Low Reynolds number flow of a conducting fluid past a sphere is considered. The classical Stokes solution is modified by a magnetic field which, at infinity, is uniform and in the direction of flow of the fluid.The formula for the drag is found to be
$D = D_S \{ 1+\frac{3}{8}M+\frac{7}{960}M^2-\frac{43}{7680}M^3+O(M^4) \},$
Where DS is the Stokes drag and M is the Hartmann number.
On the non-linear mechanics of hydrodynamic stability
Authors: Stuart J. T. 
Published: March 2006

In most work on the theory of stability of laminar flow, infinitesimal disturbances only have been considered, so that only the initial growth of the disturbance has been determined. It is the object of the present paper to extend the theory to larger amplitudes and to study the mechanics of disturbance growth with the inherent non-linearity of the hydrodynamical system taken into account.The Reynolds stress (where averages are taken with respect to some suitable space coordinate) is the fundamental consequence of the non-linearity, and its effects can be anticipated as follows. Initially a disturbance grows exponentially with time according to the linear theory, but eventually it reaches such a size that the transport of momentum by the finite fluctuations is appreciable and the associated mean stress (the Reynolds stress) then has an appreciable effect on the mean flow. This distortion of the mean flow modifies the rate of transfer of energy from the mean flow to the disturbance and, since this energy transfer is the cause of the growth of the disturbance, there is a modification of the rate of growth of the latter.It is suggested that, in many cases, an equilibrium state may be possible in which the rate of transfer of energy from the (distorted) mean flow to the disturbance balances precisely the rate of viscous dissipation of the energy of disturbance. A theory based on certain assumptions about the energy flow is given to describe both the growth of the disturbance and the final equilibrium state, and application is made to the cases of Poiseuille flow between parallel planes and flow between rotating cylinders. The distorted mean flow in the equilibrium state can be calculated and from this, in the latter case, the torque required to maintain the cylinders in motion. Good agreement is obtained with G. I. Taylor's measurements of the torque for the case when the inner cylinder rotates and the outer cylinder is at rest.
The stability of a two-dimensional laminar jet
Authors: Tatsumi T. , Kakutani T. 
Published: March 2006

This paper deals with the stability of a two-dimensional laminar jet against the infinitesimal antisymmetric disturbance. The curve of the neutral stability in the (α, R)-plane (α, the wave-number; R, Reynolds number) is calculated using two different methods for the different parts of the curve; the solution is developed in powers of (αR)−1 for obtaining the upper branch of the curve and in powers of αR for the lower branch.The asymptotic behaviour of these branches is that for branch I,$\alpha \rightarrow 2, \;\; c \rightarrow \frac{2}{3}$ for $R \rightarrow \infty$; and for branch II, $R \sim 1\cdot12\alpha^{-1|2},\; c \sim 1\cdot 20 \alpha^2$ for α → 0. Some discussion is given on the validity of the basic assumption of the stability theory in relation to the numerical result obtained here.
Two-dimensional incompressible magneto-hydrodynamic flow across an elliptical solenoid
Authors: Kemp Nelson H. , Petschek Harry E. 
Published: March 2006

An analysis has been made of the two-dimensional flow of an incompressible constant-conductivity fluid through an elliptically shaped solenoid containing a constant magnetic field directed normal to the flow plane. The effect of both Hall current and ion slip has been included in the generalized Ohm's law used for the fluid. The analysis is based on a perturbation procedure in two parameters, one being the magnetic Reynolds number Rm and the other the ratio S of magnetic force per unit area to dynamic pressure. Calculations have been carried to the first order in each parameter, and closed-form analytic expressions have been obtained for the force and moment on the solenoid, the current density, stream function, magnetic field and other pertinent physical quantities.It was found that, to the zeroth order, there is a force but no moment on the solenoid. To the first order in S, where the flow field is modified but the magnetic field is not, there is a moment and a force, the latter being anti-parallel to the zeroth order force. To the first order in Rm, where the magnetic field is modified but the flow field is not, there is a moment but no force. Thus, to the first order the lift to drag ratio is the same as in the zeroth order. Graphs which illustrate some of the effects of angle of attack, fineness ratio of the ellipse, Hall current and ion slip, on the forces and moments are presented.
A new approach to problems of shock dynamics Part 2. Three-dimensional problems
Authors: Whitham G. B. 
Published: March 2006

This paper gives the extension of the approximate theory developed in Part 1 (Whitham 1957) to three-dimensional problems. The basic equations are derived in §1, using the original assumption of a functional relation between the strength of the shock wave at any point and the area of the ray tube. An analogy with steady supersonic flow is found. For the diffraction of a plane shock wave by an obstacle, the equations and boundary conditions are exactly the same as those for steady supersonic potential flow past that obstacle, with a special choice of the density-speed relation. The successive positions of the shock wave are the equipotential surfaces of the supersonic flow. The 'shock-shocks’ introduced in Part 1, i.e. discontinuities in the slope and Mach number of the shock wave, correspond to the steady oblique shock waves in the supersonic flow problem. They arise when Mach reflexion occurs.In §2 the theory is applied in detail to the diffraction of a plane shock wave by a cone. Then, in §3, a small perturbation theory is applied to the two typical problems of (i) diffraction by a slender axi-symmetrical body of general shape, and (ii) the stability of a plane shock. Many further applications would be possible and some brief comments on these are made in §4.
A three-dimensional solution for waves in the lee of mountains
Authors: Crapper G. D. 
Published: March 2006

This paper presents a three-dimensional small-perturbation approach to the problem of waves produced in a statically stable stratified air stream flowing over a mountain. The fundamental solution for a doublet disturbance in an air stream in which the parameter l2 = gβ/V2 is constant is calculated, and then is extended to that for a disturbance due to a circular mountain in the same air stream. A simple approximation to the known two-dimensional flow over an infinite ridge is also given. The second (’upper’) boundary condition for the solutions is determined in a rigorous analytical manner, assuming the presence of small friction forces, or, alternatively, of time dependence. It is hoped that this will settle the controversy which exists over the choice of this condition.The results show that the behaviour due to a doublet is peculiar and not truly representative of that due to a mountain. The latter shows waves which decay down-stream and are contained in a strip, the width of the strip being determined by the radius of the mountain. An interesting result is that the circular mountain can give rise to waves which have greater amplitude than those produced by the infinite ridge under the same conditions.In some previous papers the waves produced by the infinite ridge have been neglected, but the present paper shows that in many cases this procedure is not justifiable. The detailed solution for the waves behind a circular mountain has a form which emphasizes the importance for lee-wave production of ’resonance’ between the width of the mountain and the characteristic length l-1 of the air stream.
The rise of a gas bubble in a viscous liquid
Authors: Moore D. W. 
Published: March 2006

The rise of a gas bubble in a viscous liquid at high Reynolds number is investigated, it being shown that in this case the irrotational solution for the flow past the bubble gives a uniform approximation to the velocity field. The drag force experienced by the bubble is calculated on this hypothesis and the drag coefficent is found to be 32/R, where R is the Reynolds number (based on diameter) of the bubbles rising motion. This result is shown to be in fair agreement with experiment.The theory is extended to non-spherical bubbles and the relation of the resulting theory, which enables both bubble shape and velocity of rise to be predicted, to experiment is discussed.Finally, an inviscid model of the spherical cap bubble involving separated flow is considered.
On the instability theory of the melted surface of an ablating body when entering the atmosphere
Authors: Feldman Saul 
Published: March 2006

Some ablating bodies entering the atmosphere will melt or soften. Under deceleration, the soft or melted surface will tend to develop instabilities of the Lamb-Taylor type. Two situations involving viscous incompressible fluids are investigated here: one where the liquid layer has constant viscosity and finite thickness, and the other, where the viscosity increases exponentially with distance away from the interface, and the layer is semi-infinite in extent.It can be demonstrated, that if one neglects gradients in the flow direction, the rate of growth of interface disturbances in a plane normal to the axis of an axially symmetric blunt body is independent of the flow velocity. The fact that the deceleration and liquid thickness vary with time along a trajectory is also included in the analysis. Results of calculations for the amplification factor and the most amplified wavelength are given.A mechanism due to the deceleration is postulated, which would cause the formation of longitudinal grooves on the surface of an axially symmetric blunt body while entering the atmosphere.
Shearing flow over a wavy boundary
Authors: Benjamin T. Brooke 
Published: March 2006

A theoretical study is made of shearing flows bounded by a simple-harmonic wavy surface, the main object being to calculate the normal and tangential stresses on the boundary. The type of flow considered is approximately parallel in the absence of the waves, being exemplified by two-dimensional boundary layers over a plane. Account is taken of viscosity; but, as the Reynolds number is assumed to be large, its effects are seen to be confined within narrow ‘friction layers’, one of which adjoins the wave and another surrounds the ‘critical point’ where the velocity of flow equals the wave velocity. The boundary conditions are made as general as possible by including the three cases where respectively the boundary is rigid, flexible yet still solid, or completely mobile as if it were the interface with a second fluid.The theory is developed on the model of stable laminar flow, although it is proposed that the same theory may usefully be applied also to examples of turbulent flow considered as ‘pseudo-laminar’ with velocity profiles corresponding to the mean-velocity distribution. Use is made of curvilinear co-ordinates which follow the contour of the wave-train. This admits a linearized form of the problem whose validity requires only that the wave amplitude be small in comparison with the wavelength, even when large velocity gradients exist close to the boundary. The analysis is made largely without restriction to particular forms of the velocity profile; but eventually consideration is given to the example of a linear profile and the example of a boundary-layer profile approximated by a quarter-period sinusoid. In § 7 some general methods are set out for the treatment of disturbed boundary-layer proses: these apply with greatest precision to thin boundary layers, but are also useful for the initially very steep but on the whole fairly diffuse profiles which occur in most practical instances of turbulent flow over waves.The phase relationships found between the stresses and the wave elevation are discussed for several examples, and their interest in connexion with problems of wave generation by wind is pointed out. It is shown that in most circumstances the stresses are distributed in much the same way as if the leeward slopes of the waves were sheltered. For instance, the pressure distribution often has a substantial component in phase with the wave slope, just as if a wake were formed behind each wave crest—although of course actual separation effects are outside the scope of the present theory. In this aspect, the analysis amplifies the work of Miles (1957).
Reverse flow and supersonic interference
Authors: Clarke Joseph H. 
Published: March 2006

First, from a volumetric formulation of the momentum theorem of linearized theory, a general analytic proof is presented of the invariance of the drag of an arbitrary spatial distribution of horseshoe vortices and sources under reversal of the undisturbed flow. By consideration of the interference drag of two such singularity distributions, a reverse-flow relation for steady subsonic or supersonic flow is then obtained. This relation, a generalization of the Ursell-Ward theorem, may be applied to configurations with bodies whose surfaces are not quasi-cylindrical and whose surface pressures are quadratically related to the perturbation velocity.The relation is used to discuss several interfering two-body arrangements in supersonic flow. It is shown that, in certain cases, the drag and lift may be determined without knowledge of the interference flow field associated with the arbitrarily prescribed body geometry. The simplicity of the results permits the formulation of optimum problems. The invariance of the drag under flow reversal with unchanged geometry is also established.
On the stability of a shear layer
Authors: Menkes J. 
Published: March 2006

The effects of density variation in the absence of gravity on the stability of a horizontal shear layer between two streams of uniform velocities is investigated. The density is assumed to decrease exponentially with height and the velocity is represented by U(y) = tanh y.The method of small disturbances is employed to obtain the neutral stability curve. It is demonstrated that disturbances with wave-numbers larger than the width of the transition layer are attenuated.Qualitative agreement with experimental evidence is obtained.
Pressure drop due to viscous flow through cylinders
Authors: Brenner Howard 
Published: March 2006

A general formula is developed which permits a calculation of the pressure drop arising from the slow steady flow of a viscous fluid through a circular cylinder for arbitrarily assigned conditions of velocity on the bounding surfaces of the cylinder. In particular, the diminution in pressure can be calculated directly from the prescribed boundary velocities without requiring a detailed solution of the equations of motion. Hence it is possible to compute, in comparatively simple fashion, the magnitude of this macroscopic parameter for a large variety of complex motions which would normally present great analytical difficulties.By way of illustration the additional pressure drop arising from the presence of a point force situated along the axis of a cylinder is calculated. The additional force required to maintain the motion in the presence of the obstacle is exactly twice the magnitude of the point force itself.
Experiments on the flow past a circular cylinder at low Reynolds numbers
Authors: Tritton D. J. 
Published: March 2006

Part I describes measurements of the drag on circular cylinders, made by observing the bending of quartz fibres, in a stream with the Reynolds number range 0·5-100. Comparisons are made with other experimental values (which cover only the upper part of this range) and with the various theoretical calculations.Part II advances experimental evidence for there being a transition in the mode of the vortex street in the wake of a cylinder at a Reynolds number around 90. Investigations of the nature of this transition and the differences between the flows on either side of it are described. The interpretation that the change is between a vortex street originating in the wake and one originating in the immediate vicinity of the cylinder is suggested.
An experiment on the stability of hypersonic laminar boundary layers
Authors: Demetriades Anthony 
Published: March 2006

An experimental investigation of the hydrodynamic stability of the laminar hypersonic boundary layer was carried out with the aid of a hot-wire anemometer. The case investigated was that of a flat surface at zero angle of attack and no heat transfer.The streamwise amplitude variation of both natural disturbances and of disturbances artifically excited with a siren mechanism was studied. In both cases it was found that such small fluctuations amplify for certain ranges of frequency and Reynolds numberRθ, and damp for others. The demarcation boundaries for the amplification (instability) zone were found to resemble the corresponding limits of boundary-layer instability at lower speeds. A ‘line of maximum amplification’ of disturbances was also found. The amplification rates and hence the degree of selectivity of the hypersonic layer were found, however, to be considerably lower than those at the lower speeds. The disturbances selected by the layer for maximum amplifications have a wavelength which was estimated to be about twenty times the boundary-layer thickness δ.