bluuebunny/crossref_metadata_2025_split huggingface dataset:
Convection in a radiating gas
Authors: Gille John , Goody Richard 
Published: March 2006

We have made a theoretical and experimental study of the effect of radiative transfer on the onset of convection by means of comparative experiments in dry air and ammonia contained between horizontal aluminium plates maintained at different temperatures.The first effect of radiative transfer is to distort the linear, diffusive profile in the initial, pre-convective state. A non-grey theory is developed and is shown to predict the non-linear profiles profiles with satisfactory accuracy. The change of radiative flux with pressure of ammonia is also predicted and confirmed. This constitutes the first successful attempt to confirm the methods used in atmospheric studies in controlled experiment.A non-grey theory of the onset of convection is developed, separating effects associated with the distortion of the static state and the dissipative effect of radiative transfer on temperature fluctuations.Experiments indicate that the critical Rayleigh number in ammonia can be greatly increaesd over the best value for air (Rac = 1786); the maximum observed being Rac = 4870. Theory and experiment are shown to agree within reasonable limits.This work confirms the validity of methods which are of great importance to astrophysics and atmospheric physics.
The buoyant motion within a hot gas plume in a horizontal wind
Authors: Csanady G. T. 
Published: March 2006

A smoke plume that has become nearly horizontal at some distance from the source behaves much like a ‘line-thermal’, for which, using a perturbation method, a solution in laminar flow may be obtained, on the supposition that excess temperatures are small and buoyant movements slow, i.e. that the Rayleigh number of the problem is suitably low. In analogy with some other problems in turbulent flow and turbulent diffusion, the laminar solution is then assumed to approximate what is observed in the turbulent case, provided that the rate of growth of the diffusing cloud is assessed realistically.The so-calculated pattern of streamlines in a cross-section of the plume agrees qualitatively with the observed behaviour of hot plumes and puffs, consisting of two vortex-like structures of opposite sense of rotation, lying on either side of the plume centre. The bodily upward movement of the plume is found to depend critically on the rate of growth of the plume. Thus when the plume diameter grows faster than linearly with distance (such behaviour characterizes the ‘quasi-asymptotic’ stage of relative diffusion predicted by Batchelor, 1952, for which Richardson's (4/3)-power law of eddy diffusivity holds) the plume tends to reach an asymptotic height. A crude theoretical estimate of the asymptotic height attained shows fair agreement with observations reported elsewhere. Although the plume nearly reaches this asymptotic height in the quasi-asymptotic phase, it retains a small gradient in the final phase which may be of importance at large distances from the source. The small-Rayleigh-number criterion restricts the validity of the solution to ‘weakly buoyant’ plumes.
A study of the turbulent separated-flow region occurring at a compression corner in supersonic flow
Authors: McDonald H. 
Published: March 2006

The turbulent separated-flow region occurring at a compression corner under certain circumstances at supersonic speed has been examined in the light of recent improvements to base pressure theory (McDonald 1964). This base pressure theory is further extended from what could be termed a single-layer model of the re-attaching boundary layer to a two-layer model, thus enabling the inviscid shock configuration which occurs at the corner to be determined. Application of this analysis to some experimental results indicates a substantial measure of agreement.While this analysis has been framed for estimating the scale of the corner interaction, the extension can of course be applied to increase the range of initial boundary-layer thicknesses to which McDonald's analysis is applicable. An example of such an application is shown to be in good agreement with experiment.
The effect of rotation on the simpler modes of motion of a liquid in an elliptic paraboloid
Authors: Ball F. K. 
Published: March 2006

The six simplest modes of motion are considered and three rotational effects investigated:The effect of the rotation of the earth.The effect of the rotation of the container.The effect of the rotation of the liquid within the container.The first two are shown to be equivalent for motion in a paraboloid, and the last two are also equivalent when the paraboloid iscircular. In the case of an elliptic paraboloid the last is rather more difficult and one must first derive a solution of the non-linear equations representing ‘elliptic rotation’ and then consider deviations from it.The changes in frequency consequent on the rotation are derived in all three cases for all six modes. In the case of the earth's rotation the disposition and character of the amphidromic (nodal) points and the amphidromic waves that rotate round these points are investigated in detail. One mode is particularly interesting because it has four amphidromic points, the waves rotate in a positive sense around two of these and in a negative sense round the other two.
Hypersonic strong-interaction similarity solutions for flow past a flat plate
Authors: Bush William B. 
Published: March 2006

The hypersonic strong-interaction regime for the flow of a viscous, heat-conducting compressible fluid past a flat plate is analysed using the Navier–Stokes equations as a basis. It is assumed that the fluid is a perfect gas having constant specific heats, a constant Prandtl number σ, whose numerical value is of order one, and a viscosity coefficient varying as a power, ω, of the absolute temperature. Limiting forms of solutions are studied as the free-stream Mach numberM, the free-stream Reynolds number based on the plate lengthRL, and the interaction parameterx= {(γM2)2+ω/RL}½, go to infinity.Through the use of asymptotic expansions and matching, it is shown that, for (1−ω) > 0, three distinct layers for which similarity exists make up the region between the shock wave and the plate. The behaviour of the flow in these three layers is analysed.
An experiment on third-order resonant wave interactions
Authors: Longuet-Higgins M. S. , Smith N. D. 
Published: March 2006

An experiment has been carried out to verify the existence of the resonant interaction between trains of gravity waves, predicted by Phillips (1960). As suggested by Longuet-Higgins (1962), two trains of waves in mutually perpendicular directions were generated in a rectangular wave tank. The ratio σ1/σ2of the wave frequencies was varied (1·4 < σ1/σ2< 2·1). When σ1/σ2[eDot ] 1·7357 it was expected that a resonant interaction would take place, generating a wave of frequency (2σ1−σ2). The amplitude of the third wave was expected to increase almost linearly in the direction of wave propagation. The shape of the response curve as a function of σ1/σ2was also predicted.In the present experiments rather large wave amplitudes had to be used, and the theoretical shape of the response curve was distorted by non-linear detuning. Nevertheless the peak amplitude of the resonant wave was found to increase with distance in very nearly the manner predicted.These experiments were carried out in 1961 but publication was deferred pending a similar but more accurate investigation by McGoldrick, Phillips, Huang & Hodgson (1966). Much of the theoretical discussion given in the present paper is relevant to their work.
On the theory of asymmetric shear flows past flat plates
Authors: Mark Richard M. 
Published: March 2006

When a semi-infinite flat plate is immersed parallel to an unbounded, plane, steady, asymmetric, constant shear flow of an incompressible viscous fluid, an interaction occurs between the surface-generated vorticity and the external vorticity. A physical assumption was made in a previous paper (Mark 1962) concerning this problem that the pressure field in a thin layer adjacent to the top-side of the plate may be accurately approximated by the undisturbed constant-pressure field—that which exists before the insertion of the plate into the flow. This means that the vorticity interaction is assumed to have no effect on the undisturbed pressure field. That this is a valid first approximation far downstream along the plate where the interaction is intense is given rigorous support in this paper.The flow below the plate is examined on a heuristic basis. It is found that there is a strong possibility for the flow to separate from the lower surface near the leading edge of the plate. However, far downstream the flow settles down to a Stokes-type flow near the plate.
The directional spectrum of ocean waves: an experimental investigation of certain predictions of the Miles–Phillips theory of wave generation
Authors: Gilchrist A. W. R. 
Published: March 2006

The directional spectrum of wind-driven surface waves has been measured under conditions of limited fetch, in order to check the predictions of the Phillips–Miles theory of wave generation (Miles 1960). The expression obtained for the directional spectrum in this theory involves the spectrum of the atmospheric pressure fluctuations, but it is possible to obtain theoretical estimates of the major features of the directional spectrum without knowledge of the pressures. Specifically, it is possible to predict the frequency at which the power spectrum should peak, and, for the higher frequencies, the range of azimuth over which high spectral values should be observed; for the lower frequencies the theory indicates a bimodal distribution in azimuth (Phillips's resonance waves), and gives the angle of travel relative to the wind as a function of frequency.The results of the measurements are in fairly good agreement with the theoretical predictions for the higher frequencies. The asymmetry of the fetch results in the prediction that the waves will travel at an angle to the wind which varies with frequency, and this was observed. The range of azimuth over which the spectral density is high is also close to the theoretical prediction. For the low frequencies the bimodal distribution was not observed: the waves were found to have a single predominant direction of travel at each frequency. However, this direction conformed closely to that of one of the two wave trains predicted by Phillips, and its variation with frequency was also that given by the theory. There is reason to suppose that the peculiarities of the experimental site may be responsible for the absence of the second wave train, especially as it would be difficult to account for the observed effects on any basis other than that of Phillips's theory.
A theoretical study of non-equilibrium blunt-body flows
Authors: Conti Raul J. 
Published: March 2006

Non-equilibrium inviscid flows behind a spherical-segment shock wave are investigated with the method of series truncation. This semi-analytical technique developed at Stanford is based on a systematic co-ordinate-perturbation scheme. The flow variables are expanded in series in powers of the longitudinal curvilinear co-ordinate leading away from the stagnation point. The problem is thus reduced to one of numerical integration of ordinary differential equations for functions of the normal co-ordinate. Unlike the similar situation of the Blasius series in boundary-layer theory, the present scheme–having to deal with elliptic equations–must resort to series truncation. As a consequence, a truncation error is introduced. The present paper shows a simple way of reducing this error.The simplified air chemistry adopted is based on non-equilibrium dissociation and recombination of oxygen diluted in inert nitrogen. A wide spectrum of non-equilibrium régimes is investigated for a fixed set of flight conditions. In particular, near-frozen flows are followed to the vicinity of the stagnation point through a region of large temperature and concentration gradients located near the body. This equilibrium-drive region, arising from the singular nature of the frozen limit, is studied in some detail.
The effects of pressure gradients on turbulent flow near a smooth wall
Authors: Mellor George L. 
Published: March 2006

A dimensional argument is presented leading to a functional form for the effective viscosity which embraces the hypothesis of a previous paper (Mellor & Gibson 1966; hereafter referred to as paper A) in the defect portion of a turbulent boundary layer. The new argument also suggests a way of determining the effective viscosity in the viscous sublayer when the flow is subjected to mainstream pressure gradients.It will be shown that the large wall-velocity profiles and the defect-velocity profiles automatically overlap, even in the absence of a logarithmic portion. It will be shown further that equilibrium flows are uniquely determined by β andR.
The constraints imposed on tornado-like vortices by the top and bottom boundary conditions
Authors: Turner J. S. 
Published: March 2006

A laboratory model of a tornado vortex has been produced, incorporating two features which are believed to be important to the understanding of the atmospheric phenomenon, but which have been largely ignored in previous studies. First, it has been shown that a vortex can be driven fromaboveby a mechanism analogous to convection in a cloud, and that density differences within the funnel itself are not essential. Associated with this mechanism of formation is a circulation in the vertical, with an upflow in the centre surrounded by a compensating annular downflow. Secondly, the bottom boundary is seen to have a strong influence on the vortex, since the down and up flows are linked there by a rapid radial inflow in a thin boundary layer.In the present paper an approximate theoretical description of such a vortex is proposed. The interior and boundary layer flows are first examined separately, and then a condition is sought which makes the two solutions consistent. The starting-point of the theory is the assumption of a form of stream function which describes a circulation in the vertical having the essential features of that observed. The result of the matching procedure is to fix both the form of the tangential velocity profile, and the relative magnitudes of the three components of velocity. These deductions are not critically dependent on the assumed form of the motion in the vertical, and are in good agreement with the first measurements in the laboratory vortices, though the quantitative experimental results are not emphasized here.
Heat transfer from turbulent separated flows
Authors: Spalding D. B. 
Published: March 2006

A power-law relation is derived between the Stanton number and the Reynolds number, expressing the law of heat transfer for a wall adjacent to a region of turbulent separated flow. The derivation is based on Prandtl's (1945) proposal for the laws of dissipation, diffusion and generation of turbulent kinetic energy. The constants appearing in these laws are determined by reference to experimental data for the hydrodynamic properties of the constant-stress and the linear-stress layers.The agreement between the resulting predictions and the experimental data of other workers is sufficiently good to suggest that the actual mechanism of heat transfer from separated flows has much in common with that which is postulated. Closer agreement can be expected only after the present one-dimensional analysis has been superseded by a two-dimensional one.
Aerodynamics of oscillating disks and a right-circular cylinder
Authors: Willmarth W. W. , Hawk N. E. , Galloway A. J. , Roos F. W. 
Published: March 2006

Detailed studies are reported of the free and forced oscillation of disks and a right-circular cylinder constrained to rotate about a fixed diametrical axis passing through the centre of the body and normal to the free-stream direction. When a disk is free to rotate, it oscillates at a definite frequency with slowly varying amplitude and phase. A right-circular cylinder also oscillates at a definite frequency but with rapidly increasing amplitude. When the amplitude becomes large, after a few cycles of oscillation, the cylinder rotates steadily in one direction.Analogue computer elements, position sensors and a dynamic moment balance were used to study the static restoring moment, dynamic restoring moment, average damping moment, statistical properties of the disk motion and power spectrum of the turbulent moment. The behaviour of the disk and cylinder are explained using the measurements and the theory for random excitation of a linear system. The turbulent exciting moment is caused by the unsteady flow in the wake and can be changed by placing disks and splitter plates in the wake. A model is proposed for the unsteady flow field in the wake behind the disk. The model relates the turbulent moment to the vortex shedding process in the wake.
The disintegration of wave trains on deep water Part 1. Theory
Authors: Benjamin T. Brooke , Feir J. E. 
Published: March 2006

The phenomenon in question arises when a periodic progressive wave train with fundamental frequency ω is formed on deep water—say by radiation from an oscillating paddle—and there are also present residual wave motions at adjacent side-band frequencies ω(1 ± δ), such as would be generated if the movement of the paddle suffered a slight modulation at low frequency. In consequence of coupling through the non-linear boundary conditions at the free surface, energy is then transferred from the primary motion to the side bands at a rate that, as will be shown herein, can increase exponentially as the interaction proceeds. The result is that the wave train becomes highly irregular far from its origin, even when the departures from periodicity are scarcely detectable at the start.In this paper a theoretical investigation is made into the stability of periodic wave trains to small disturbances in the form of a pair of side-band modes, and Part 2 which will follow is an account of some experimental observations in accord with the present predictions. The main conclusion of the theory is that infinitesimal disturbances of the type considered will undergo unbounded magnification if
\[
0 < \delta \leqslant (\sqrt{2})ka,
\]
where k and a are the fundamental wave-number and amplitude of the perturbed wave train. The asymptotic rate of growth is a maximum for δ = ka.
Viscoelastic flow past a wedge with a soluble coating
Authors: Hsu Chen-Chi 
Published: March 2006

The steady, two dimensional, incompressible flow of a viscoelastic fluid past a wedge of 90 degrees coated with the viscoelastic material is studied theoretically using constitutive equations proposed by Oldroyd in 1958. The effect of diffusion of the coating as well as its material properties (viscosity, relaxation time, retardation time, etc.) on the frictional force is investigated.A boundary-layer analysis is performed on the constitutive equations as well as on the momentum equations. A similarity transformation is found for the set of boundary-layer equations. Series expansion and Laplace's method are employed to obtain the solution in the asymptotic series of gamma functions.The results obtained show that:
The thinner displacement thickness does not necessarily imply a large frictional force for the viscoelastic flow.For a homogeneous viscoelastic flow, the frictional force increases as the degree of dilatancy of the material increases, and decreases with increasing degree of pseudo-plasticity of the material.For a non-homogeneous viscoelastic flow with given material constants, depending on whether the material is pseudoplastic or dilatant and on the ratio of the material concentration of outer flow and the concentration at the body, the frictional coefficient will decrease or increase from that of the homogeneous flow with the concentration at the body as the Schmidt number increases, and will approach a limit when the Schmidt number becomes very large. This limit is the frictional coefficient of the homogeneous flow with the concentration of the outer flow.
Detached shear layers in a rotating fluid
Authors: Hide R. , Titman C. W. 
Published: March 2006

The occurrence of detached shear layers should, according to straightforward theoretical arguments, often characterize hydrodynamical motions in a rapidly rotating fluid. Such layers have been produced and studied in a very simple system, namely a homogeneous liquid of kinematical viscosity v filling an upright, rigid, cylindrical container mounted coaxially on a turn-table rotating at Ω0 rad/s about a vertical axis, and stirred by rotating about the same axis at Ω1 rad/s a disk of radius a cm and thickness b’ cm immersed in the liquid with its plane faces parallel to the top and bottom end walls of the container. By varying Ω0, Ω1 and a, ranges of Rossby number, the modulus of ε ≡ (Ω1 + Ω0)/½ (Ω1 + Ω0), from 0·01 to 0·3, and Ekman number, E ≡ 2v/a2(Ω1 + Ω0), from 10−5 to 5 × 10−4 were attained. Although the apparatus was axisymmetric, only when |ε| did not exceed a certain critical value, |εT|, was the flow characterized by the same property of symmetry about the axis of rotation. Otherwise, when |ε| > |εT|, non-axisymmetric flow occurred, having the form in planes perpendicular to the axis of rotation of a regular pattern of waves, M in number, when ε was positive, and of a blunt ellipse when ε was negative.The axial flow in the axisymmetric detached shear layer, and the uniform rate of drift of the wave pattern characterizing the non-axisymmetric flow when ε is positive, depend in relatively simple ways on ε and E. The dependence of|εT| on E can be expressed by the empirical relationship |εT| = AEn, where A = 16·8 ± 2·2 and n = 0·568 ± 0·013 (= (4/7) × (1·000 − (0·005 ± 0·023))!), standard errors, 25 determinations. M does not depend strongly on E but generally decreases with increasing ε.
The motion of a fluid due to a moving source of heat at the boundary
Authors: Davey A. 
Published: March 2006

Experiments performed by Fultz et al. (1959) and Stern (1959) indicate that if a flame is rotated around the bottom exterior of a pan or of a circular cylindrical annulus containing water then the fluid acquires a net vertical component of angular momentum in a direction opposite to that of the flame's motion. Stern gave an analysis showing how fluid, bounded by two horizontal plates subjected to small two-dimensional sinusoidal travelling temperature perturbations, could acquire and maintain such momentum. An assumption in Stern's analysis was that the density variations were constant between the plates. Here we shall examine the importance of the relaxation of this assumption. Also, another model, in which the upper surface of the fluid is free, is analysed, because this model conforms more closely with the experiments of Fultz et al. and Stern.For the problem of flow between two plates we shall show that there is a net flux of momentum in the direction opposite to the motion of the thermal field for all frequencies thereof. The same result holds in the case with a free surface when conditions are comparable with those in the experiments.In both problems the phase lag of the thermal expansion wave with height produces a skewed thermal field. This field is the most important mechanism in producing velocity correlations. It is due to these correlations and the associated Reynolds stress that the fluid acquires its momentum.