bluuebunny/crossref_metadata_2025 huggingface dataset:
The three-dimensional nature of boundary-layer instability
Authors: Klebanoff P. S. , Tidstrom K. D. , Sargent L. M.
Published: March 2006

An experimental investigation is described in which principal emphasis is given to revealing the nature of the motions in the non-linear range of boundary-layer instability and the onset of turbulence. It has as its central purpose the evaluation of existing theoretical considerations and the provision of a sound physical model which can be taken as a basis for a theoretical approach. The experimental method consisted of introducing, in a two-dimensional boundary layer on a flat plate at ‘incompressible’ speeds, three-dimensional disturbances under controlled conditions using the vibrating-ribbon technique, and studying their growth and evolution using hot-wire methods. It has been definitely established that longitudinal vortices are associated with the non-linear three-dimensional wave motions. Sufficient data were obtained for an evaluation of existing theoretical approaches. Those which have been considered are the generation of higher harmonics, the interaction of the mean flow and the Reynold stress, the concave streamline curvature associated with the wave motion, the vortex loop and the non-linear effect of a three-dimensional perturbation. It appears that except for the latter they do not adequately describe the observed phenomena. It is not that they are incorrect or may not play a role in some aspect of the local behaviour, but from the over-all point of view the results suggest that it is the non-linear effect of a three-dimensional perturbation which dominates the behaviour. A principal conclusion to be drawn is that a new perspective, one that takes three-dimensionality into account, is required in connexion with boundary-layer instability. It is demonstrated that the actual breakdown of the wave motion into turbulence is a consequence of a new instability which arises in the aforementioned three-dimensional wave motion. This instability involves the generation of ‘hairpin’ eddies and is remarkably similar in behaviour to ‘inflexional’ instability. It is also shown that the results obtained from the study of controlled disturbances are equally applicable to ‘natural’ transition.
Particle motions in sheared suspensions XIII. The spin and rotation of disks
Authors: Goldsmith H. L. , Mason S. G.
Published: March 2006

The motions of single disks suspended in a liquid undergoing Couette flow have been studied in detail. The angular rotation and the axial spin of the disks were found to be in good agreement with the theory of Jeffery, provided the equivalent axis ratio re was used instead of the measured axis ratio r. It was found that non-interacting disks move in constant orbits without a tendency to drift into orbits corresponding to a minimum dissipation of energy. Discontinuous changes in orbit were observed to occur following two-body collisions.
An almost-inviscid geostrophic flow
Authors: Hocking L. M.
Published: March 2006

An almost rigid rotation of a viscous fluid is produced by dividing the containing cylinder into two sections and rotating them at slightly different speeds. The fluid velocity can be separated into two parts, a swirl about the axis and a streaming motion in the axial planes. When the difference in the speeds of rotation of the two sections is small, the equations of motion can be linearized. The solution is found for large Reynolds numbers and provides an illustration of the way in which the conditions of geostrophic flow (no velocity variation in the axial direction and an inability to insist on undistrubed flow at infinity) are approached as the Reynolds number tends to infinity.
The supersonic and low-speed flows past circular cylinders of finite length supported at one end
Authors: Sykes D. M.
Published: March 2006

The flow past circular cylinders of finite length, supported at one end and lying with their axes perpendicular to a uniform stream, has been investigated in a supersonic stream at Mach number 1.96 and also in a low-speed stream. In both stream it was found that the flow past the cylinders could be divided into three regions: (a) a central region, (b) that near the free end of the cylinder, and (c) that near the supported end. The locations of the second and third regions were found to be almost independent of the cylinder length-to-diameter ratio, provided that this exceeded 4, while the flow within and the extent of the first region were dependent on this ratio. Form-drag coefficients determined in the central region in the supersonic flow were in close agreement with the values determined at the same Mach number by other workers. In the low-speed flow the local form-drag coefficients were dependent on length-to-diameter ratio and were always less than that of an infinite-length cylinder at the same Reynolds number.
The correction of hot-wire readings for proximity to a solid boundary
Authors: Wills J. A. B.
Published: March 2006

When using a hot wire for velocity measurements close to a solid boundary, errors may be introduced if the effect of the boundary on the rate of heat loss from the wire is ignored. An experimental determination of the effect is described, in which a hot wire was mounted at various distances from a metal surface forming one wall of a two-dimensional channel. The rate of heat loss was determined electrically, and the air velocity at the wire found from the known laminar velocity profile. The application of the results to turbulent flows is discussed briefly.
The initial motion of a gas bubble formed in an inviscid liquid Part 1. The two-dimensional bubble
Authors: Walters J. K. , Davidson J. F.
Published: March 2006

The paper deals with the initial motion of a two-dimensional bubble starting from rest in the form of a cylinder with its axis horizontal. The theory is based on the assumptions of irrotational motion in the liquid round the bubble, constant pressure within the bubble, and small displacements from the cylindrical form. This theory predicts that the bubble should rise with the acceleration of gravity, over a distance of at least the initial bubble radius, and that a tongue of liquid should be projected up from the base of the bubble into its interior. These predictions are confirmed by experiments which also show how the vorticity necessary for steady motion in the spherical-cap form is generated by the detachment of two small bubbles from the back of the main bubble.
The formation of vortex streets
Authors: Abernathy Frederick H. , Kronauer Richard E.
Published: March 2006

The formation of vortex streets in the wake of two-dimensional bluff bodies can be explained by considering the non-linear interaction of two infinite vortex sheets, initially a fixed distance, h, apart, in an inviscid incompressible fluid. The interaction of such sheets (represented in the calculation by rows of point-vortices) is examined in detail for various ratios of h to the wavelength, a, of the initial disturbance. The number and strength of the concentrated regions of vorticity formed in the interaction depend very strongly on h/a. The non-linear interaction of the two vortex sheets explains both the cancellation of vorticity and vortex-street broadening observed in the wakes of bluff bodies.
A theory of anisotropic fluids
Authors: Hand George L.
Published: March 2006

A theory is proposed in which the stress tensor is a function of the components of the rate of deformation tensor and a symmetric tensor describing the microscopic structure of a fluid. The expression for the stress tensor can be written in closed form using results from the Hamilton-Cayley theorem. This theory is shown to contain Prager's theory of dumbbell suspensions as a special case. By limiting the type of terms in the constitutive equations, various stress components can be evaluated for simple shear. These exhibit non-Newtonian behaviour typical of certain higher polymer solutions.

Some of the results of the anisotropic fluid theory are compared with experimental measurements of normal stress and apparent viscosity. Certain high polymers in solution show good agreement between theory and experiment, at least for low enough values of the rate of shear.
Some specific features of atmospheric tubulence
Authors: Oboukhov A. M.
Published: March 2006

The spectrum of atmospheric turbulence is very broad by comparison with spectra in wind tunnels. We introduce the notion of small-scale and large-scale turbulence. Small-scale turbulence consists of a set of disturbances, the scales of which do not exceed the distance to the wall and for which the hypothesis of three-dimensional isotropy is valid in a certain rough approximation. Large-scale turbulence is essentially anisotropic; the horizontal scale in the atmosphere is much larger than the vertical one, the latter being confined to a certain characteristic height H. The horizontal scale varies widely according to the external conditions and characteristics of the medium.
A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number
Authors: Kolmogorov A. N.
Published: March 2006

The hypotheses concerning the local structure of turbulence at high Reynolds number, developed in the years 1939-41 by myself and Oboukhov (Kolmogorov 1941 a,b,c; Oboukhov 1941 a,b) were based physically on Richardson's idea of the existence in the turbulent flow of vortices on all possible scales l < r < L between the ‘external scales’ L and the ‘internal scale’ l and of a certain uniform mechanism of energy transfer from the coarser-scaled vortices to the finer.
On the behaviour of small disturbances in plane Couette flow
Authors: Gallagher A. P. , Mercer A. McD.
Published: March 2006

The problem considered here is concerned with small disturbances of plane Couette flow. As is usual in such problems it is assumed that the disturbance velocities are sufficiently small to allow the Navier-Stokes equations to be linearized. There results a special case of the well-known Orr-Sommerfeld equation and this is solved by an exact method using a digital computer. The problem has previously been considered by several authors, mostly using approximate methods and their results have been compared where possible with those obtained here. It was possible to proceed to values of αR not in excess of 1000 (α being the wave-number of the disturbance and R the Reynolds number of the basic flow), and the results tend to confirm the belief that Couette flow is stable at all Reynolds numbers.
Second-order supercavitating hydrofoil theory
Authors: Chen C. F.
Published: March 2006

The second-order problem of Helmholtz flow past lifting hydrofoils and symmetric struts has been formulated and solved. The solution involves elementary operations on the known solutions of the first-order problem. The second-order lift and drag coefficients are given in integral form. Results obtained for a flat plate at incidence and a symmetric wedge agree with the exact solutions up to the second order. In terms of quantitative improvements, the present second-order theory predicts a lift coefficient for a flat plate at 45° incidence with an error of 8%, and a drag coefficient for a symmetric wedge of 50° included angle with an error of 5%; the corresponding angles at which the linear theory would predict force coefficients incurring the same errors are 5° and 15° respectively.
A consequence of the zero fourth cumulant approximation
Authors: O'Brien Edward E. , Francis George C.
Published: March 2006

Recent investigations by Kraichnan (1961) and Ogura (1961) have raised doubts concerning the usefulness of the zero fourth cumulant approximation in turbulence dynamics. It appears extremely tedious to examine, by numerical computation, the consequences of this approximation on the turbulent energy spectrum although the appropriate equations have been established by Proudman & Reid (1954) and Tatsumi (1957). It has proved possible, however, to compute numerically the sequences of an analogous assumption when applied to an isotropic passive scalar in isotropic turbulence.

The result of such computation, for specific initial conditions described herein, and for stationary turbulence, is that the scalar spectrum does develop negative values after a time approximately $2 \Lambda | {\overline {(u^2)}} ^{\frac {1}{2}}$, Where Λ is a length scale typical of the energy-containing components of both the turbulent and scalar spectra and $\overline {(u^2)}^{\frac {1}{2}}$ is the root mean square turbulent velocity.
Impulsive motion of an infinite plate in a compressible fluid with non-uniform external flow
Authors: Traugott S. C.
Published: March 2006

The impulsive movement of a plate (Rayleigh problem) is considered for a compressible flow in which, prior to initiation of the motion, both velocity and enthalpy gradients exist normal to the plate. The solution is valid for large times, and the external gradients are chosen of such magnitude that their effects enter to the same order as displacement effects due to induced vertical velocity. This displacement effect is influenced by the external enthalpy gradient. Both insulated wall and a step change in wall enthalpy are considered. For the insulated wall it is found that the part of the displacement solution which is uninfluenced by the external gradient requires a term in the logarithm of Reynolds number (based on time). This differs in principle from the case for a constant wall enthalpy. Displacement with uniform outside flow affects heat transfer but not skin friction, just the opposite from the corresponding results for the steady two-dimensional semi-infinite flat plate. The influence of external gradients on skin friction, heat transfer and adiabatic wall enthalpy is given.
The final approach to steady, viscous flow near a stagnation point following a change in free stream velocity
Authors: Kelly R. E
Published: March 2006

The flow field near a stagnation point in two-dimensional, incompressible, viscous flow is considered to change with time in such a way that the inviscid flow is steady after some given finite instant of time. The final approach to steady flow throughout the field is shown to be characterized by exponential decay with time of perturbations from the steady velocity field. The characteristic factors in the exponents arise from the solution of an eigenvalue problem in ordinary linear differential equations.

Similar behaviour exists for the axially symmetric case. A comparable analysis furnishes, however, a meaningless result in the case of a two-dimensional, semiinfinite flat plate which is moving in its own plane, normal to its leading edge.
Radiation stress and mass transport in gravity waves, with application to ‘surf beats’
Authors: Longuet-Higgins M. S. , Stewart R. W.
Published: March 2006

This paper studies the second-order currents and changes in mean surface level which are caused by gravity waves of non-uniform amplitude. The effects are interpreted in terms of the radiation stresses in the waves.

The first example is of wave groups propagated in water of uniform mean depth. The problem is solved first by a perturbation analysis. In two special cases the second-order currents are found to be proportional simply to the square of the local wave amplitude: (a) when the lengths of the groups are large compared to the mean depth, and (b) when the groups are all of equal length. Then the surface is found to be depressed under a high group of waves and the mass-transport is relatively negative there. In case (a) the result can be simply related to the radiation stresses, which tend to expel fluid from beneath the higher waves.

The second example considered is the propagation of waves of steady amplitude in water of gradually varying depth. Assuming no loss of energy by friction or reflexion, the wave amplitude must vary horizontally, to maintain the flux of energy constant; it is shown that this produces a negative tilt in the mean surface level as the depth diminishes. However, if the wave height is limited by breaking, the tilt is positive. The results are in agreement with some observations by Fairchild.

Lastly, the propagation of groups of waves from deep to shallow water is studied. As the mean depth decreases, so the response of the fluid to the radiation stresses tends to increase. The long waves thus generated may be reflected as free waves, and so account for the 'surf beats’ observed by Munk and Tucker.

Generalle speaking, the changes in mean sea level produced by ocean waves are comparable with those due to horizontal wind stress. It may be necessary to allow for the wave stresses in calculating wind stress coefficients.
Magnetohydrodynamic pipe flow. Part 1
Authors: Gold Richard R.
Published: March 2006

The solution is obtained to the problem of the steady one-dimensional flow of an incompressible, viscous, electrically conducting fluid through a circular pipe in the presence of an applied (transverse) uniform magnetic field. A no-slip condition on the velocity is assumed at the non-conducting wall. The solution is exact and thus valid for all values of the Hartmann number. Excellent agreement exists between the present theoretical results and the experimental values obtained by Hartmann & Lazarus (1937) in the low to medium Hartmann number range. The high Hartmann number case is treated by Shercliff (1962) in the following paper.
Vertical motion of a floating sphere in a sine-wave sea
Authors: Barakat Richard
Published: March 2006

The vertical motion (heave) of a freely floating sphere is studied under the action of incident sine waves. Forced heave is defined as the vertical motion of sphere in still water, while free heave is defined as the vertical motion of sphere in the sine-wave sea. The total velocity potential describing the motion is decomposed into three terms: incident wave potential, diffracted wave potential (potential as if the sphere were fixed in sine-wave sea), and forced heave potential (potential as if the sphere were in forced vertical motion in still water). The forced heave and diffraction problems are solved separately. The linearized equation of motion is then used to effect the synthesis of the free motion via two unknowns: amplitude of vertical displacement and phase difference.

Both the radiation and diffraction problems are solved by expansions of non-orthogonal functions (wave-free potentials). These functions are trivial solutions of the Sommerfeld radiation condition in the sense that they attenuate faster than O(r−½) and it is necessary to add multipole terms which have the proper behaviour at infinity. Infinite systems of linear equations are obtained for the unknown expansion coefficients and the unknown source strengths of the multipole. The added mass, damping coefficient and wave-making coefficient in forced heave are studied as well as the force on the fixed sphere. In addition the added mass and damping coefficient in free heave are obtained.

The horizontal motion (surge) of the freely floating sphere can be obtained by methods similar to those employed for the vertical motion. The author is presently working on this problem. Surge and heave are not independent motions but can be treated separately because of the symmetry of the sphere.
Hydromagnetic waves in a cylindrical plasma
Authors: Woods L. C.
Published: March 2006

This paper contained several extensions of the theory of hydromagnetic waves in a partially ionized gas. The gas is confined in a cylindrical tube through which passes an axial magnetic field. The tube wall is assumed to be either a perfect conductor or a material of small or zero conductivity.

The effects of the viscosity and compressibility of the ionized and neutral gases are included in the theory, as also are the contributions of finite conductivity and the ion-cyclotron term. The non-isotropic character of the viscosity and conductivity coefficients of the ionized gas is taken into account. New boundary conditions are derived for tubes with insulating walls, and it is shown that the only pure modes that can be propagated along such tubes are just two special cases of those waves having no azimuthal dependence.

The principal result of the paper is a new dispersion relation which allows for all the dissipative effects just mentioned and which is valid for a range of frequencies which extends well beyond the ion cyclotron frequency, but falls short of the frequency at which electron inertia and displacement currents became effective.
On the stability of a laminar incompressible boundary layer over a flexible surface
Authors: Landahl Marten T.
Published: March 2006

The stability of small two-dimensional travelling-wave disturbances in an incompressible laminar boundary layer over a flexible surface is considered. By first determining the wall admittance required to maintain a wave of given wave-number and phase speed, a characteristic equation is deduced which, in the limit of zero wall flexibility, reduces to that occurring in the ordinary stability theory of Tollmien and Schlichting. The equation obtained represents a slight and probably insignificant improvement upon that given recently by Benjamin (1960). Graphical methods are developed to determine the curve of neutral stability, as well as to identify the various modes of instability classified by Benjamin as ‘Class A’, ‘Class B’, and ‘Kelvin-Helmholtz’ instability, respectively. Also, a method is devised whereby the optimum combination of surface effective mass, wave speed, and damping required to stabilize any given unstable Tollmien-Schlichting wave can be determined by a simple geometrical construction in the complex wall-admittance plane.

What is believed to be a complete physical explanation for the influence of an infinite flexible wall on boundary-layer stability is presented. In particular, the effect of damping in the wall is discussed at some length. The seemingly paradoxical result that damping destabilizes class A waves (i.e. waves of the Tollmien-Schlichting type) is explained by considering the related problem of flutter of an infinite panel in incompressible potential flow, for which damping has the same qualitative effect. It is shown that the class A waves are associated with a decrease of the total kinetic and elastic energy of the fluid and the wall, so that any dissipation of energy in the wall will only make the wave amplitude increase to compensate for the lowered energy level. The Kelvin-Helmholtz type of instability will occur when the effective stiffness of the panel is too low to withstand, for all values of the phase speed, the pressure forces induced on the wavy wall.

The numerical examples presented show that the increase in the critical Reynolds number that can be achieved with a wall of moderate flexibility is modest, and that some other explanation for the experimentally observed effects of a flexible wall on the friction drag must be considered.
The growth of localized disturbances in a laminar boundary layer
Authors: Criminale William O. , Kovasznay Leslie S. G.
Published: March 2006

The classical theory of the instability of laminar flow predicts the growth (or decay) rate and phase velocity of two-dimensional small disturbance waves. In order to study the growth and dispersion of an originally localized spot-like disturbance, the initial disturbance is built up from all possible simple-harmonic waves. The propagation velocity and amplification rate for each vector wave-number then follows from the two-dimensional theory by Squire's generalization. The initial development can be solved explicitly by a power series in time, and the asymptotic behaviour is also predicted. For times between initial and final periods, exact numerical calculations have been made using an IBM 709 electronic computer. The role which localized disturbances can play in ultimate transition to turbulent motion is also indicated.
Stability of a hard-core fluid jet of small electrical conductivity
Authors: Talwar S. P. , Tandon J. N.
Published: March 2006

The stability of a hard-core fluid jet is investigated under the assumption of small electrical conductivity of the fluid for parallel and antiparallel current systems. For axisymmetric deformations the parallel current has a destabilizing influence whereas the antiparallel current improves the stability of the configuration. However, for non-axisymmetric deformations characterized by m = 1, it is shown that the jet becomes unstable in general, both for parallel and antiparallel current systems. The presence of an external conductor has been shown to have a stabilizing influence on kink instability.
Effects of viscous dissipation in natural convection
Authors: Gebhart B.
Published: March 2006

The effect of viscous dissipation in natural convection is appreciable when the induced kinetic energy becomes appreciable compared to the amount of heat transferred. This occurs when either the equivalent body force is large or when the convection region is extensive. Viscous dissipation is considered here for vertical surfaces subject to both isothermal and uniform-flux surface conditions. A perturbation method is used and the first temperature perturbation function is calculated for Prandtl numbers from 10−2 to 104. The magnitude of the effect depends upon a dissipation number, which is not expressible in terms of the Grashof or the Prandtl number.
Gas-ionizing shock and combustion waves in magnetogasdynamics
Authors: Helliwell J. B.
Published: March 2006

Some general properties of one-dimensional deflagration waves in a non-conducting inviscid gas at rest are discussed when ionization of the gas takes place across a shock wave which precedes the flame front, and electromagnetic fields are present. The direction of wave propagation, the electric field and magnetic field are taken as a mutually orthogonal triad of vectors. The jump relationships across the gas-ionizing shock wave and magnetogasdynamic combustion wave are investigated and the two Hugoniot curves analysed in detail in the pressure-specific volume plane. The possible types of wave are indicated for arbitrary magnitudes of the upstream electromagnetic field. It is shown that weak gasionizing shock waves cannot exist. For suitably chosen electromagnetic field strenghts the density ratio across the shock wave may be greater than the ordinary gasdynamic limit and, in such cases, the pressure and density ratios are related in an inverse manner, in contrast to the behaviour for ordinary gasdynamic or magnetogasdynamic shock waves. The magnetogasdynamic combustion wave has similar properties to that in ordinary gasdynamics.
A solution for three-dimensional vortex flows with strong circulation
Authors: Lewellen W. S.
Published: March 2006

The Navier-Stokes equations for a viscous, incompressible fluid are considered for a steady, axisymmetric flow composed of a strong rotation combined with radial sink flow which exhausts axially inside a finite radius. The equations are reduced to two coupled partial differential equations in terms of the stream function and circulation. The equations contain three dimensionless parameters: the radial Reynolds number, a characteristic ratio of mass flow per unit lenght to circulation, and a characteristic ratio of an axial dimension to a radial dimension. The product of these last two dimensionless parameters is used as a new expansion parameter for generating an asymptotic series solution. To zeroth order in this parameter, the solution for the stream function is a linear distribution between two axial boundary values. First-order correction terms are calculated for a specific example.

In discussing these equations the limitations of the exact solutions due to Donaldson & Sullivan (1960) and Long (1961) are noted. These exact solutions are contrasted with the approximate treatment of this type of vortex originated by Einstein & Li (1951) and generalized by Deissler & Perlmutter (1958).
On the hydrodynamic and hydromagnetic stability of swirling flows
Authors: Howard Louis N. , Gupta A. S.
Published: March 2006

Some general stability criteria for non-dissipative swirling flows are derived, and extended to the case of an electrically conducting fluid in the presence of axial magnetic field and current. In particular it is shown that the analogy between a rotating and a stratified fluid holds in this case, and that an important determinant of stability is a ‘Richardson number’ based on the analogue of the density gradient and the shear in the axial flow.
Magnetohydrodynamic wakes
Authors: Glauert M. B.
Published: March 2006

The most notable feature of the magnetohydrodynamic flow at large distances from a three-dimensional body is the formation of two wakes, within which vorticity and electric current are confined. In this paper results are obtained for the effective diffusivity and the relation between current and vorticity in each wake, for the balance between the strengths of the disturbances in the wakes and in the irrotational current-free flow outside, and for the lift and drag forces acting on the body. The final answers take the form of remarkably simple extensions of the corresponding formulae for non-conducting flow. In spite of the extra wake and the presence of a magnetic as well as a velocity field, the flow perturbation at large distances still has only three degrees of freedom.
On the stable shape of subliming bodies in a high-enthalpy gas stream
Authors: Simpkins Peter G.
Published: March 2006

This paper describes a series of experiments carried out in a high-enthalpy stream of argon on materials that are known to sublime. The results confirm that an axisymmetric Teflon model ablates to a stable shape which is independent of the initial nose profile. The effect of changing the total enthalpy of the gas is simply to alter the recession rate of the nose. The experimental results show poor agreement with a simple theory which ignores the effects of mass transfer in the boundary layer.
On shear-layer instability, breakdown and transition
Authors: Greenspan H. P. , Benney D. J.
Published: March 2006

The problem of the linear stability of a time-dependent shear flow is investigated and the effects of contraction and expansion of the layer are discussed. Models of flows observed prior to breakdown are constructed and used to investigate the resulting secondary instabilities which are shown to be extremely violent and in essential agreement with recent experiments. In relatively short time, one half period of the primary oscillation, the energy in the secondary disturbance increases by two orders of magnitude; the wave-number corresponding to maximum amplification is five times that of the primary wave.
Free convection laminar boundary layers in oscillatory flow
Authors: Nanda R. S. , Sharma V. P.
Published: March 2006

The effect of harmonic oscillations in the magnitude of the surface temperature on the free-convection laminar velocity and temperature boundary layers on a flat plate is analysed. Low-and high-frequency solutions are developed separately. The results obtained are in striking contrast to the corresponding results for forced-convection flows.
The round turbulent jet in a cross-wind
Authors: Keffer J. F. , Baines W. D.
Published: March 2006

The flow of a jet directed normal to a uniform, steady cross-wind is considered. Experimental results show that for various jet strengths, the position of the jet in space, when stretched by the ratio of jet to cross-wind momenta, is described by a single function. Exceptions exist at very low velocity ratios where a shift of the potential core is evident. A natural system of axes is used to define important directions of the flow. The integrated equation of motion along the primary jet flow direction is made dimensionless after the general method of Morton (1961) and a virtual source is defined for the flow. It is shown that a single functional behaviour of the axial jet velocity exists for various velocity ratios if the jet is considered to originate from this source. Lateral velocity profiles show a similarity when scaled by appropriate lengths and velocities but true self-preservation is not attained.
On the energy balance of a turbulent mixing layer
Authors: Csanady G. T.
Published: March 2006

An analysis of experimental results shows that the three most important terms in the energy balance of a mixing layer—the production, diffusion and dissipation terms—may be expressed in terms of an eddy viscosity, eddy diffusivity for turbulent energy, and a microscale, respectively, all being constant for a given cross-section. A first-order solution calculated for the resulting differential equation yields a turbulent intensity profile in qualitative agreement with experiment. The peak value of the turbulent intensity is found to depend on a dissipation constant and on the ratio of eddy diffusivity for turbulent energy to eddy viscosity. Experiments carried out with the intention of reducing turbulent intensities by means of extraneous vortices, generated by small delta wings, have shown slight increases in intensity, presumably because eddy viscosity increases with eddy diffusivity.
On the Rayleigh-Taylor problem in magneto-hydrodynamics with finite resistivity
Authors: Jukes J. D.
Published: March 2006

In order to elucidate the importance of the infinite conductivity assumption in MHD a simple problem has been studied. This is a Rayleigh-Taylor problem of two superposed fluids under gravity partially stabilized by a uniform, horizontal magnetic field. It is found that the inclusion of a small, but finite resistivity introduces new and unexpected solutions. For instance, moderately long, stabilized’ waves are now found to grow aperiodically and unexpectedly rapidly at a rate ∝ ($\rm {resistivity}^{\frac{1}{3}$). Other modes are found to be periodic and damped at a rate ∝ ($\rm {resistivity}^{\frac{1}{3}$).
On the stability of heterogeneous shear flows. Part 2
Authors: Miles John W.
Published: March 2006

Small disturbances relative to a horizontally stratified shear flow are considered on the assumptions that the velocity and density gradients in the undisturbed flow are non-negative and possess analytic continuations into a complex velocity plane. It is shown that the existence of a singular neutral mode (for which the wave speed is equal to the mean speed at some point in the flow) implies the existence of a contiguous, unstable mode in a wave-number (α), Richardson-number (J) plane. Explicit results are obtained for the rate of growth of nearly neutral disturbances relative to Hølmboe's shear flow, in which the velocity and the logarithm of the density are proportional to tanh (y/h). The neutral curve for this configuration, J = J0(α), is shown to be single-valued. Finally, it is shown that a relatively simple generalization of Hølmboe's density profile leads to a configuration having multiple-valued neutral curves, such that increasing J may be destabilizing for some range (s) of α.
Magnetogasdynamic deflagration and detonation waves with ionization
Authors: Helliwell J. B.
Published: March 2006

The propagation of a one-dimensional combustion wave into a non-ionized gas at rest in the presence of an electromagnetic field is considered when ionization of the gas occurs across either the combustion wave or a preceding shock wave. The electric and magnetic fields in the undisturbed gas ahead of the waves are mutually perpendicular and orthogonal to the direction of wave propagation. It is shown that steady detonation occurs at a point which is analogous to the Chapman-Jouguet point of ordinary gasdynamic combustion theory. Numerical calculations are made of the state of the gas between and behind the waves in two particlar models, in both of which the upstream electric field is zero. The models are then equivalent to magnetogasdynamic phenomena in a perfectly conducting gas. First, the case of steady detonation is studied. Secondly, steady deflagration in a tube, closed at one end, is discussed.
Magnetohydrodynamic flow in a rectangular tube at high Hartmann number
Authors: Williams W. E.
Published: March 2006

Asymptotic forms, valid for high Hartmann numberM, are obtained for the mean velocity for laminar magnetohydrodynamic flow in a rectangular tube. For a tube with non-conducting walls it is found that, neglecting exponentially damped terms, the mean velocity can be expressed in closed form in terms of tabulated functions. The first three terms of the expansion of the mean velocity in inverse powers ofMare in extremely close agreement with a corresponding expansion obtained by Shercliff (1953) using a boundary-layer method.

For perfectly conducting walls the first five terms of an expansion in inverse powers ofMare obtained.
Turbulent free convection above a heated plate inclined at a small angle to the horizontal
Authors: Tritton D. J.
Published: March 2006

An investigation has been made of the structure of the motion above a heated plate inclined at a small angle (about 10°) to the horizontal. The turbulence is considered in terms of the similarities to and differences from the motion above an exactly horizontal surface. One effect of inclination is, of course, that there is also a mean motion.

Accurate data on the mean temperature field and the intensity of the temperature fluctuations have been obtained with platinum resistance thermometers, the signals being processed electronically. More approximate information on the velocity field has been obtained with quartz fibre anemometers. These results have been supplemented qualitatively by simultaneous observations of the temperature and velocity fluctuations and also by smoke experiments.

The principal features of the flow inferred from these observations are as follows. The heat transfer and the mean temperature field are not much altered by the inclination, though small, not very systematic, variations may result from the complexities of the velocity field. This supports the view that the mean temperature field is largely governed by the large-scale motions. The temperature fluctuations show a systematic variation with distance from the lower edge and resemble those above a horizontal plate when this distance is large. The largescale motions of the turbulence start close to the lower edge, but the smaller eddies do not attain full intensity until the air has moved some distance up the plate. The mean velocity receives a sizable contribution from a ‘through-flow’ between the side-walls. Superimposed on this are developments that show that the momentum transfer processes are complex and certainly not capable of representation by any simple theory such as an eddy viscosity. On the lower part of the plate there is surprisingly large acceleration, but further up the mixing action of the small eddies has a decelerating effect.
Cavitation of a viscous fluid in narrow passages
Authors: Taylor G. I.
Published: March 2006

The conditions which determine the existence and position of cavitation in the narrow passages of hydrodynamically lubricated bearings have been assumed to be the same as those which produce cavitation bubbles, namely a lowering of pressure below that at which gas separates out of fluid. This assumption enables certain predictions to be made which in some cases are verified, but it does not provide a physical description of the interface between oil and air. Theoretical analysis of the situation seems to be beyond our present capacity, and in none of the experiments so far published has it been possible to measure both the most important relevant data, namely the minimum clearance and the oil flow through it.

A method is described here which enables this to be done. It turns out that two physically different kinds of cavitation can occur. One of these is well described by the existing theory and assumption. Surface tension plays no part in it, and in most text books on hydrodynamic lubrication is not even mentioned. The other kind, which is akin to hydrodynamic separation rather than bubble cavitation, depends essentially on surface tension. Both kinds appear clearly in published photographs taken through transparent bearings, but the experimenters do not seem to have distinguished between them.

The reason why surface tension, which is only able to supply stresses that are exceedingly small compared with the pressure variation in the fluid itself, may have a large effect on the flow can be understood by considering the flow of a viscous fluid in a tube when blown out by air pressure applied at one end. For any given length of fluid the rate of outflow depends almost entirely on the pressure applied, the surface tension force being negligible; but the amount of fluid left in the tube after the air column has reached the end depends essentially on surface tension.
Observations on oblique shock waves in gaseous detonations
Authors: Edwards D. H. , Jones T. G. , Price B.
Published: March 2006

An account is given of photographic and pressure observations made on the oblique shock waves occurring in the wake of self-sustaining detonation waves in hydrogen-oxygen mixtures initially at atmospheric pressure. Four explosion tubes were employed, of which three are of circular cross-section with internal diameters of 10, 5 and 1·6 cm and the fourth is a square-section tube of side 1·5 in.

On the assumption that the oblique shocks are sufficiently weak to be regarded as Mach waves, the flow Mach number relative to the detonation front is determined; these are found to be substantially higher than the values predicted by deal one-dimensional theory. The measured flow Mach numbers in the rarefaction are then used to calculate the pressure distribution in this region on the basis of the supersonic nozzle model due to Fay (1959, 1962). The predictions of this model are found to disagree with with the observed static pressure profiles. Moreover, the pressure following the initial peak persists at a higher value than the theoretical for distances of the order of 5–10 cm behind the front. This phenomenon implies that the wall boundary-layer pressure remains higher than the C-J value and it is suggested that the pressure difference across the boundary layer can account for the formation of the oblique waves.

The supersonic features of the flow can be accounted for by the turbulent-structure hypothesis of White (1961). Some validation of this hypothesis is provided here by the observation of the absence of the oblique shocks in overdriven detonation waves caused by the diminished effects of turbulence. This observation is consistent with the view that the oblique shocks are generated by the pressure difference across the boundary layer near the front as this difference would also be diminished in an over-driven wave.
The stability of Couette flow in the presence of an axial magnetic field
Authors: Kurzweg Ulrich H.
Published: March 2006

The stability of Couette flow between concentric, co-rotating cylinders in an axial magnetic field is examined for fluids of arbitrary magnetic Prandtl number Pm = ν/η, where ν is the kinematic and η the magnetic viscosity of the fluid. It is assumed that the gap spacing d between the cylinders is small compared to the mean radius and that no magnetic disturbances penetrate into the cylinder walls. The critical Taylor number at which non-oscillatory disturbances are marginally stable is determined as a function of the magnetic Prandtl number and the dimensionless parameter S = (Vad/v)2, where Va is the Alfvén velocity. Asymptotic formulas relating the critical Taylor number to the magnitude of the magnetic field are derived for the limiting conditions of very small and very large magnetic Prandtl number.
Experiments on the pressure drop created by a sphere settling in a viscous liquid
Authors: Pliskin Irwin , Brenner Howard
Published: March 2006

Experimental measurements were made of the difference in pressure at large distances on either side of a spherical particle settling slowly along the axis of a long circular tube filled with viscous liquid. At low particle Reynolds numbers and for small sphere-cylinder diameter ratios, it was found that the product of the pressure difference and the cross-sectional area of the tube is equal to twice the drag on the particle, in accord with theory.
Unsteady heat transfer for flow over a flat plate
Authors: Riley N.
Published: March 2006

The boundary-layer flow over a semi-infinite flat plate is investigated. For time t < 0 there is the usual steady velocity boundary layer and, neglecting viscous dissipation, no thermal boundary layer. At t = 0 a temperature boundary layer is initiated without altering the velocity, and the subsequent temperature distributionn is studied for large and small t.
Theory of a two-stage hypervelocity launcher to give constant driving pressure at the model
Authors: Smith F.
Published: March 2006

The increase in hypervelocity launcher velocities, the tendency for models to become more fragile and the use of sabot techniques has made it increasingly more important to reduce peak accelerations during the launch phase. At the same time a high acceleration must be maintained to enable a launcher barrel of reasonable length to be used. This paper considers the theoretical design of a launcher to give constant acceleration to the model. A similarity solution is found for the launcher barrel and the solution is extended to the first stage of the launcher. Departure from ideal gas laws is also discussed and the theory is extended to include the effect of molecular volume. The motion of the driving piston in the first stage is considered in detail and techniques to ensure that the piston motion results in constant base pressure on the model are presented.
Non-equilibrium flow through a nozzle
Authors: Blythe P. A.
Published: March 2006

Vibrationally relaxing flow through a nozzle is examined in the case when the amount of energy in the lagging mode is small. It is shown that there exists a ‘boundary-layer’ region in which relatively large departures from equilibrium occur. The position of this region is given by the type of criterion that has previously been used to predict the onset of ‘freezing’. An analytical solution for the distribution of the vibrational energy in the nozzle is obtained for a particular nozzle geometry, and an expression for the final asymptotic ‘frozen’ value of the vibrational energy far downstream is found. This asymptotic solution can be obtained from conditions at the ‘freezing’ point provided a suitable boundary condition is applied there.
On free-surface oscillations in a rotating paraboloid
Authors: Miles John W. , Ball F. K.
Published: March 2006

Lamb's analysis of small-amplitude, shallow-water oscillations in a rotating paraboloid, interpreted by him in the inconsistent context of an approximately plane free surface, is re-interpreted to obtain results that are valid for
$0 \le \omega^2l|2g \; \textless \;1$
(ω = rotational speed, l = latus rectum of paraboloid); no equilibrium is possible for ω2l/2g > 1. It is shown that the frequencies of the dominant modes for the azimuthal wave numbers 0 (axisymmetric motion) and 1 are independent of ω for an observer in a non-rotating reference frame and that the frequencies of all other axisymmetric modes are decreased by rotation (Lamb concluded that they would be increased). An axisymmetric mode of zero frequency, which was over-looked by Lamb, also is found.

Exact solutions to the non-linear equations of motion, which reduce to the aforementioned dominant modes for small amplitudes, are determined. The axisymmetric solution is inferred from similarity considerations and is found to contain all harmonics of the fundamental frequency. The finite motion of azimuthal wave-number 1 is a quasi-rigid displacement of the liquid and is found to be simple harmonic except for a second-harmonic component of the free-surface displacement (but the horizontal velocity at a given point remains simple harmonic).
Further results on the over-all density ratios of shock waves in carbon dioxide
Authors: Zienkiewicz H. K. , Johannesen N. H. , Gerrard J. H.
Published: March 2006

Previous results on the over-all density ratio of shock waves in CO2, confirming experimentally the theoretical equilibrium value, have been extended to a shock Mach number of 7·3. The discrepancy between our results and earlier Princeton results approaches 18% at a Mach number of 7. Possible reasons for this are discussed, with particular reference to the interferometer technique, but no explanation has been found.