bluuebunny/crossref_metadata_2025 huggingface dataset:
An experimental investigation of stability and interfacial waves in co-current flow of two liquids
Authors: Charles M. E. , Lilleleht L. U.
Published: March 2006

The stability of the co-current stratified flow of oil and water was investigated experimentally in a horizontal rectangular conduit. Laminar-turbulent transitions were determined for both phases. With the two-phase system the transition to turbulence in the water phase occurred at a higher Reynolds number in the presence of a laminar oil layer provided the input water-to-oil ratio was relatively high, while the transition in the oil phase took place at a lower Reynolds number in the presence of a turbulent water layer. The appearance of first interfacial waves coincided with the transition to turbulence of the less viscous or water phase. This suggests that in the system investigated the resonance mechanism as proposed by Phillips (1957) was responsible for the generation of these first waves. However, at relatively high water flow rates and water-to-oil ratios more pronounced waves were observed which appeared to be generated by an instability in the mean flow.
Excitation of internal waves by a turbulent boundary layer
Authors: Townsend A. A.
Published: March 2006

In a barotropic fluid, a free turbulent flow induces a fluctuating potential flow which is determined by the instantaneous flow near the edge of the turbulent flow. If the surrounding fluid is stably stratified, internal wave-motions are possible and, in general, wave-energy accumulates until it is sufficient to modify the turbulent flow. Here the growth of wave-motion from rest is examined with particular reference to the atmospheric problem of wave excitation by the surface boundary layer. Wind shear is supposed negligible outside the turbulent flow and the disturbances from the boundary layer are assumed to travel with a convection velocity V relative to the upper air. For times large compared with {−g/ρ(dρ/dz)}−½ (ρ is the potential density), most of the wave-energy resides in components of phase-velocity near the convection velocity. For a model atmosphere with increased stability above a tropopause, this resonance mechanism leads to the formation of wave-groups with crests at right-angles to the convection velocity and wavelengths near 2πV[−g/ρ(dρ/dz)]−½. Using likely values for the surface disturbances, wave-amplitudes of order 100 m can develop within several hours of the initiation of the boundary layer but sufficient amplitude to produce overturning or breaking is unlikely within a reasonable time.
The decay of a turbulent swirl in a pipe
Authors: Kreith Frank , Sonju O. K.
Published: March 2006

This paper presents a linearized theory for the average decay of a tape-induced fully developed turbulent swirl in flow through a pipe. In the Reynolds number range between 104and 105the theoretical analysis was found to be in good agreement with experimental data obtained with water in a 1 in. pipe, provided the eddy diffusivity was chosen appropriately.

It was observed that a turbulent swirl decays to about 10–20% of its initial intensity in a distance of about 50 pipe diameters, the decay being more rapid at smaller than at larger Reynolds numbers. The theoretical swirl velocity distribution agreed qualitatively with experimental measurements at distances less than 20 diameters downstream from the outlet of the swirl inducer, but deviated from the experimental results further downstream.
A three-dimensional turbulent boundary layer
Authors: Perry A. E. , Joubert P. N.
Published: March 2006

The purpose of this paper is to provide some possible explantions for certain observed phenomena associated with the mean-velocity profile of a turbulent boundary layer which undergoes a rapid yawing. For the cases considered the yawing is caused by an obstruction attached to the wall upon which the boundary layer is developing. Only incompressible flow is considered.

§1 of the paper is concerned with the outer region of the boundary layer and deals with a phenomenon observed by Johnston (1960) who described it with his triangular model for the polar plot of the velocity distribution. This was also observed by Hornung & Joubert (1963). It is shown here by a first-approximation analysis that such a behaviour is mainly a consequence of the geometry of the apparatus used. The analysis also indicates that, for these geometries, the outer part of the boundary-layer profile can be described by a single vector-similarity defect law rather than the vector ‘wall-wake’ model proposed by Coles (1956). The former model agrees well with the experimental results of Hornung & Joubert.

In §2, the flow close to the wall is considered. Treating this region as an equilibrium layer and using similarity arguments, a three-dimensional version of the ‘law of the wall’ is derived. This relates the mean-velocity-vector distribution with the pressure-gradient vector and wall-shear-stress vector and explains how the profile skews near the wall. The theory is compared with Hornung & Joubert's experimental results. However at this stage the results are inconclusive because of the lack of a sufficient number of measured quantities.
The investigation of a standing wave due to gas blowing upwards over a liquid film; its relation to flooding in wetted-wall columns
Authors: Shearer C. J. , Davidson J. F.
Published: March 2006

A theory is given to predict the shape and amplitude of a standing wave formed on a liquid film running down a vertical surface, and due to an upward flow of gas over the liquid surface. The wave is maintained in position by the pressure gradients induced within the gas stream by acceleration over the windward part of the wave; over the leeward part of the wave, the gas pressure is roughly constant due to breakaway of the gas flow.

The wave amplitude is found to be very sensitive to gas velocity so that the theory predicts a critical gas velocity beyond which the wave amplitude becomes very large; this critical velocity is confirmed by experiment, and the experiments confirm the predicted wave shape. The critical gas velocity also agrees reasonably well with published values of the flooding velocity in empty wetted-wall tubes; this velocity is defined as the point at which countercurrent flow of gas and liquid becomes unstable. The phenomenon of flooding, which has puzzled chemical engineers for many years, may thus be due to wave formation on the liquid film.

From the theory are derived three dimensionless groups, namely, Weber number $We \equiv \rho_g U_c^2t_0|T$, liquid-film Reynolds number $Re \equiv 4\rho_l Q|\mu, and Z \equiv T(\rho_l|\mu g)^{1/3}|\mu$. Here Uc is the critical gas velocity, Q is the liquid volume flow rate per unit wetted perimeter, ρg and ρl are the gas and liquid densities, μ is the liquid viscosity and T is its surface tension; $t_0 = (3\mu Q|\rho_lg)^{1/3}$ is the liquid film thickness in the absence of gas flow. We, Re and Z are uniquely related at the flooding point, and a diagram is presented to show this relation. This diagram will enable designers to predict flooding in wetted-wall tubes, though more experimental verification is required.
Properties of inviscid, recirculating flows
Authors: Wood W. W.
Published: March 2006

Integral relations are derived for steady, incompressible recirculating motions with small viscous forces. The circuit time of a fluid particle on a closed streamline in steady, inviscid flow is shown to be the same for all the closed streamlines on a surface of constant total head.

The discontinuities of velocity and velocity gradient that occur in the motion of inviscid fluid filling a closed, rotating cylinder set in a rotating support with the two rotation axes slightly misaligned are then investigated.
On two-dimensional inviscid flow in a waterfall
Authors: Clarke N. S.
Published: March 2006

This paper is concerned with the two-dimensional flow in a free waterfall, falling under the influence of gravity, the fluid being considered to be incompressible and inviscid. A parameter ε, such that 2/ε is the Froude number based on conditions far upstream, is defined and considered to be small. A flowline co-ordinate system is used to overcome the difficulty that the boundary geometry is not known in advance. An asymptotic expansion based on ε is constructed as an approximation valid upstream and near the edge, but singular far downstream. Another asymptotic expansion, based upon the thinness of the fall, is constructed as an approximation valid far downstream, but failing to satisfy the conditions upstream. The two expansions are then matched to give a solution covering the whole flow field. The shapes of the free streamlines are shown for a number of values of ε for which the solutions are seemingly valid.
The lift on a small sphere in a slow shear flow
Authors: Saffman P. G.
Published: March 2006

It is shown that a sphere moving through a very viscous liquid with velocity V relative to a uniform simple shear, the translation velocity being parallel to the streamlines and measured relative to the streamline through the centre, experiences a lift force 81·2μVa2k½/v½ + smaller terms perpendicular to the flow direction, which acts to deflect the particle towards the streamlines moving in the direction opposite to V. Here, a denotes the radius of the sphere, κ the magnitude of the velocity gradient, and μ and v the viscosity and kinematic viscosity, respectively. The relevance of the result to the observations by Segrée & Silberberg (1962) of small spheres in Poiseuille flow is discussed briefly. Comments are also made about the problem of a sphere in a parabolic velocity profile and the functional dependence of the lift upon the parameters is obtained.
The effect of non-linearity at the free surface on flow past a submerged cylinder
Authors: Tuck E. O.
Published: March 2006

Plane potential flow past a circular cylinder beneath a free surface under gravity is investigated in order to determine the importance or otherwise of non-linear effects from the free-surface boundary condition. It is shown that non-linear second-order corrections to the first-order linearized expressions for the wave-induced forces on the cylinder are considerably larger than second-order effects which are present even with a linear free-surface condition. Further evidence for the importance of non-linearity is presented in the form of streamline plots of the first-order solution showing strange behaviour at wave crests.
Hypersonic non-equilibrium flow over slender bodies
Authors: Lee Richard S.
Published: March 2006

An analytical study is made of non-equilibrium effects on hypersonic, inviscid flow over slender, axisymmetric bodies. Also, two-dimensional results are obtained for the purpose of comparison. The rate process under consideration is that of molecular vibration of the gas. The exact problem is solved by successive approximations based on a double-expansion scheme involving two small parameters: one represents the fact that the bodies considered are slender; the other represents the facts that the vibrational internal energy is small in comparison to the total enthalpy. The exact differential equations and boundary conditions are simplified to the hypersonic-small-disturbance-approximation form. The unknown quantities in this approximate problem are expanded into series of the small parameter, (γ − 1)/(γ + 1), which is ⅙ for a diatomic gas. In this formulation it is found that the classical hypersonic similitude can be extended by slight modifications to cover the added consideration of vibrational non-equilibrium. The modifications introduced are the normalization of all lengths by the characteristic relaxation length of the gas and the addition of a new dimensionless parameter, which is a measure of the excitation level of the vibrational internal energy in the flow field. Explicit, uniformly valid solutions are obtained for the specific problems of flow over a slender cone and of that over a thin wedge. The successive approximations are carried as far as necessary to show the non-equilibrium effect, which differs in order of magnitude for the various flow quantities. One interesting feature of the solutions is the non-monotonic behaviour in the relaxation of the surface pressure of both the cone and the wedge, in contrast to intuitive expectation. The result for a 20° cone in a free stream of oxygen at 300° K and a Mach number of 15 is displayed and compared with the numerical solution of the exact problem using the method of characteristics.
On the general theory of contained rotating fluid motions
Authors: Greenspan H. P.
Published: March 2006

A general linear theory is developed to describe the manner in which rigid fluid rotation is established from a prescribed initial state of motion in a container of arbitrary shape. The container rotates with uniform angular velocity and is filled with a viscous incompressible fluid.

A new mean circulation theorem is proved and used to separate the flow into geostrophic motion and inertial oscillations. The basic eigenvalue problem is studied and important properties concerning spectrum, orthogonality and completeness are deduced. The effect of viscosity on the inviscid modes is calculated in a manner that maintains the solution uniformly valid through the spin-up time. All modes decay in this time scale which characterizes the entire transition to rigid rotation in all configurations.
Incompressible slip flow past a semi-infinite flat plate
Authors: Murray J. D.
Published: March 2006

An asymptotic solution to the Navier-Stokes equation is obtained for the incompressible flow of a viscous fluid past a semi-infinite flat plate when a slip boundary condition is applied at the plate. The results for the shear stress (and hence the slip velocity) on the plate differ basically from those obtained by previous authors who considered the same problem using some form of the Oseen equations.
On the curvature and torsion of an isolated vortex filament
Authors: Betchov Robert
Published: March 2006

We consider a very thin vortex filament in an unbounded, incompressible and inviscid fluid. The filament is not necessarily plane. Each portion of the filament moves with a velocity that can be approximated in terms of the local curvature of the filament. This approximation leads to a pair of intrinsic equations giving the curvature and the torsion of the filament, as functions of the time and the arc length along the filament. It is found that helicoidal vortex filaments are elementary solutions, and that they are unstable.

The intrisic equations also suggest a linear mechanism that tends to produce concentrated torsion and a non-linear mechanism tending to disperse such singularities.
On fluid flow induced by a rotating magnetic field
Authors: Moffatt H. K.
Published: March 2006

The interior of an insulating cylindrical container is supposed filled with an incompressible, electrically conducting, viscous fluid. An externally applied magnetic field is caused to rotate uniformly about an axis parallel to the cylinder generators (by applying two alternating components out of phase at right angles). Induced currents in the fluid give rise to a Lorentz force which drives a velocity field, which in general may have a steady and a fluctuating component. The particular case of a circular cylindrical container in a transverse magnetic field is studied in detail. Under certain reasonable assumptions, the resulting flow is shown to have only the steady component, and the distribution of this component is determined. Some conjectures are offered about the stability of this flow and about the corresponding flows in cavities of general shape.
The stability of an unsteady Kelvin–Helmholtz flow
Authors: Kelly R. E.
Published: March 2006

The investigation concerns the stability of an interface between two inviscid fluids of different densities which flow parallel to each other in an oscillatory manner. When the difference in the mean speeds is below the steady, critical speed for instability but is large compared to the amplitude of the fluctuations, parametric amplification of waves at the interface occurs, and the interface exhibits a resonance of a subharmonic nature. The paper concludes with a discussion of the stability of unsteady shear layers on the basis of the results.
The distortion of a magnetic field by the flow of a conducting fluid past a circular cylinder
Authors: Seebass R. , Tamada K.
Published: March 2006

The distortion of a uniform magnetic field, aligned with the flow at infinity, by the potential flow of an inviscid conductor about a circular cylinder is determined. Potential flow of the fluid occurs when the interaction parameter is small; this is the case studied here. In the flow-potential and stream-function plane the problem may be formulated as a singular integral equation. Solutions of this equation show that for small fluid conductivities the magnetic field lines are distorted in the sense of being dragged along by the motion of the fluid. This process continues as the conductivity increases, with fewer and fewer of the magnetic field lines entering the body. For large conductivity this reduced flux of field lines enters over most of the body surface and exits in the neighbourhood of the rear stagnation point; behind the body there is a jet-like structure of magnetic field lines.
The three-dimensional laminar boundary layer on a flat plate
Authors: Sowerby L.
Published: March 2006

A series expansion is derived for the three-dimensional boundary-layer flow over a flat plate, arising from a general main-stream flow over the plate. The series involved are calculated as far as terms of order ξ2, where ξ is a non-dimensional parameter defining distance measured from the leading edge of the plate. The results are applied to an example in which the main stream arises from the disturbance of a uniform stream by a circular cylinder mounted downstream from the leading edge of the plate, the axis of the cylinder being normal to the plate. Calculations are made for shear stress components on the plate, and for the deviation of direction of the limiting streamlines from those in the main stream.
Shock-shock interaction on a slender supersonic cone
Authors: Blankenship Victor D.
Published: March 2006

The transient pressure field produced behind a plane shock wave of arbitrary strength, which encounters a slender supersonic cone head on, is theoretically predicted. The analysis is restricted to small cone angles (in order that Mach-reflexion will occur at the surface) and to inviscid flow.

A conical-flow technique is utilized to transform the small-perturbation equations of time-dependent rotational motion of the fluid behind the deflected plane shock into time-independent equations. From these equations, a boundary-value problem for pressure alone, in the Mach-reflexion region, is derived which is solved numerically. Results for the small perturbation pressure field of the cone are contrasted with Smyrl's (1963) results, which hold for a moving wedge, for a range of values of cone and plane shock speeds.
The steady motion of a particle of arbitrary shape at small Reynolds numbers
Authors: Cox R. G.
Published: March 2006

The results given by Brenner & Cox (1963) for the resistance of a particle of arbitrary shape in translation at small Reynolds numbers are generalized. Thus we consider here a single particle of arbitrary shape moving with both translation and rotation in an infinite fluid, the Reynolds number R of the fluid motion being assumed small. With the additional assumption that the motion is steady with respect to some inertial frame of reference, we calculate both the force and couple on the body as an expansion in the Reynolds number to O(R2 In R). This force and couple are expressed entirely in terms of various Stokes flows for the given body in rotation or translation.

A discussion is given of the form taken by the formulae for the force and couple for cases in which the body possesses symmetry properties. Quantitative results are obtained for both a spheroid and a dumb-bell-shaped body in pure translation and also for a translating rotating sphere and for a dumb-bell-shaped body in pure rotation.

The application of the general results to ‘quasi-steady’ problems is considered, with particular reference to a freely falling spheroid (of small eccentricity) which is shown to orientate itself so that it is broad-side on to its direction of motion.

Finally the general results are compared with those that would be obtained by the use of the Oseen equations. By consideration of a particular example it is shown that the Oseen equations do not in general give the correct value of the force on the body to O(R).
Some experiments on cavities behind disks
Authors: Gadd G. E. , Grant S.
Published: March 2006

Measurements of cavities behind disks in a water tunnel show that at high enough speeds the cavity pressure is not more than 30–40% higher than water-vapour pressure, even when at atmospheric pressure the tunnel water is nearly saturated with air. No other hard conclusions can be drawn from the investigations, which showed many puzzling features, discussed below. It is hoped, however, that the qualitative discussion may prove useful to theoreticians who may seek to improve existing mathematical models of cavitation by taking a more realistic account of the physics of the flow.
Low Reynolds numbers flow past an ellipsoid of revolution of large aspect ratio
Authors: Shi Yun-Yuan
Published: March 2006

The results of Proudman & Pearson (1957) and Kaplun & Lagerstrom (1957) for a sphere and a cylinder are generalized to study an ellipsoid of revolution of large aspect ratio with its axis of revolution perpendicular to the uniform flow at infinity. The limiting case, where the Reynolds number based on the minor axis of the ellipsoid is small while the other Reynolds number based on the major axis is fixed, is studied. The following points are deduced: (1) although the body is three-dimensional the expansion is in inverse power of the logarithm of the Reynolds number as the case of a two-dimensional circular cylinder; (2) the existence of the ends and the variation of the diameter along the axis of revolution have no effect on the drag to the first order; (3) a formula for drag is obtained to higher order.
On similarity solutions of the boundary-layer equations with algebraic decay
Authors: Brown S. N. , Stewartson K.
Published: March 2006

Similarity solutions in which the vorticity decays algebraically towards the outer limit of the viscous layer are shown to be possible limit solutions of the full boundary-layer equations with exponential decay. The discussion is illustrated by consideration of a mainstream applicable to viscous flow in a cone.
The velocity of rise of distorted gas bubbles in a liquid of small viscosity
Authors: Moore D. W.
Published: March 2006

The terminal velocity of rise of small, distorted gas bubbles in a liquid of small viscosity is calculated. Small viscosity means that the dimensionless group gμ4/ρT3 where g is the acceleration of gravity, μ the viscosity, ρ the density and T the surface tension, is less than 10−8. It is assumed—and the numerical accuracy of the assumption is discussed—that the distorted bubbles are oblate ellipsoids of revolution. The drag coefficient is found by extending the theory given recently (Moore 1963) for the boundary layer on a spherical gas bubble. The results are in reasonable quantitative agreement with the experimental data.
Self-preserving development within turbulent boundary layers in strong adverse pressure gradients
Authors: Townsend A. A.
Published: March 2006

The development of a turbulent boundary layer in a strong adverse pressure gradient can be described by the two-layer model proposed by Stratford (1959), in which the outer part of the flow is assumed to be unmodified by the pressure-rise and the inner part described by two local parameters, the surface stress and the pressure gradient. The description suggests that the modification of the original flow is in some sense self-preserving, and it is shown here that self-preserving development of the modification is consistent with the Reynolds equations of turbulent flow in particular pressure distributions. For these distributions, the predictions of the two-layer model are confirmed without any need to make the sharp and arbitrary distinction between the two parts of the boundary layer.
Magnetogasdynamic deflagration under the Chapman-Jouguet condition
Authors: Gordon A. R. , Helliwell J. B.
Published: March 2006

An investigation is made into the propagation of a one-dimensional combustion wave, which consists of a flame front and a precursor shock wave which pass down a tube closed at one end, in the presence of a transverse magnetic field in the undisturbed gas at rest. The shock wave is assumed to be of sufficient strength to ionize completely the initially non-electrically-conducting gas and the conditions at the flame front are taken to satisfy the Chapman–Jouguet condition. Details of the solution are compared with the corresponding results for ordinary gasdynamic deflagration.
The Malkus theory applied to magnetohydrodynamic turbulent channel flow
Authors: Nihoul Jacques C. J.
Published: March 2006

The turbulent flow of a weakly conducting liquid between parallel plates in the presence of a transverse magnetic field is investigated. The form of the mean velocity profile is determined by a series of constraints resulting from the boundary conditions and the Navier–Stokes equations and by the Malkus postulates on the spectrum of the mean vorticity gradient. The width of the transition regions near the walls is derived in terms of the governing dimensionless numbers and this expression is checked, in the asymptotic laminar case, against the well-known Hartmann result. A graphical method, exploiting the relation between the boundary region thickness and the smallest scale of motion defined by the Malkus theory is proposed to determine thescaleof the velocity profile, i.e. the flow rate in terms of the pressure gradient and the magnetic field strength.
The method of characteristics for the three-dimensional unsteady magnetofluid dynamics of a multi-component medium
Authors: Sauerwein Harry Sauerwein
Published: March 2006

A general numerical method of characteristics applicable to problems in magneto-fluid dynamics as well as ordinary fluid dynamics is described. The method can be applied to unsteady three-dimensional flows of chemically reacting, non-equilibrium, multi-component media. Dissipative phenomena must be neglected in order to make the governing equations of change hyperbolic, because the method can be applied only to quasi-linear, hyperbolic, partial differential equations. Practical restrictions on computation time usually require unsteady problems to be limited to cases with short transient times although theoretically the method applies to all unsteady flows. In steady flow the local velocity must be greater than the largest local wave speed. The characteristic and compatibility equations are derived for the most general case of magnetofluid dynamics. A new finite-difference network and its corresponding equations are developed similarly. Specialization of the general method to consider simpler problems is outlined. Preliminary numerical results of calculations using the method are presented. The practicality and feasibility of utilizing the general numerical method of characteristics on presently available, electronic digital computers is evaluated in the light of recent experience in calculating multi-dimensional flows with the method.
Velocity spikes in separated flows
Authors: Hanson F. B. , Kozak S. H. , Richardson P. D.
Published: March 2006

In a recent study related to transition in the wake flows behind circular cylinders held transversely to an air stream, Bloor (1964) has reported the observation of velocity ‘spikes’ and attributed these to the close proximity to the hot wire of vortex centres on the opposite side of the von Kármán vortex street. Further observations of spikes are reported here, and the characteristics of their distribution indicate that other explanations of their form must be found. Some idealized flows are considered, and it is concluded that observations of spikiness within the hot-wire output may be accountable in terms of large-scale distributions of vorticity within the flow convected past the wire, the distributions being reasonable representations of a separated flow. The observations also provide some evidence that small vortices of Strouhal frequency exist on the inside of the coherent separated shear layer, and this may assist in the understanding of the feed-back mechanism where by the von Kármán street establishes itself as a self-perpetuating phenomenon.
Results of an attempt to generate a homogeneous turbulent shear flow
Authors: Rose W. G.
Published: March 2006

An approximately homogeneous turbulent shear flow is generated in an open-return wind tunnel test-section by a plane parallel-rod grid of uniform rod diameter and non-uniform rod spacing. The grid design is based upon an analysis by Owen & Zienkiewicz (1957). Hot-wire measurements taken in this flow include mean velocities, component turbulence intensities, shear and two-point space correlations, and energy spectra. In addition, microscales, obtained both from instantaneous time derivatives of the hot-wire signal and from two-point space correlations, and integral scales, calculated both from correlations and energy spectra, are reported.

Based upon these results, it is concluded that, far enough away from the grid and the test-section wall boundary layers:

The turbulence intensities are maintained at uniform values by the nearly constant mean shear.

The turbulent shear stress approaches an asymptotic value.

Measured two-point space correlation coefficients and one-dimensional energy spectra attain self-preserving forms.

When distance downstream of the grid is measured in terms of the number of ‘local’ grid rod spacings, (see discussion of microscales obtained from time derivatives), the Taylor microscale defined by the correlation coefficientRuu(rX, 0, 0) grows linearly with this ‘effective’ distance over most of the region measured.

The limited number of integral scale determinations and experimental uncertainty allow only the statements that the magnitude of the longitudinal scale is roughly one-eighth the lateral dimension of the square test-section and tends to increase slightly with ‘effective’ distance from the grid.

The lateral integral scales are approximately one-half the longitudinal scales and also increases with distance from the grid.

The integral scale which characterizes the size of the eddy primarily responsible for momentum transfer is roughly one-tenth the test-section lateral dimension (measured at one point only).
On the damping of internal gravity waves in a continuously stratified ocean
Authors: LeBlond Paul H.
Published: March 2006

The problem studied here is that of the attenuation of internal waves through turbulent mixing in a weakly and exponentially stratified fluid. The equations are linearized and it is assumed that the action of turbulence can be parametrically represented by eddy mixing coefficients and that the influence of bottom friction is restricted to a thin bottom boundary layer. The simple case where there is no rotation and only one component to the stratification is first examined in detail, and the modifications caused by introducing rotation and a second component are subsequently investigated. Subject quantitatively to the choice made for the eddy coefficients, but qualitatively not strongly dependent on that choice, the following conclusions are drawn: (i) very short internal waves (length < 100 m) are strongly damped in basins of all depths; (ii) long internal waves or seiches in shallow seas (depth ≃ 100 m) will not last more than a few cycles as free oscillations; (iii) the attenuation rate for long internal tides is small enough that these should be observable very far from the coasts, but large enough to exclude the possibility of oceanic standing wave systems; (iv) for very long internal waves the damping is predominantly due to the effect of bottom friction, and the attenuation rate becomes almost independent of the actual form of the stratification present in the fluid.
The three-dimensional structure of the wake of a circular cylinder
Authors: Gerrard J. H.
Published: March 2006

A critical scrutiny of the nature of the three-dimensional characteristics of the vortex wake of a circular cylinder serves to suggest lines for further investigation and furnishes some ideas on the nature of the growth and development of these non-uniformities. It is suggested that the basic occurrence in the growth of three-dimensionality is the continuation of vortex lines, oriented more or less parallel to the body, into the direction of the free stream. The causes of this vary, as do the details of the development with the particular situation considered.

Experiments were performed in a wind tunnel at Reynolds numbers based on cylinder diameter of 85, 235 and 2 × 104, at which stable, transitional and turbulent vortices were investigated.
Magneto-gasdynamic flow over a wedge
Authors: Pack D. C. , Swan G. W.
Published: March 2006

The solution for the flow of a fully ionized gas over a wedge of finite angle is known for the case when the applied magnetic field is aligned with the incident stream. In this flow there are current sheets on the surfaces of the wedge. When the magnetic field is allowed to deviate slightly from the stream, the current sheets may move into the gas and become shock waves. The magnetic fields adjacent to the wedge above and below it have to be matched. A perturbation method is introduced by means of which expressions for the unknown quantities in the different regions may be determined when there are four shocks attached to the wedge. The results give insight into the manner in which the shock-wave pattern develops as the obliquity of the magnetic field to the stream increases. The question of the stability of the shock waves is also examined.
The shock-expansion method and Whitham's rule
Authors: Lick Wilbert
Published: March 2006

The assumptions of the shock-expansion method are re-examined. Although the shock-expansion method and Whitham's rule are used to treat two different classes of problems, certain similarities between these two methods are noted. It is suggested that a single procedure leads to solutions for the entire flow field for both classes of problems.
The shape of low-speed capillary jets of Newtonian liquids
Authors: Goren Simon L. , Wronski Stanislaw
Published: March 2006

The shape of a jet of Newtonian liquid issuing from a capillary needle into air is considered. The results of two theoretical approaches are presented. One approach is a perturbation analysis about the final state of the jet and the other is a boundary-layer analysis near the point of jet formation. Comparison of the predictions with experimental jet shapes shows them to be in semi-quantitative agreement. Especially interesting is the presence of a ‘discontinuity’ in the empirical exponential decay rate of the jet radius occurring at a Reynolds number somewhere between 14 and 20 and the correspondence of this discontinuity with the peculiar behaviour in this range of the Reynolds number of the theoretical eigenvalue.
Some remarks on ‘Perturbation solutions in laminar boundary theory’
Authors: Fox Herbert , Chen Shun
Published: March 2006

A procedure is introduced to extend the usefulness of some perturbation solutions previously presented by Libby & Fox (1963) and Fox & Libby (1964). The perturbations are now formulated about a Blasius solution with an unknown origin. This origin, an additional degree of freedom, is selected, in the spirit of local similarity, so that it will yield a better approximation to the initial profile. With this modification the basic solution will handle a much wider class of problems successfully. Numerical examples are presented to demonstrate the improved accuracy and applicability of this new scheme.
Measurements of third-order resonant wave interactions
Authors: Mcgoldrick L. F. , Phillips O. M. , Huang N. E. , Hodgson T. H.
Published: March 2006

This paper presents the results of experiments on the resonant interaction of gravity waves. Two mutually-orthogonal primary wave trains are generated in a tank and their interaction products studied at various positions on the surface. Under suitable conditions, the growing resonant third-order interaction product is identified; its amplitude is shown to be a linear function of the interaction distance. The band-width of the response decreases with increasing distance, as is characteristic of the phenomenon of resonance. The ratio of the frequencies of the primary waves at resonance is very close to that predicted theoretically; the growth rate of the third component is close to, though about 20% higher than, the predicted value. Conditions far from resonance are also studied; it is found that the growing tertiary wave is absent in this case.

These results offer the first unambiguous experimental demonstration of resonant wave interactions.
A second approximation for the velocity of a large gas bubble rising in an infinite liquid
Authors: Collins R.
Published: March 2006

A second approximation for the velocity of a large gas bubble in an infinite liquid is derived from a linear perturbation of the first approximation. Previously known experimental results are in excellent agreement with the resulting velocity,
\[
U = 0.652(g\overline{a})^{\frac{1}{2}},
\]
where $\overline{a}$ is the apparent radius of curvature of the front part of the bubble, and g the acceleration due to gravity. The shape of this second approximation is seen to be indistinguishable from spherical over a large region near the front stagnation point.
Fluctuating lift and drag on a long cylinder of square cross-section in a smooth and in a turbulent stream
Authors: Vickery B. J.
Published: March 2006

The paper presents the results of measurements of fluctuating lift and drag on a long square cylinder. The measurements include the correlation of lift along the cylinder and the distribution of fluctuating pressure on a cross-section. The magnitude of the fluctuating lift was found to be considerably greater than that for a circular cross-section and the spanwise correlation much stronger.

It was found that the presence of large-scale turbulence in the stream had a marked influence on both the steady and the fluctuating forces. The most significant changes were at small angles of attack (%alpha; < 10°) and included a reduction in base suction and a decrease in fluctuating lift of about 50%.
Measured distortion of a laminar circular Couette flow by end effects
Authors: Coles D. , Atta C. Van
Published: March 2006

Measurements at moderately large Reynolds numbers in a finite laminar circular Couette flow show that the tangential motion near the axial plane of symmetry is two-dimensional, within experimental accuracy, but is nevertheless strongly modified by end conditions.
Free gravitational oscillations in rotating rectangular basins
Authors: Rao Desiraju B.
Published: March 2006

The study of free oscillations of a homogeneous liquid under gravity in rotating rectangular basins of uniform depth is undertaken from both theoretical and experimental considerations.

The theoretical study is in the framework of the quasistatic equations. It is also assumed that the curvature of the free surface can be ignored. Numerical computations for the frequencies and modal structures were carried out for several of the slowest antisymmetric and symmetric modes in a square basin and in a rectangular basin of two-to-one dimension ratio, without any restriction on the angular speed of rotation of the basin. These computations are in agreement with a numerical value obtained many years ago by Taylor, and also with several values found by Corkan & Doodson. They exhibit the typical frequency-splitting associated with certain multiplets in the zero-rotation spectrum. Further, the theoretical calculations indicate that the slopes of the curves of frequency versus speed of rotation change sign for some of the modes in rectangular geometry. Such behaviour is not present in circular basins. Negative modes are found to be ‘unstable’ in the sense of Corkan & Doodson; that is, they are transformed into positive modes for sufficiently high rotation. Calculations were also made for the slowest longitudinal oscillations in highly elongated basins to demonstrate the decreasing importance of rotation on the frequencies of these modes.

Experimental work was carried out in a flat-bottomed square tank for the slowest positively and negatively propagating antisymmetric modes and the slowest positively propagating symmetric mode. Good agreement was found between theory and experiment.
A note on slow vibrations in a viscous fluid
Authors: Williams W. E.
Published: March 2006

An approximate expression is obtained for the force on an arbitrary body executing slow vibrations in a viscous fluid.
Magnetohydrodynamic flows of non-equilibrium plasmas
Authors: Sherman Arthur
Published: March 2006

The present paper studies the interaction between non-equilibrium ionization phenomena in a plasma and the non-uniform flow of that plasma. The characteristics of non-equilibrium conditions are reviewed for the uniform flow situation in which electric and magnetic fields may exist. In order to permit study of the non-uniform flow situation a single-fluid theory is proposed in which the electrical conductivity is assumed to be a function of the absolute magnitude of the current density. The resulting highly simplified system of equations are then used to formulate the Hartmann-flow problem. For this case the formerly linear problem becomes non-linear. Despite this, solutions to within a quadrature are obtained when the Hall effect is neglected. The more complex problem including the Hall effect is solved numerically. Solutions showing velocity and current profiles are given. For certain values of the parameters governing the problem it is shown that no solutions exist.
Application of a magnetic mass spectrometer to ionization studies in impure shock-heated argon
Authors: Sturtevant B.
Published: March 2006

A study of the unique role of impurities in the initial stages of ionization relaxation in shock-heated argon, using a sampling mass spectrometer to determine the ionic products of the reaction, is described. The ions are extracted from the shock tube through a small orifice in the end wall after they have diffused through the dense thermal layer adjacent to the wall from the ionizing gas behind the reflected shock wave. The ion diffusion is analysed in detail to assess the possibility that the sampling process alters the reaction products. It is shown that this is unlikely because the impurities are in dilute concentration and the reaction is studied in its initial stages. This mode of sampling is compared with others.

The experiments were conducted in argon at temperature of 16,600 °K and pressure of 16 mmHg with an estimated impurity level of 300 parts per million. A surprisingly large number of different ions were detected during the initial stages of ionization. O+and H+were found in much greater amounts than any of the other products, each being about five times more abundant than A+. The results suggest that H2O is probably quite generally the most important impurity in thermal-ionization experiments, and that ionization ‘incubation’ is due to dissociation of molecular impurities (especially H2O) before ionization commences. Possible explanations of the well-known efficiency of small amounts of impurities in initiating ionization are discussed.
The use of a contraction to improve the isotropy of grid-generated turbulence
Authors: Comte-Bellot Geneviéve , Corrsin Stanley
Published: March 2006

It is found that when the average kinetic energies of normal velocity components in decaying, grid-generated turbulence are equilibrated by a symmetric contraction of the wind tunnel, this equality can persist downstream. A second result is further confirmation of the fact that the best power-law fit to the inverse turbulent energy during the early part of decay is near (x–x1)1·25, for both rod grids and disk grids. The Kolmogorov decay law $\sim (t - t_1)^{\frac{10}{7}}$ is re-derived by a spectral method which is essentially equivalent to the original. Finally, a crude theoretical estimate of component energies in the straight duct after a weak contraction seems to support the experiments.
On transition in a separated laminar boundary layer
Authors: Freymuth Peter
Published: March 2006

This paper deals with the growth of small disturbances in a separated laminar boundary layer for high Reynolds numbers as a function of the dimensionless flow parameters. Using a hot-wire technique, the experiments show that spatially growing disturbances are only affected by the Strouhal number. Thus the basic equations of the process become relatively simple. The experiments show good agreement with theoretical results obtained by means of hydrodynamic stability theory for spatially growing disturbances.
On the formation of weak plane shock waves by impulsive motion of a piston
Authors: Moran John P. , Shen S. F.
Published: March 2006

The piston problem for a viscous heat-conducting gas is studied under the assumption that the piston Mach number ε is small. The linearized Navier–Stokes equations are found to be valid up to times of the order of ε−2mean free times after the piston is set in motion, while at large times the solution is governed by Burgers's equation. Boundary conditions for the large-time solution are supplied by the matching principle of the method of inner and outer expansions, which is also used to construct a composite solution valid both for small and for large times.
Intermittency measurements in the turbulent boundary layer
Authors: Fiedler H. , Head M. R.
Published: March 2006

An improved version of Corrsin & Kistler's method has been used to measure intermittency in favourable and adverse pressure gradients, and the characteristic parameters of the intermittency have been related to the form parameterHof the mean velocity profiles.

It is found that with adverse pressure gradients the centre of intermittency moves outward from the surface while the width of the intermittent zone decreases. The converse is true of favourable pressure gradients, and it seems likely that at sufficiently low values ofHthe flow over the full depth of the layer is only intermittently turbulent.

A new method of intermittency measurement is presented which makes use of a photo-electric probe. Smoke is introduced into the boundary layer and illuminated by a narrow beam of parallel light normal to the surface. The photoelectric probe is focused on the illuminated region and a signal is generated when smoke passes through the focal point of the probe lens. Comparison of this signal with the output from a hot-wire at very nearly the same point shows the identity of smoke and turbulence distributions.
The collapse time of a closed cavity
Authors: Miles John W.
Published: March 2006

The collapse time of a closed cavity that is initially at rest in an incompressible, inviscid fluid of density ρ and ambient pressurep∞has the form\[ t_1 = \{\rho/(p_{\infty} - p_c)\}^{\frac{1}{2}}\ell, \]wherepcis the internal pressure, which is assumed to remain constant during collapse, and [ell ] is a length that depends only on the geometry of the cavity. A variational formulation of the dynamical problem is constructed from Jacobi's statement of the principle of least action. A single-degree-of-freedom approximation is developed from the similarity hypothesis that the cavity collapses through a family of similar surfaces with volume as the generalized co-ordinate. Two-degree-of-freedom approximations are given for both prolate and oblate spheroidal cavities and are used to obtain error estimates for the similarity approximation (approximately 2% for the limiting case of a needle-like, prolate spheroid and approximately ½ % for a disk-like, oblate spheroid). A perturbation analysis is developed for an approximately spherical cavity, which is found to have the same collapse time as a spherical cavity of equal volume within a factor 1 +O(e4), whereeis a representative eccentricity. A first-order correction for surface tension is obtained.