bluuebunny/crossref_metadata_2025 huggingface dataset:
The field boundary of two line currents immersed in a streaming plasma
Authors: Sozou C. , Loizou G.
Published: March 2006

The cavity in which the magnetic field of two arbitrary line currents is confined by a streaming plasma which is assumed cold and perfectly conducting is investigated by using conformal transformations. When the magnetic field at the boundary is always directed in the same sense the finite breadth of the cavity at infinity depends only on the algebraic sum of the inducing currents and not their position. If the two line currents are of opposite sign the boundary magnetic field may change sign at two ‘pseudo-singularities’.
Propulsion by oscillating sheets and tubes in a viscous fluid
Authors: Drummond J. E.
Published: March 2006

Taylor's formula for the velocity of an oscillating sheet in a viscous fluid is extended to larger amplitudes of motion and his formula for the velocity of a rotating or oscillating filament is proved to be valid for amplitudes of motion small but greater than the filament radius. A simple formula is derived for the velocity of a sheet or filament in any general oscillatory motion of small amplitude. The forces and energy involved in oscillating tubes are calculated.
Influence of viscosity, surface tension, and inclination angle on motion of long bubbles in closed tubes
Authors: Zukoski E. E.
Published: March 2006

An experimental study has been made of the motion of long bubbles in closed tubes. The influence of viscosity and surface tension on the bubble velocity is clarified. A correlation of bubble velocities in vertical tubes is suggested and is shown to be useful for the whole range of parameters investigated. In addition, the effect of tube inclination angle on bubble velocity is presented, and certain features of the flow are described qualitatively.
Roughness, bluntness, and angle-of-attack effects on hypersonic boundary-layer transition
Authors: Nagamatsu H. T. , Graber B. C. , Sheer R. E.
Published: March 2006

An investigation was conducted in a hypersonic shock tunnel to study the laminar boundary-layer transition on a highly cooled 10° cone of 4 ft. length over the Mach-number range of 8·5 to 10·5 with a stagnation temperature of 1400 °K. The effects on transition of tip surface roughness, tip bluntness, and ± 2° angle of attack were investigated. With fast-response, thin film surface heat-transfer gauges, it was possible to detect the passage of turbulent bursts which appeared at the beginning of transition. Pitot-tube surveys and schlieren photographs of the boundary layer were obtained to verify the interpretation of the heat-transfer data. It was found that the surface roughness greatly promoted transition in the proper Reynolds-number range. The Reynolds numbers for the beginning and end of transition at the 8·5 Mach-number location were 3·8 × 106−9·6 × 106and 2·2 × 106−4·2 × 106for the smooth sharp tip and rough sharp tip respectively. The local skin-friction data, determined from the Pitot-tube survey, agreed with the heat-transfer data obtained through the modified Reynolds analogy. The tip-bluntness data showed a strong delay in the beginning of transition for a cone base-to-tip diameter ratio of 20, approximately a 35% increase in Reynolds number over that of the smooth sharp-tip case. The angle-of-attack data indicated the cross flow to have a strong influence on transition by promoting it on the sheltered side of the cone and delaying it on the windward side.
Computation and measurement of Hall potentials and flow-field perturbations in magnetogasdynamic flow of an axisymmetric free jet
Authors: Otis David R.
Published: March 2006

The interaction was observed between a supersonic free jet of partially ionized argon and the magnetic field of a coil concentric with the jet. Nominal values of the parameters were: Mach number, 3; Reynolds number, 1000; magnetic Reynolds number, 0·2; magnetic interaction parameter, 1; Hall parameter, 1. The jet was strongly channelled. Axial and radial electric fields were observed in the jet with a net rise in potential across the interaction.

These observations were consistent with predictions based on the single fluid, macroscopic equations, and a simple slug flow model. The current equation was solved to second order in the Hall parameter giving a closed form expression for the Hall potential which agreed with the experiments for weak fields. Flow perturbations were calculated for Mach numbers of 3.11, 6.08, and 10.05, neglecting Hall currents; the calculations are in qualitative agreement with the experiments and show Joule heating to be the main factor in perturbing the flow at high Mach numbers.
Inviscid hypersonic flow on cusped concave surfaces
Authors: Sullivan Philip A.
Published: March 2006

An analysis of the exact equations of the inviscid flow of a perfect gas over cusped concave bodies is described. The field is examined in the limit of infinite free-stream Mach numberM∞. The slope of the shock wave in a small region adjacent to the leading edge is strongly dependent onM∞, while much further downstream the shock-wave slope is controlled primarily by the body slope. Consequently the region near the leading edge introduces into the field downstream a thin layer of gas, adjacent to the body, where the entropy is much lower than that of the gas above it. This layer is so dense that the gas velocity along it is not appreciably slowed by the pressure gradient along the body. However, it is so thin that there is little pressure change across it.

The well-known self-similar solutions to the hypersonic small-disturbance equations have previously only been used to study the flow on blunted slender convex surfaces. They are known to behave singularly at the body. It is shown that there is a region on concave power-law shapes where the self-similar solutions are the correct first approximation to the exact inviscid equations in the limitM∞→ ∞; and that, further, they predict the correct first-order surface pressure.

Numerical results for surface pressure from the similar solutions are presented, and comparisons are made with certain approximate theories available for more general shapes. Pressure measurements taken on a cubic surface in the Imperial College gun tunnel are presented and compared with the theoretical distributions.
The spanwise perturbation of two-dimensional boundary layers
Authors: Crow S. C.
Published: March 2006

Large spanwise variations of boundary-layer thickness and surface shear have been found recently in wind tunnels designed to maintain two-dimensional flow. Bradshaw (1965) argues that these variations are caused by minute deflexions in the free-stream flow rather than by any intrinsic instability of the boundary layers. This paper is a study of the effect of a small, periodic transverse flow on a flat-plate boundary layer. The perturbation flow Reynolds number is assumed to be O(1) as it is in the experiments.
The stability of a family of Jeffery–Hamel solutions for divergent channel flow
Authors: Eagles P. M.
Published: March 2006

A set of Jeffery–Hamel profiles (for radial, viscous, incompressible flow) have been shown by Fraenkel (1962, 1963) to approximate to profiles in certain two-dimensional divergent channels. The stability of a family of these profiles is investigated by a numerical solution of the Orr-Sommerfeld problem. Neutralstability curves are calculated in the (R,k)-planes (where R is the Reynolds number of the basic flow and k is the wave-number of the disturbance), and fairly low critical Reynolds numbers are found. For those profiles that have regions of reversed flow, negative wave velocities are found on the lower branch of the neutral curve, and also it is found that Rk tends to a finite limit as R → ∞ on the lower branch. These unexpected results are further discussed and verified by independent methods. The relation of the calculations to some experiments of Patterson (1934, 1935) is discussed.
Boundary effects in Stokes flow
Authors: Williams W. E.
Published: March 2006

An integral-equation approach is used to calculate the first-order effect of the proximity of a boundary on the Stokes resistance of a body. It is shown, that this approach gives both a simple derivation of the modified Stokes resistance and a method of investigating the accuracy of the final result. The problem of two settling particles is also considered briefly.
Internal waves produced by a convective layer
Authors: Townsend A. A.
Published: March 2006

Fluid impacts on the base of a stably stratified region of fluid cause internal-wave ripples whose spread is predominantly horizontal if the duration of the impacts is long compared with the natural period of the stratified fluid. The development of a single ripple in a slightly viscous fluid is calculated, first with a constant vertical gradient of potential density and then with a gradient varying linearly with height. The single-ripple results are used to find the intensity of the statistically steady wave motion generated by impacts which are randomly distributed in space and time. Above a critical height, dependent on the viscosity and stability of the fluid and on the time and length scales of the impacts, wave energy falls off as the −5/3 power of the height with a constant density gradient and as the −25/6 power with a linearly varying gradient. The predictions are compared with observations of temperature fluctuations in the stable region of an ice-water convection system and with observations of ‘clear-air turbulence’ over strato-cumulus cloud. Reasonable numerical agreement can be obtained with plausible values for the scales of the convective motion which provides the impacts.
On the stability of forward and rearward slug flows due to the motion of a body through a perfectly conducting liquid
Authors: Lessen M. , Zien H. M. , Leibovich S.
Published: March 2006

The stability of forward and rearward slug flows due to the motion of a body through a perfectly conducting liquid with an embedded magnetic field aligned to the direction of motion is studied. It is found that, for sub-Alfvénic flows, the forward and rearward slug flows predicted by Stewartson, Leibovich and Ludford are stable. For super-Alfvénic flows, if at all meaningful, both the forward and the rearward slug flows are stable also.
Asymptotic expansions for laminar forced-convection heat and mass transfer Part 2. Boundary-layer flows
Authors: Goddard J. D. , Acrivos Andreas
Published: March 2006

This is the second of two articles by the authors dealing with asymptotic expansions for forced-convection heat or mass transfer to laminar flows. It is shown here how the method of the first paper (Acrivos & Goddard 1965), which was used to derive a higher-order term in the large Péclet number expansion for heat or mass transfer to small Reynolds number flows, can yield equally well higher-order terms in both the large and the small Prandtl number expansions for heat transfer to laminar boundary-layer flows. By means of this method an exact expression for the first-order correction to Lighthill's (1950) asymptotic formula for heat transfer at large Prandtl numbers, as well as an additional higher-order term for the small Prandtl number expansion of Morgan, Pipkin & Warner (1958), are derived. The results thus obtained are applicable to systems with non-isothermal surfaces and arbitrary planar or axisymmetric flow geometries. For the latter geometries a derivation is given of a higher-order term in the Péclet number expansion which arises from the curvature of the thermal layer for small Prandtl numbers. Finally, some applications of the results to ‘similarity’ flows are also presented.
On convective instability induced by surface-tension gradients
Authors: Smith K. A.
Published: March 2006

The linearized stability problem for steady, cellular convection resulting from gradients in surface tension is examined in some detail. Earlier work by Pearson (1958) and Sternling & Scriven (1959, 1964) has been extended by considering the effect of gravity waves. In order to avoid the use of an assumed coupling mechanism at the interface, the relevant dynamical equations were retained for both phases. It is shown that the existence of a critical Marangoni number is assured, and that for many situations this critical value is essentially that which is appropriate to the case of a non-deformable interface. Usually, surface waves are important only at very small wave-numbers, but they are dominant for unusually thin layers of very viscous liquids.
The stability and transition of an axisymmetric wake
Authors: Sato Hiroshi , Okada Osami
Published: March 2006

Experimental and theoretical investigations were made of the instability and transition of the wake behind an axisymmetric slender body at high Reynolds number. The sound from a loudspeaker was used as an artificial disturbance. The velocity fluctuations induced by the sound are selectively amplified depending on the frequency. The wavelength, the phase velocity and the amplification rate of the velocity fluctuations were measured. A linearized stability equation of the disturbance superposed on the axisymmetric wake was solved numerically for both neutral and amplified disturbances. Theoretical results on eigenvalues and eigenfunctions of the stability equation show good agreement with experimental results.

Measurements on phase distributions in streamwise and azimuthal directions indicate that the line of same phase forms a helix and not a series of discrete closed loops.
An experimental investigation of the instability of an incompressible, separated shear layer
Authors: Browand F. K.
Published: March 2006

The investigation of a separated shear layer was undertaken to clarify the non-linear mechanisms associated with instability and transition to turbulence. Such an investigation is of practical importance since profiles which resemble the separated shear layer are a common occurrence.

A two-dimensional free shear layer was formed by separation of a laminar boundary layer from a rearward-facing step. The free-stream speed was approximately 16 ft./sec. Hot-wire measurements were made in the region directly downstream of the plate trailing edge. The measurements included mean velocity profiles, frequency spectra of the longitudinal fluctuation, and root-mean-square amplitude and phase distributions of various spectral components of the longitudinal fluctuation. Several measurements were designed to detect the presence of periodic spanwise structure.

The most important findings were:

Significant non-linear distortion of the initial unstable wave occurred without periodic spanwise structure.

Non-linear distortion was first manifest by the growth of a subharmonic oscillation, which was strongly intermittent. Numerous harmonics of the sub-harmonic oscillation were also present.

Strong evidence suggests that secondary instabilities were present, which created still higher frequencies.
The solitary wave of maximum amplitude
Authors: Lenau Charles W.
Published: March 2006

The maximum amplitude of the solitary wave of constant form is determined to be 0·83b, where b is the depth far from the crest. In the analysis it is assumed that the crest is pointed and the motion is two-dimensional and irrotational. The complex velocity potential is expressed in terms of known singularities and an infinite power series with unknown coefficients. Approximate solutions are obtained by truncating the power series after N terms, where N = 1, 3, 5, 7, and 9. The amplitude, a measure of the error, and several other pertinent quantities are computed for each value of N.
The flow of a jet from a body opposing a supersonic free stream
Authors: Finley P. J.
Published: March 2006

A series of experiments is described in which a jet issues from an orifice at the nose of a body in supersonic flow to oppose the mainstream. An analytical model of the flow is developed which suggests that the aerodynamic features of a steady flow depend primarily on a jet flow-force coefficient, and the Mach number of the jet in its exit plane. A sufficient condition for steady flow is developed. The experiments are found to agree well with predictions based on the flow model. A short account is presented of some previous investigations, and some of their conclusions are re-examined in the light of the present study.
Wind-generated waves in thin liquid films
Authors: Craik Alex D. D.
Published: March 2006

In the presence of an air stream, a uniform liquid film on a horizontal flat plate may be unstable to small disturbances, and waves may arise. In this paper the hydrodynamic stability of thin liquid films is examined both experimentally and theoretically.

The experiments concern water films thinner than those which have been examined in the past. It is found that, when the film thickness is sufficiently small, a previously unknown type of instability occurs. The theoretical analysis explains this surprising phenomenon.

Due to interaction of the mean airflow and small disturbances of the liquid-air interface, normal and tangential stress perturbations are produced at the liquid surface. It is shown that small wave-like disturbances become unstable when the joint influence of the component of normal stress in phase with the wave elevation and the component of tangential stress in phase with the wave slope is sufficient to overcome the ‘stiffness’ of the liquid surface due to gravity and surface tension. It is found that the destabilizing role of the tangential stress component is dominant for very thin films, and that instability may occur whatever the velocity of the air stream, provided the film is made sufficiently thin.
Report on the I.U.T.A.M. symposium on rotating fluid systems
Authors: Bretherton F. P. , Carrier G. F. , Longuet-Higgins M. S.
Published: March 2006

A symposium on ‘Rotating fluid systems’ was held at La Jolla, California, from 28 March to 1 April 1966. The meeting was organized under the auspices of the International Union of Theoretical and Applied Mechanics, and took place at the Institute of Geophysics and Planetary Physics of the University of California. There were 75 participants, and attendance was by invitation. The subjects discussed included steady flows, both thermally driven and non-thermal; transient motions and instabilities; planetary waves and gravity waves affected by rotation; inertial oscillations; and hydromagnetic flows relating to the Earth's interior. The following is a brief account of the proceedings as seen by the authors. No formal volume of the papers presented is to be published, but references to published or unpublished work are given at the end of this article.
Dynamics of rotating fluids: a survey
Authors: Lighthill M. J.
Published: March 2006

The dynamics of rotating fluids was, in the main, developed by methods special to the field, using the equationsof motion of a fluid inarotatingframe of reference. It is, nevertheless, possible to derive all the leading results from the classical principles of fluid dynamics in non-rotating frames; specifically, from the rules governing rate of change of vorticity. Although writers on the subject have adopted this approach increasingly often in recent years, the author believes that a broad survey of the field, deriving results from those classical rules concerning vorticity, has not previously been given and may be of some interest to fluid dynamicists in general.

The present survey was read to the IUTAM Symposium on Rotating Fluid Systems at La Jolla, California, on 28 March 1966. It states briefly (§2) the rules governing rate of change of vorticity, and then applies them, first, to problems of steady relative motion of rotating fluids; in particular, of the atmosphere (§3), of rotating fluids in the laboratory (§4), and of the oceans (§5). Waves and wavy movements are then studied, first (§6) for systems with constant Coriolis parameter, including inertial waves, surface waves, ‘long waves’ and internal waves, and, secondly (§7)) for systems with variable Coriolis parameter, including Rossby-Haurwitz waves with and without the influence of tidal effects, as well as problems of barotropic and baroclinic instability. Vorticity principles are used as the sole theoretical tool throughout the survey.
The vorticity jump across a flow discontinuity
Authors: Berndt Sune B.
Published: March 2006

Expressions are obtained for the jump in vorticity across a discontinuity surface which is not a contact surface. Admitting arbitrary motion of the fluid and the discontinuity, the most general of these is established on a purely kinematical basis. More specific expressions are obtained by successively enforcing the momentum equation of the flow and the conditions of conservation of mass and momentum across the discontinuity. Eventually Hayes's (1957) result for a gasdynamic discontinuity is recovered.
On the instability of ventilated cavities
Authors: Woods L. C.
Published: March 2006

It has been found that ventilated cavities extending behind hydrofoils, plates, and other two-dimensional bodies, oscillate when the air supply rate is sufficient to reduce the cavitation number to about one-fifth of its natural value. As the rate increases further, higher modes of oscillation occur in which the cavity–water interface supports several waves that are convected downstream towards the wake, which, owing to a pinching-off action replacing the usual entrainment sink, consists of a sequence of large bubbles drifting downstream. A theory of such flows that allows both for the convected velocity fluctuations in the cavity, and for the transport of bubble volume down the wake, is given in this paper. Coupled with a rather simple phenomenological relation between the pressure fluctuations within the cavity and the departure of the pinched-off rear portion of the cavity—explained in terms of the action of the re-entrant jet—this theory successfully predicts the resonance frequencies obtained in experiments by Silberman & Song.

The theory also provides a solution of the more general problem of determining the fluctuations in the pressure distribution over the whole surface of the body, when it is in a prescribed unsteady motion along its axis of symmetry (the theory is confined to symmetrical bodies and flows). Thus the growth in drag due to a sudden increment in the upstream velocity can be predicted, and also the damping forces acting on the body when it is forced to oscillate at a given frequency. It is shown that in all cases the body is unstable.

One important feature of the mathematical model chosen is that it completely avoids the presence of a time-dependent sink at infinity—with its associated infinite pressures—by conserving total volume of wake and cavity in just the same way as vorticity is conserved in unsteady aerofoil theory.
Thermal equilibration behind an ionizing shock
Authors: Wong H. , Bershader D.
Published: March 2006

The physical mechanisms underlying the relaxation process leading to thermal equilibrium behind ionizing shock waves in argon have been studied through use of optical techniques. The non-equilibrium condition in the relaxation region was investigated experimentally by measuring the shift in the fringes due to a change in the refractive index of the medium with a Mach–Zehnder interferometer. Both electron- and mass-density profiles from the shock front to the equilibrium region were determined. The experimental work has been supplemented by a theoretical analysis of the ionization mechanism to explain the measured profiles and relaxation times.
Turbulent boundary layers in decreasing adverse pressure gradients
Authors: Perry A. E.
Published: March 2006

The results of a detailed mean velocity survey of a smooth-wall turbulent boundary layer in an adverse pressure gradient are described. Close to the wall, a variety of profiles shapes were observed. Progressing in the streamwise direction, logarithmic, ½-power, linear and$\frac{3}{2}$-power distributions seemed to form, and generally each predominated at a different stage of the boundary-layer development. It is believed that the phenomenon occurred because of the nature of the pressure gradient imposed (an initially high gradient which fell to low values as the boundary layer developed) and attempts are made to describe the flow by an extension of the regional similarity hypothesis proposed by Perry, Bell & Joubert (1966). Data from other sources is limited but comparisons with the author's results are encouraging.
Bed forms in alluvial channels
Authors: Raudkivi A. J.
Published: March 2006

A solution is offered for the relative phase relationship of bed, depth and surface waves observed in alluvial channels, and is found to be in good agreement with observation in laboratory flumes. The solution does not depend on an assumption of a phase lag between the velocity and sediment movement. The emphasis of the paper is on the mechanics of bed-wave formation.
The boundary-layer regime for convection in a rectangular cavity
Authors: Gill A. E.
Published: March 2006

This paper studies the two-dimensional convective motion in a rectangular cavity, the two vertical sides of which are maintained at different temperatures. This system is studied for the special case in which the temperature difference ΔT between the two vertical walls is so large that the transfer of heat from one vertical wall to the other is achieved almost entirely by convection. Heat transfer by conduction is assumed to be of importance only in thin boundary layers adjoining the walls. For a cavity of height H, the boundary layers on the two vertical walls are found to have thickness proportional to [ell ], where [ell ]4 = κνH/γgΔT, and the condition for the boundary-layer regime to be established is that [ell ] be small compared with the width of the cavity. An approximate solution of the problem is obtained for the case of large values of the Prandtl number ν/κ, and found to be in satisfactory agreement with experimental results obtained by Elder (1965).
Magnetohydrodynamic lubrication flow between parallel plates
Authors: Maki E. Roland , Kuzma Dennis C. , Donnelly Russell J.
Published: March 2006

The magnetohydrodynamic lubrication flow in an externally pressurized thrust bearing is investigated both theoretically and experimentally. The ordinary magnetohydrodynamic lubrication theory for this bearing is extended to include fluid inertia effects. Very good agreement is obtained between theory and experiment.
Harmonic generation in Taylor vortices between rotating cylinders
Authors: Snyder H. A. , Lambert R. B.
Published: March 2006

A theory of finite-amplitude secondary flow between concentric rotating cylinders has been published by Davey (1962). A necessary feature of the theory is the generation of harmonics of the spatial periodicity in the axial direction of the velocity field. A method has been devised to measure the amplitude of each harmonic separately and experimental results for the fundamental and first three harmonics are presented here for Taylor numbers up to 100 times the critical value. The agreement with Davey's theory is excellent, and the agreement extends far beyond the range where the theory is expected to be valid. It is shown that all the harmonics are in phase with the fundamental. This result requires that jets and shock-like structure must be present in the velocity field.
The separation of Newtonian shock layers
Authors: Ockendon J. R.
Published: March 2006

The separation points which occur in the Newtonian theory of hypersonic flow are treated by locally modifying the shock-layer equations. This approach leads to direct verification of the free-layer theory for separation on certain bodies with discontinuous curvature. Separation points on bodies with continuous curvature have already been treated by matching the upstream shock-layer solution to the downstream free-layer solution. The agreement that is found between these results and those of the present approach provides further confirmation of the free-layer theory.
Numerical solutions of the steady-state vorticity equation in rectangular basins
Authors: Bye John A. T.
Published: March 2006

The Navier-Stokes vorticity equation is solved numerically for the circulation induced in a vertical plane, by a constant stress acting on a liquid, enclosed in a basin of uniform depth and vertical sides.

Solutions of the linearized vorticity equation are obtained for all Reynolds numbers (τsD2/4ρν2 where νs is the surface stress, ρ is the density, ν is the kinematic viscosity, and D is the depth of the liquid) and solutions of the complete vorticity equation for Reynolds numbers 0–400.

The notable feature of the solutions is the totally different end circulations. At the upwind end the flow becomes very slack, and the vorticity equation has a boundary-layer limit, while at the downwind end a damped wave occurs and the equation has an inviscid limit.

At Reynolds numbers between 400 and 600, the streamlines at the downwind end lead to a condition of hydrodynamic instability, in approximate agreement with some experimental observations by G. H. Keulegan.
Periodic oscillations in a model of thermal convection
Authors: Keller Joseph B.
Published: March 2006

Periodic oscillations are found in a one-dimensional model of thermal convection. The model consists of a fluid-filled tube bent into rectangular shape and standing in a vertical plane. The fluid is heated at the centre of the lower horizontal segment and cooled at the centre of the upper horizontal segment. When a certain parameter exceeds unity, a periodic motion of the fluid is found in which the flow is always in the same direction but in which the speed varies. Inertia is unimportant for this oscillation, which depends upon the interplay between frictional and buoyancy forces.
The refraction of a plane shock wave at a gas interface
Authors: Henderson L. F.
Published: March 2006

The paper deals with the refraction of a plane shock wave by an interface between two different gases. It is shown that the equations of motion can be reduced to a single polynomial equation of degree 12. Detailed numerical results are presented for the air-CH4 and the air-CO2 interfaces, which are respectively ‘slowfast’ and ‘fast–slow’ combinations. When the results are compared with experiment good agreement is obtained. The numerical data are multi-valued, but it is found that it is always the weakest solution that agrees with the experimental data. The multiple roots of the equation are often found to be associated with the appearance of degenerate and irregular wave systems and some attempt is made to analyse and discuss these systems.
The influence of simple supports on the radiation from turbulent flow near a plane compliant surface
Authors: Williams J. E. Ffowcs
Published: March 2006

The paper deals with an extension of previous work on the radiation properties of turbulent flow formed on compliant surfaces. The effect of simple supports is shown to be acoustically equivalent to an extended dipole system of strength equal to the support stress. The dipole radiation is reduced by a transmission factor below that radiated into a uniform environment. A particular example is worked out in detail. That example deals with the case of a single point support on an otherwise homogeneous surface excited by boundary-layer turbulence.
Wind action on water standing in a laboratory channel
Authors: Hidy G. M. , Plate E. J.
Published: March 2006

The development of waves and currents resulting from the action of a steady wind on initially standing water has been investigated in a wind–water tunnel. The mean air flow near the water surface, the properties of wind waves, and the drift currents were measured as they evolved with increasing fetch, depth and mean wind speed. The results suggest how the stress on the water surface changes with an increasingly wavy surface, and, from a different viewpoint, how the drift current and the waves develop in relation to the friction velocity of the air. The amplitude spectra calculated for the wavy surface reflected certain features characteristic of an equilibrium configuration, especially in the higher frequencies. The observed equilibrium range in the high frequencies of the spectra fits the f−5 rule satisfactorily up to frequencies f of about 15 c/s. The wave spectra also revealed how the waves grow in the channel, both with time at a fixed point, and with distance from the leading edge of the water. These results are discussed in the light of recent theories for wave generation resulting from the action of pressure fluctuations in the air, and from shearing flow instabilities near the wavy surface. The experimental observations agree reasonably well with the predictions of the recent theory proposed by Miles, using growth rates calculated for the mechanism suggesting energy transfer to the water through the viscous layer in the air near the water surface.
The mechanism of entrainment in free turbulent flows
Authors: Townsend A. A.
Published: March 2006

A considerable quantity of observations and measurements exists concerning the phenomenon of intermittency which is connected closely with the entrainment process in free turbulent flows. A number of these are described in the first part of the paper and conclusions are drawn about the shape and motion of the bounding surface that separates turbulent and non-turbulent fluid. The salient features are that indentations of the surface grow and decay cyclically, that each cycle leads to substantial entrainment of ambient fluid into the turbulent region, that the indentations move at a considerable speed relative to the free stream, and that the surface has a comparatively simple form. The growth–decay cycle of the indentations suggests that a critical condition for growth exists, but the pressure field consequent on the convection velocity of the indentations makes for a Helmholtz type of instability that is unlikely to be stabilized by purely viscous behaviour of the turbulent fluid. It is known that the initial response of turbulent fluid to distortion is elastic in character, with incremental Reynolds stress proportional to increment of total strain, and sufficient rigidity could stabilize the bounding surface. A simple flow model–an inviscid stream flowing over an elastic jelly—is examined and the condition for marginal stability is compared with the observed properties of the flow. The model leads to the conclusion that indentations of more than a critical wave-number are stable, and provides reasons for the comparatively simple form of the surface and for the occurrence of indentations in groups of about three. The relative values of entrainment constants in different flows of uniform density do not depend critically on the nature of the entrainment process provided that the main turbulent motion remains geometrically similar, but the correlation between entrainment constant and relative depth of the indentations found by Gartshore (1966) appears as a consequence of the ‘elastic’ control of the growth–decay cycle. Lastly, the properties of the engulfment mechanism are used to show that the entrainment constant for a jet is proportional to the square root of the ratio of ambient density to the average density inside the jet. In contrast, the corresponding result for engulfment controlled by an eddy viscosity is variation as the ratio of the mean of the ambient and inside density to the inside density. Observations of high-speed jets of water in air and air in water give some support to the ‘elastic’ hypothesis.
Dynamics of flexible slender cylinders in axial flow Part 1. Theory
Authors: Paidoussis M. P.
Published: March 2006

A general theory is presented to account for the small, free, lateral motions of a flexible, slender, cylindrical body immersed in fluid flowing parallel to the position of rest of its axis. The cylinder is either clamped or pinned at both ends, or clamped at the upstream end and free at the other; it lies in a horizontal plane wherein all motion is considered to be confined. It is shown that for sufficiently large flow velocities the cylinder may be subject to buckling and oscillatory instabilities in its first and higher flexural modes, respectively. It is shown that for cylinders with both ends supported the oscillatory instabilities are specifically caused by lateral frictional forces, and that in the absence of hydrodynamic-drag effects only buckling is possible. The same applies for cylinders supported at the upstream end and with a very long, gradually tapering free end. The critical conditions of stability, expressed in dimensionless form, are evaluated extensively for clamped-free and pinned-pinned cylinders, illustrating the effect of the various system parameters on stability.
Subcritical convective instability Part 2. Spherical shells
Authors: Joseph Daniel D. , Carmi Shlomo
Published: March 2006

In this paper we consider the effect of internal heat generation and a spatial variation of the gravity field on the onset of thermal convection in spherical shells. If the temperature gradient and gravity fields have the same spatial variation, then initially quiet fluids are subcritically stable. For these flows the effect of inertially non-linear disturbances is not destabilizing if the Rayleigh number is below the critical value set by linear theory plus ‘exchange of stabilities’. For subcritically-stable flows a principle of exchange of stabilities is not necessary; a stronger statement of stability for the same stability limit can be made. For the many cases calculated here in which subcritical instabilities can exist, the difference between the linear and energy limits is small and can be contracted only toward the energy limit by an improved linear theory.
Jets and plumes with negative or reversing buoyancy
Authors: Turner J. S.
Published: March 2006

The motion of turbulent jets of heavy salt solution injected upwards into a tank of fresh water has been compared with that of plumes which are initially buoyant but become heavy as they mix with the environment. The reversal of buoyancy in the latter case is produced by using fluids having a non-linear density change on mixing, a laboratory analogue of the density changes occurring at the top of a cumulus cloud due to evaporation. The behaviour in the two cases is quite different; salt jets reach a steady height about which only small fluctuations occur, while the plumes with reversing buoyancy exhibit violent regular oscillations. This phenomenon, which is clearly a property of the ‘evaporation’ and not just of the geometry, is suggested as a likely explanation of the observed oscillation of the tops of cumulus towers. Dimensional arguments have been used to relate the experimental results to the volume, momentum and buoyancy fluxes at the source. An application of one of the deduced relations to the atmosphere gives realistic periods for the cloud-top oscillations.
Nearly equilibrium dissociating boundary-layer flows by the method of matched asymptotic expansions
Authors: Inger George R.
Published: March 2006

The approach to equilibrium in a non-equilibrium-dissociating boundary-layer flow along a catalytic or non-catalytic surface is treated from the standpoint of a singular perturbation problem, using the method of matched asymptotic expansions. Based on a linearized reaction rate model for a diatomic gas which facilitates closed-form analysis, a uniformly valid solution for the near equilibrium behaviour is obtained as the composite of appropriate outer and inner solutions. It is shown that, under near equilibrium conditions, the primary non-equilibrium effects are buried in a thin sublayer near the body surface that is described by the inner solution. Applications of the theory are made to the calculation of heat transfer and atom concentrations for blunt body stagnation point and high-speed flat-plate flows; the results are in qualitative agreement with the near equilibrium behaviour predicted by numerical solutions.
The influence of Coriolis force on surface-tension-driven convection
Authors: Vidal A. , Acrivos Andreas
Published: March 2006

The effect of uniform rotation on surface-tension-driven convection in an evaporating fluid layer is considered both theoretically and experimentally. The theoretical analysis follows the usual small-disturbance approach of perturbation theory and leads, at the neutral state, to a functional relation between the Marangoni and Taylor numbers which is then computed numerically. In addition, it is shown analytically that, in the limit of rapid rotation, the velocity and temperature fluctuations are confined to a thin Ekman layer near the surface, and that Mc = 4·42T½ and ac = 0·5T¼, where Mc and ac are, respectively, the critical Marangoni number and the critical wave number for neutral stability, and T is the Taylor number.

The experimental part deals primarily with the flow pattern of a 50% solution of ethyl ether in n-heptane evaporating into still air. In this case, the convective flow is surface-tension-driven and its structure was observed using schlieren optics. In the absence of rotation, the flow shows a remarkable cellular pattern when the layer is shallow, but when the depth of the layer is increased the pattern quickly becomes highly irregular. In contrast, for T > 103, a cellular structure is always observed even for deep layers, a result which is attributable to the stabilizing effect of the Coriolis force. A further increase in T leaves the flow pattern unchanged except that the size of the cells is found to decrease as T−¼ which is in agreement with the results of the linear stability analysis.
On the viscous flow in the nose region of a symmetric blunt body in hypersonic flow
Authors: Rarity B. S. H.
Published: March 2006

The flow field in the nose region of a blunt body in hypersonic flow is studied by considering the transport of vorticity and enthalpy. The entire region between body and shock is considered to be viscous, not necessarily thin in comparison with the nose radius of the body and to be of slowly varying density. The (given) post-shock vorticity need not be small and the density ratio ρ∞/ρs may either be small or near unity, the analysis being valid asymptotically at both limits.

It is found that the vorticity equation may be uncoupled from the total enthalpy equation if μ√ρ is constant. While the equations are not expected to be necessarily restricted to the immediate vicinity of the stagnation line, only there can the solution be written down explicitly; elsewhere, numerical integration is required.
Thermal convection with shear at high Rayleigh number
Authors: Ingersoll Andrew P.
Published: March 2006

A fluid is contained between rigid horizontal planes which move relative to each other with constant horizontal velocity. A gravitationally unstable temperature difference is maintained at the boundaries, and the heat flux and momentum flux (stress) transmitted by the fluid are measured. The Nusselt number,Nu, and the dimensionless momentum flux,Mo, are obtained for small mean rates of shear. The Rayleigh number,R, and the Prandtl number, σ, are both large in these experiments. The data are consistent with the following relations:\[ Nu \propto Mo \sigma^{\frac{1}{2}} \propto R^{\frac{1}{3}}. \]

Kraichnan's mixing-length theory of turbulent thermal convection is extended to the present situation, and the above experimental dependence ofNuandMoonRand σ is obtained. The agreement between mixing-length theory and experiment provides strong support for Kraichnan's concise treatment of turbulent convection. The importance of this result is that heat and momentum fluxes may be calculated in this way for a variety of flows in geophysics.
The boundary layer in crossed-fields m.h.d.
Authors: Sears W. R.
Published: March 2006

This study of the boundary layer of steady, incompressible, plane, crossed-fields m.h.d. flow at large Reynolds numberReand magnetic Reynolds numberRmbegins with a review of Hartmann's case, where a boundary layer occurs whose thickness is proportional to (Re Rm)−½. Following this clue, it is shown that in general the boundary layer is a ‘local Hartmann boundary layer’. Its profiles are always exponential and it is determined completely by local quantities. The skin friction and the total electric current in the layer are proportional to the square root of the magnetic Prandtl number, i.e. to (Rm/Re)½. Thus the exterior-flow problem, the solution of which precedes a boundary-layer solution, generally involves a current sheet at the fluid-solid interface.

This inviscid-flow problem becomes tractable if (Rm/Re)½is small enough to permit a linearized solution. The flow field about a flat plate at zero incidence is calculated in this approximation. It is pointed out that the thin-cylinder solutions of Sears & Resler (1959), which pertain toRm/Re= 0, can immediately be extended to small, non-zero values of this parameter by linear combination with this flat-plate solution.
Internal waves of finite amplitude and permanent form
Authors: Benjamin T. Brooke
Published: March 2006

A theory is derived for the class of long two-dimensional waves, comprising solitary and periodic cnoidal waves, that can propagate with unchanging form in heterogeneous fluids. The treatment is generalized to the extent that the waves are supposed to arise on a horizontal stream of incompressible fluid whose density and velocity are arbitrary functions of height, and the upper surface of the fluid is allowed either to be free or to be fixed in a horizontal plane. Explicit formulae for the wave properties and a general interpretation of the physical conditions for the occurrence of the waves are achieved without need to specify particular physical models; but in a later part of the paper, §4, the results are applied to three examples that have been worked out by other means and so provide checks on the present theory. These general results are also shown to accord nicely with the principle of ‘conjugate-flow pairs’ which was explained by Benjamin (1962b) with reference to swirling flows along cylindrical ducts, but which is known to apply equally well to flow systems of the kind in question here.

The theory reveals certain physical peculiarities of a type of flow model often used in theoretical studies of internal-wave phenomena, being specified so as to make the equation for the stream-function linear. In an appendix, some observations are also made regarding the ‘Boussinesq approximation’, which too is often used as a simplifying assumption in this field. It is shown, adding to a recent discussion by Long (1965), that finite internal waves may depend crucially on small effects neglected in this approximation.
Numerical solutions of the Krook kinetic equation
Authors: Anderson Donald G.
Published: March 2006

Because of the relative simplicity of the statistical model for molecular interactions, numerically exact solutions of the Krook kinetic equation can be obtained. Comparison of exact and approximate solutions of the model equation allows the evaluation of approximate procedures for solving the Boltzmann equation. Exact and approximate numerical solutions have been obtained for Couette flow with heat transfer and the structure of a plane shock wave. The present paper summarizes the work of the author in obtaining the numerically exact solutions.
Aligned-field hydromagnetic flow past a slender body
Authors: Leibovich S. , Ludford G. S. S.
Published: March 2006

This is a continuation of our previous work (1965) on the Sears–Resler–Stewartson controversy, in the context of axially symmetric flow. A new approach is presented using boundary-layer arguments, which remove much of the old complexity.

For resistive bodies of shape R(x) we uncover a similarity with plane airfoils of shape F(x) = R2(x). As before, Stewartson's slug flows develop fore and aft. For bodies of very high conductivity the Sears–Resler (steady-state) solution turns out to be one possibility. It pertains to bodies (of much higher conductivity than the liquid) into which the initial magnetic field has not diffused.