bluuebunny/crossref_metadata_2025 huggingface dataset:
Some data on the distance-neighbour function for relative diffusion
Authors: Sullivan Paul J.
Published: March 2006

Repeated observations of dye plumes on Lake Huron are interpreted according to the theoretical proposals of Richardson (1926) and Batchelor (1952) about the characteristics of a dispersing cloud of marked fluid within a field of homogeneous turbulence. The results show the average of several instantaneous concentration distributions about their centre of gravity to be approximately Gaussian and the distance-neighbour function to be of approximately Gaussian form. The data are consistent with the theoretical description given by Batchelor, namely,
\[
q(y,t) = (2\pi\overline{y^2})^{-\frac{1}{2}}\exp (-y^2/2\overline{y^2}),\quad (\overline{y^2} = (\frac{2}{3}\alpha t)^3),
\]
where q(y, t) is the distance-neighbour function and α is the constant of the ‘4/3-power law’. The average value of α is estimated to be 0·12 cm2/3 sec−1. The rate of turbulent energy dissipation in the near-surface currents of Lake Huron is estimated as ε ∼ 2·1 × 10−3 cm2sec−3.
Acoustic beaming and reflexion from wave-bearing surfaces
Authors: Crighton D. G.
Published: March 2006

The field radiated by an acoustic monopole in the presence of an infinite membrane, or plate, is studied, with emphasis on the case when fluid loading effects are small and when a free wave in the surface has supersonic phase speed relative to the fluid. Coupling between fluid and surface is then specified by a Mach angle θMand by a fluid loading parameter ε, with ε [Lt ] 1. Asymptotic expressions for the field are derived which are uniform in the observation angle θ, measured from the surface. Previous descriptions have suggested the formation of a strong two-dimensional beaming effect along the surface of the Mach cone θ = θM. Here it is shown that this effect is a spurious consequence of nonuniform asymptotics. A beam is indeed formed, and persists without attenuation or distortion to large distancesk0R∼ ε−2. However, the beam amplitude is small compared with that of the three-dimensional reflected field, while at distancesk0R[Gt ] ε−2only the reflected wave survives. Some interesting features of the reflexion coefficient and of the field near to the membrane are also discussed. In particular, it is shown that the pressure field generated by a subsonic surface wave is also confined to a conical zone, the transition across the generators of the cone being described by Fresnel functions of a familiar kind.
Experimental evidence of waves in the sublayer
Authors: Morrison W. R. B. , Bullock K. J. , Kronauer R. E.
Published: March 2006

Two-dimensional frequency-wave-number spectra [Fcy ](kx, ω) and [Fcy ](kz, ω) of the longitudinal velocity component are presented for the sublayer in fully developed turbulent pipe flow, at Reynolds numbers between 10600 and 46400. All of these sublayer spectra apparently scale by introducing dimensionless quantities based on a chara cteristic length scale ν/UTand a characteristic time scale ν/UT2.

Representative convection velocities have been obtained from the [Fcy ](kxω) spectra. The characteristic convection velocity in the sublayer is independent of wave-number and is the same at all positions in the layercx≃ 8·0UT. This result has led to the conclusion that sublayer turbulence is wave-like.

Existing visualization data seem to indicate that the sublayer waves are also relatively periodic at least at low values of Reynolds number. Characteristic dimensions of the sublayer waves are λ+x≃ 630, and λz+= 135. Results of the visualization studies of Fage & Townend (1932) and of Runstadler, Kline & Reynolds (1963) and Klineet al.(1967) do not appear to conflict with a wave model for the sublayer.

All of the existing measurements of the sublayer have been for relatively low Reynolds numbers. Some of the present results for positions just outside the sublayer suggest that at Reynolds numbers greater than 30000, the structure and properties will change substantially from those observed to date. In particular the streaky structure which is commonly regarded as being characteristic of the sublayer will probably not be detected at sufficiently high Reynolds numbers.
The spin down of rotating stratified fluids
Authors: Siegmann W. L.
Published: March 2006

The transient process by which an incompressible dissipative rotating stratified fluid adjusts to a small change in the rotation rate of its container is examined theoretically. The aim is to clarify the effects of the imposed density stratification and of the boundary condition specified for the density perturbation on the behaviour of the fluid, particularly during the time span when the adjustment is performed in a homogeneous fluid. For a weakly stratified fluid in a cylinder, it is shown how these two factors govern the nature and intensity of boundary layers on the vertical wall which close the secondary meridional circulation generated by Ekman layers along the horizontal boundaries. For a more strongly stratified fluid, the usefulness and importance of potential vorticity conservation in determining the quasi-steady motion is verified, and a calculation for a spherical container demonstrates some new features that arise only when the container boundaries are not normal or parallel to the rotation axis. It is shown that experimental results of Holton (1965) are in less good agreement with predictions of the linear theory than had been previously indicated.
Magneto-fluid-mechanic pipe flow in a transverse magnetic field. Part 1. Isothermal flow
Authors: Gardner R. A. , Lykoudis P. S.
Published: March 2006

An experimental investigation was conducted in a circular pipe to examine the influence of a transverse magnetic field on the structure of turbulent shear flow of a conducting fluid (mercury). In the present paper, part 1, mean velocity profiles, turbulence intensity profiles, velocity fluctuation spectra, axial pressure drop profiles, and skin friction data are presented which quantitatively exhibit the Hartmann effect and damping of the velocity fluctuations over a broad range of Reynolds numbers and magnetic fields. The results of heat transfer experiments will be reported by the authors in the following paper, part 2.
Static and dynamic calibrations of constant-temperature hot-wire systems
Authors: Perry A. E. , Morrison G. L.
Published: March 2006

The conventional hot-wire static calibration procedure for the measurement of absolute turbulence intensities with constant-temperature hot-wire anemometers is investigated and serious errors are found. An alternative calibration procedure is developed which involves shaking the wire at low frequencies in a uniform flow. A series of tests indicate that this dynamic calibration method is more accurate and consistent than the conventional procedure.

A method for verifying various calibration procedures is demonstrated. This method involves the measurement of velocity perturbations in a series of Karman vortex streets. The velocity perturbation amplitude is held fixed, but the frequency varies from one vortex street to another. This method also acts as a direct check of the hot-wire system frequency response.
Convective instability in liquid pools heated from below
Authors: Palmer Harvey J. , Berg John C.
Published: March 2006

The linear hydrodynamic stability analysis of liquid pools heated from below combining surface tension and buoyancy effects as presented by Nield (1964) is confirmed by experiment for a series of silicone oils. The experimental method used is an adaptation of the Schmidt–Milverton technique, in which the stability limit is located by the change of slope in the plot of heat flux versus temperature drop across the liquid pool.
The effect of normal blowing on the flow near a rotating disk of infinite extent
Authors: Kuiken H. K.
Published: March 2006

The effect of blowing through a porous rotating disk on the flow induced by this disk is studied. For strong blowing the flow is almost wholly inviscid. First-order viscous effects are encountered only in a thin layer at some distance from the disk. The results of an asymptotic analysis are compared with numerical integrations of the full equations and complete agreement is found.
On the flow properties of a fluid between concentric spheres
Authors: Philander S. G. H.
Published: March 2006

Proudman (1956) and Stewartson (1966) analyzed the dynamical properties of a fluid occupying the space between two concentric rotating spheres when the angular velocities of the spheres are slightly different, in other words, when the motion relative to a reference frame rotating with one of the spheres is due to an imposed azimuthal velocity which is symmetric about the equator. The consequences of forcing motion across the equator are explored here. Whereas the flow inside the cylinder [Cscr ] circumscribing the inner sphere and having generators parallel to the axis of rotation is similar to that which results when the driving is symmetric, the flow outside [Cscr ] is quite different. The Ekman layer on the outer sphere persists outside [Cscr ] - its dynamics is modified in the vicinity of the equator - and is instrumental in transferring fluid from one hemisphere to the other. The divergence of this Ekman layer causes slow, axial motion in the inviscid region outside [Cscr ]. On [Cscr ], two shear layers of thicknessO(R−2/7) andO(R−1/3) (whereRis the Reynolds number, assumed large) remove discontinuities in the flow field and return fluid from one hemisphere to the other (rather than one Ekman layer to the other as is the case when the driving is azimuthal).
Shallow-water waves, the Korteweg-deVries equation and solitons
Authors: Zabusky N. J. , Galvin C. J.
Published: March 2006

A comparison of laboratory experiments in a shallow-water tank driven by an oscillating piston and numerical solutions of the Korteweg-de Vries (KdV) equation show that the latter can accurately describe slightly dissipative wavepropagation for Ursell numbers (h1L2/h03) up to 800. This is an input-output experiment, where the initial condition for the KdV equation is obtained from upstream (station 1) data. At a downstream location, the number of crests and troughs and their phases (or relative locations within a period) agree quantitatively with numerical solutions. The crest-to-trough amplitudes disagree somewhat, as they are more sensitive to dissipative forces. This work firmly establishes the soliton concept as necessary for treating the propagation of shallow-water waves of moderate amplitude in a low-dissipation environment.
The development of concentrated vortices: a numerical study
Authors: Leslie L. M.
Published: March 2006

Amongst the more important laboratory experiments which have produced concentrated vortices in rotating tanks are the sink experiments of Long and the bubble convection experiments of Turner & Lilly. This paper describes a numerical experiment which draws from the laboratory experiments those features which are believed to be most relevant to atmospheric vortices such as tornadoes and waterspouts.

In the numerical model the mechanism driving the vortices is represented by an externally specified vertical body force field defined in a narrow neighbourhood of the axis of rotation. The body force field is applied to a tank of fluid initially in a state of rigid rotation and the subsequent flow development is obtained by solving the Navier–Stokes equations as an initial-value problem.

Earlier investigations have revealed that concentrated vortices will form only for a restricted range of flow parameters, and for the numerical experiment this range was selected using an order-of-magnitude analysis of the steady Navier–Stokes equations for sink vortices performed by Morton. With values of the flow parameters obtained in this way, concentrated vortices with angular velocities up to 30 times that of the tank are generated, whereas only much weaker vortices are formed at other parametric states. The numerical solutions are also used to investigate the comparative effect of a free upper surface and a no-slip lid.

The concentrated vortices produced in the numerical experiment grow downwards from near the top of the tank until they reach the bottom plate whereupon they strengthen rapidly before reaching a quasi-steady state. In the quasi-steady state the flow in the tank typically consists of the vortex at the axis of rotation, strong inflow and outflow boundary layers at the bottom and top plates respectively, and a region of slowly-rotating descending flow over the remainder of the tank. The flow is cyclonic (i.e. in the same sense as the tank) in the vortex core and over most of the bottom half of the tank and is anticyclonic over the upper half of the tank away from the axis of rotation.
A solution for hypersonic flow past slender bodies
Authors: Hui W. H.
Published: March 2006

A solution to the hypersonic small disturbance equations is obtained for a class of two-dimensional bodies supporting logarithmic shock waves by reducing the partial differential equation to an ordinary differential equation. The body shape is calculated and shown not to be logarithmic if γ ≠ 1, where γ is the ratio of the specific heats of the gas.
The effect of laminar viscosity on the solution of the undular bore
Authors: Byatt-Smith J. G. B.
Published: March 2006

In this paper we look at the problem of an undular bore entering still water. The effect of the boundary-layer at the channel bottom is considered. The motion is assumed to be laminar and inviscid, apart from the thin boundary layer, where the normal boundary-layer approximations are used to find the velocity components. The effect on the main flow then appears in the equations of motion as a shear stress.
Vortex shedding from a turbulent jet in a cross-wind
Authors: McMahon H. M. , Hester D. D. , Palfery J. G.
Published: March 2006

Measurements in the wake behind turbulent jets exhausting from a solid surface into a cross-wind indicate that vortex shedding occurs as in the case of flow past solid bluff bodies. The Strouhal numbers for flow past a circular and a blunt jet are in qualitative agreement with those for corresponding solid bodies, provided that the width of the spreading jet some distance from the surface is used rather than the jet exit plane dimension.
Long waves generated by ground motion
Authors: Slatkin Montgomery W.
Published: March 2006

The initial-value problem for waves generated by ground motion near a shore is solved using linear shallow water theory and an exponential bottom profile. It is found that long waves can be trapped along the coast and travel with the deep water wave speed, (gh)½. The energy in these waves decays with x−½ instead of x−1 so that more energy would be observed on this coast than expected on the basis of deep water wave amplitudes.
Measurements of atmospheric pressure on wind-generated sea waves
Authors: Dobson Fred W.
Published: March 2006

Simultaneous measurements of wave elevation and atmospheric pressure on wind-driven sea waves were made using a vertical wave-sensing rod and a small (23 cm diameter) pancake-shaped styrofoam buoy in which was embedded a sensitive pressure transducer; the wave probe constrained the buoy to move with the waves only in the vertical direction. Care was taken to avoid contamination of the pressure signal with dynamic pressures caused by flow distortion around the buoy.

Results are presented as power and cross-spectra of wave elevation and pressure, spectra of the fluxes of energy and momentum from the wind to the waves, and spectra of ζ the fractional increase in wave energy per radian.

The phase shifts of the pressure signal are compared with the laboratory and field results of other investigators, and with the theoretical predictions of Miles's (1957) inviscid laminar model of wave growth. Agreement is reasonably good among the experimental results, but observed phase shifts are an order of magnitude larger than the theoretically predicted values.

Integrals under the momentum flux spectra are compared in all runs with the predictions of the standard empirical formula, and in two cases are compared with the values of the total wind stress as measured with a sonic anemometer; the indication is that a large fraction of the total flux of momentum from the air to the sea goes initially into the wave field.

The ζ spectra are compared with the field results of Snyder & Cox (1966) and with the theoretical predictions of Miles's (1957) model; agreement is again good between the field results while the theory underpredicts ζ by factors of between 5 and 8.

A simple dimensionless relation is found between ζ and the ratio of wind speed to wave phase speed.
A note on the role of the buoyancy layer in a rotating stratified fluid
Authors: Pedlosky J.
Published: March 2006

In the theory of steady stratified rotating fluid motions developed by Barcilon & Pedlosky (1967) (hereafter referred to as B & P) for flows within a circular, cylindrical container it was asserted that the innermost boundary layer on the vertical side wall was absent to lowest order when the side wall is thermally insulated. That is to say, the buoyancy layer is not required to close the vertical mass flux. This result has been disputed in a recent note by Harrington & Johnson (1969) (hereafter referred to as H & J). It is the purpose of this note to reiterate the earlier result of B & P and to show that H & J is in error. Further the result is placed on firmer ground by using the fundamental dynamical characteristics of the inviscid interior and viscous boundary layers and by avoiding the algebraic snares of manipulating Fourier series.
Statistical properties of velocity derivatives in a turbulent field
Authors: Frenkiel Françlois N. , Klebanoff Philip S.
Published: March 2006

High-speed digital computing methods are applied to the study of the statistical behaviour of turbulent velocity derivatives in a nearly isotropic turbulent field downstream of a grid. Higher-order correlations of turbulent velocity gradients, up to the eighth order, are measured. Contrary to the case of velocities, the higher even-order correlations of velocity gradients more clearly evidence the departure from a two-dimensional Gaussian probability distribution. Using non-Gaussian probability distribution laws the relations between different odd-and even-order correlations are obtained and compared with the experimental measurements. The conditions of similarity and isotropy are evaluated for the small-scale structure as evidenced by the behaviour of the turbulent velocity gradients. The concept of intermittency of the small-scale structure is also discussed.
On laminar boundary-layer blow-off. Part 2
Authors: Kassoy D. R.
Published: March 2006

Several examples of incipient blow-off phenomena described by the compressible similar laminar boundary-layer equations are considered. An asymptotic technique based on the limit of small wall shear, and the use of a novel form of Prandtl's transposition theorem, leads to a complete analytical description of the blow-off behaviour. Of particular interest are the results for overall boundarylayer thickness, which imply that, for a given large Reynolds number, classical theory fails for a sufficiently small wall shear. A derivation of a new distinguished limit of the Navier–Stokes equations, the use of which will lead to uniformly valid solutions to blow-off type problems for Re → ∞, is included. A solution for uniform flow past a flat plate with classical similarity type injection, based on the new limit, is presented. It is shown that interaction of the injectant layers and the external flow results in a favourable pressure gradient, which precludes the classical blow-off catastrophy.
The drag on oscillating flat plates in liquids at low Reynolds numbers
Authors: Shih Cornelius C. , Buchanan Harry J.
Published: March 2006

An experimental investigation was conducted to describe the fluid flow about oscillating flat plates and to determine the magnitude and nature of forces acting on the plates at low Reynolds numbers. In the experiment, the Reynolds number was varied from 1·01 to 1057·0; three period parameters, 1·57, 2·07 and 4·71, were applied; two fluids, water and SAE 30 motor oil, and three flat plates of various sizes with or without end plates were used. The analysis of data resulted in graphical presentation of the relationships among the drag coefficient, the Reynolds number and period parameter. The drag coefficient becomes less dependent on the Reynolds number for values greater than 250. The relationship between the drag coefficient and period parameter is pronounced throughout the entire range of the Reynolds number tested.
Simple Eulerian time correlation of full-and narrow-band velocity signals in grid-generated, ‘isotropic’ turbulence
Authors: Comte-Bellot Geneviève , Corrsin Stanley
Published: March 2006

Space-time correlation measurements in the roughly isotropic turbulence behind a regular grid spanning a uniform airstream give the simplest Eulerian time correlation if we choose for the upstream probe signal a time delay which just ‘cancels’ the mean flow displacement. The correlation coefficient of turbulent velocities passed through matched narrow-band niters shows a strong dependence on nominal filter frequency (∼ wave-number at these small turbulence levels). With plausible scaling of the time separations, a scaling dependent on both wave-number and time, it is possible to effect a good collapse of the correlation functions corresponding to wave-numbers from 0·5 cm−1, the location of the peak in the three-dimensional spectrum, to 10 cm−1, about half the Kolmogorov wave-number. The spectrally local time-scaling factor is a ‘parallel’ combination of the times characterizing (i) gross strain distortion by larger eddies, (ii) wrinkling distortion by smaller eddies, (iii) convection by larger eddies and (iv) gross rotation by larger eddies.
Sting-free drag measurements on ellipsoidal cylinders at transition Reynolds numbers
Authors: Judd M. , Vlajinac M. , Covert E. E.
Published: March 2006

The drag coefficient for a family of axially symmetric ellipses of fineness ratio 4, 5 and 8 was measured using magnetically suspended models. The Reynolds number ranged up to 106. Thus, only the blockage interference is present, which may be partially allowed for by classical wind tunnel procedures. It is expected that the drag values presented here are accurate to 1%.
Stability of time-dependent rotational Couette flow Part 2. Stability analysis
Authors: Chen C. F. , Kirchner R. P.
Published: March 2006

The stability of the flow induced by an impulsively started inner cylinder in a Couette flow apparatus is investigated by using a linear stability analysis. Two approaches are taken; one is the treatment as an initial-value problem in which the time evolution of the initially distributed small random perturbations of given wavelength is monitored by numerically integrating the unsteady perturbation equations. The other is the quasi-steady approach, in which the stability of the instantaneous velocity profile of the basic flow is analyzed. With the quasi-steady approach, two stability criteria are investigated; one is the standard zero perturbation growth rate definition of stability, and the other is the momentary stability criterion in which the evolution of the basic flow velocity field is partially taken into account. In the initial-value problem approach, the predicted critical wavelengths agree remarkably well with those found experimentally. The kinetic energy of the perturbations decreases initially, reaches a minimum, then grows exponentially. By comparing with the experimental results, it may be concluded that when the perturbation kinetic energy has grown a thousand-fold, the secondary flow pattern is clearly visible. The time of intrinsic instability (the time at which perturbations first tend to grow) is about ¼ of the time required for a thousandfold increase, when the instability disks are clearly observable. With the quasi-steady approach, the critical times for marginal stability are comparable to those found using the initial-value problem approach. The predicted critical wavelengths, however, are about 1½ to 2 times larger than those observed. Both of these points are in agreement with the findings of Mahler, Schechter & Wissler (1968) treating the stability of a fluid layer with time-dependent density gradients. The zero growth rate and the momentary stability criteria give approximately the same results.
Third-harmonic resonance in the interaction of capillary and gravity waves
Authors: Nayfeh Ali Hasan
Published: March 2006

The method of multiple scales is used to determine the temporal and spatial variation of the amplitudes and phases of capillary-gravity waves in a deep liquid at or near the third-harmonic resonant wave-number. This case corresponds to a wavelength of 2·99 cm in deep water. The temporal variation shows that the motion is always bounded, and the general motion is an aperiodic travelling wave. The analysis shows that pure amplitude-modulated waves are not possible in this case contrary to the second-harmonic resonant case. Moreover, pure phase-modulated waves are periodic even near resonance because the non-linearity adjusts the phases to yield perfect resonance. These periodic waves are found to be unstable, in the sense that any disturbance would change them into aperiodic waves.
On the determination of the zones of influence and dependence for three-dimensional boundary-layer equations
Authors: Wang K. C.
Published: March 2006

The zones of influence and dependence for three-dimensional boundary-layer equations first studied by Raetz are re-examined from the viewpoint of the subcharacteristics. It is shown that in contrast, the zones of influence and dependence for a totally hyperbolic system are determined by the characteristics; for the present parabolic system of three-dimensional boundary-layer equations, the zones are determined by the characteristics and subcharacteristics. The same idea should be applicable to more general systems of equations of similar type.
Inviscid instability of an unbounded heterogeneous shear layer
Authors: Maslowe S. A. , Kelly R. E.
Published: March 2006

Stability curves are computed for both spatially and temporally growing disturbances in a stratified mixing layer between two uniform streams. The low Froude number limit, in which the effects of buoyancy predominate, and the high Froude number limit, in which the effects of density variation are manifested by the inertial terms of the vorticity equation, are considered as limiting cases. For the buoyant case, although the spatial growth rates can be predicted reasonably well by suitable use of the results for temporal growth, spatially growing disturbances appear to have high group velocities near the lower cutoff wave-number. For the inertial case, it is demonstrated that density variations can be destabilizing. More precisely, when the stream with the higher velocity has the lower density, both the wave-number range of unstable disturbances and the maximum spatial growth rate are increased relative to the case of homogeneous flow. Finally, it is shown how the growth rate of the most unstable wave in the inertial case diminishes as buoyancy becomes important.
Experiments on laminar flow in curved channels of square section
Authors: Baylis J. A.
Published: March 2006

Recently Cheng & Akiyama (1970) published a numerical analysis of laminar flow in curved channels of square and rectangular section. Experimental results are presented here for flow in curved channels of square section. The channels were toroidal in shape, and the flow was driven electromagnetically. Various ratios of the channel dimension d to the channel radius of curvature, R, were used to investigate the dependence of friction factor, f, on the Dean number K, and the Reynolds number, Re. For 5 × 102 < K < 7 × 104 the formula (fRe) = 1·51 K½ was found to fit all the results, although R/d was varied from 17·5 down to the low value of 1·75. At lower values of K the analysis of Cheng & Akiyama was approximately validated.
MHD flow in an annular channel; theory and experiment
Authors: Baylis J. A. , Hunt J. C. R.
Published: March 2006

The theory of Hunt & Stewartson (1965) for MHD flow in a rectangular duct with conducting walls parallel and non-conducting walls perpendicular to the magnetic field is applied to the problem of electrically driven MHD flow in a rectangular annulus. It is assumed that the Hartmann numberMis sufficiently great for secondary flow effects to be negligible. The experiment described here satisfied the conditions of the theory and thus provides a sensitive experimental check on Hunt & Stewartson's theory. The theory is found to agree with the experiments to within the accuracy of the asymptotic theory.
On the phenomenon of vortex street breakdown
Authors: Durgin William W. , Karlsson Sture K. F.
Published: March 2006

A von Kármán vortex street generated in the usual way was subjected to a deceleration, thereby changing the ratio of longitudinal to lateral spacing between the vortices. Distortion of the individual vortices followed which resulted in annihilation of concentrated vortex regions and creation of a stationary wake flow. This wake flow was itself dynamically unstable and developed into a new vortex street of a different frequency from the initial one. The breakdown of the initial vortex street is qualitatively explained by considering the convection of a concentrated vortex region due to the motion imposed by all the other vortices.
Orderly structure in jet turbulence
Authors: Crow S. C. , Champagne F. H.
Published: March 2006

Past evidence suggests that a large-scale orderly pattern may exist in the noiseproducing region of a jet. Using several methods to visualize the flow of round subsonic jets, we watched the evolution of orderly flow with advancing Reynolds number. As the Reynolds number increases from order 102 to 103, the instability of the jet evolves from a sinusoid to a helix, and finally to a train of axisymmetric waves. At a Reynolds number around 104, the boundary layer of the jet is thin, and two kinds of axisymmetric structure can be discerned: surface ripples on the jet column, thoroughly studied by previous workers, and a more tenuous train of large-scale vortex puffs. The surface ripples scale on the boundary-layer thickness and shorten as the Reynolds number increases toward 105. The structure of the puffs, by contrast, remains much the same: they form at an average Strouhal number of about 0·3 based on frequency, exit speed, and diameter.

To isolate the large-scale pattern at Reynolds numbers around 105, we destroyed the surface ripples by tripping the boundary layer inside the nozzle. We imposed a periodic surging of controllable frequency and amplitude at the jet exit, and studied the response downstream by hot-wire anemometry and schlieren photography. The forcing generates a fundamental wave, whose phase velocity accords with the linear theory of temporally growing instabilities. The fundamental grows in amplitude downstream until non-linearity generates a harmonic. The harmonic retards the growth of the fundamental, and the two attain saturation intensities roughly independent of forcing amplitude. The saturation amplitude depends on the Strouhal number of the imposed surging and reaches a maximum at a Strouhal number of 0·30. A root-mean-square sinusoidal surging only 2% of the mean exit speed brings the preferred mode to saturation four diameters downstream from the nozzle, at which point the entrained volume flow has increased 32% over the unforced case. When forced at a Strouhal number of 0·60, the jet seems to act as a compound amplifier, forming a violent 0·30 subharmonic and suffering a large increase of spreading angle. We conclude with the conjecture that the preferred mode having a Strouhal number of 0·30 is in some sense the most dispersive wave on a jet column, the wave least capable of generating a harmonic, and therefore the wave most capable of reaching a large amplitude before saturating.
Aerodynamic noise
Authors: Fisher M. J. , Lowson M. V.
Published: March 2006

A symposium on aerodynamic noise was held at Loughborough University from 14 to 17 September 1970 under the sponsorship of the Royal Aeronautical Society and the British Acoustical Society. The objective of the meeting was to focus attention on unsolved theoretical and experimental problems which will require attention over the next few years. Areas which were covered included jet noise, nonlinear acoustics, rotor noise, and diffraction theory. The symposium was successful in bringing together several new themes in aerodynamic noise research. The most significant of these were the existence of a degree of order in turbulent jet flows, and the dominant effect of inflow conditions on rotor noise radiation. In addition an improved and unified basis for jet noise theory seems to be evolving.
Centrifugal convection and its effect on the asymptotic stability of a bounded rotating fluid heated from below
Authors: Homsy G. M. , Hudson J. L.
Published: March 2006

Centrifugally driven circulations in a rapidly rotating cylinder of fluid heated differentially in the vertical are considered. Boundary-layer solutions obtained previously are extended to include large diameter/height aspect ratios and a centrifugal acceleration of the same magnitude as that of gravity. The ratio of convective to conductive heat transfer is small in the region of parameter space considered. The effect of the circulations on the asymptotic stability of a fluid heat from below and subjected to Coriolis force is then considered. Away from the side wall of the cylinder the basic state circulation increases the critical Rayleigh number at which gravitational instabilities occur; however, a destabilization near the side wall is possible.
Stability of vertical natural convection boundary layers: some numerical solutions
Authors: Hieber C. A. , Gebhart B.
Published: March 2006

Linear stability theory is applied to the natural convection boundary layer arising from a vertical plate dissipating a uniform heat flux. By using a numerical procedure which is much simpler than those previously employed on this problem, computer solutions are obtained for a much larger range of the Grashof number (G). For a Prandtl number (σ) of 0·733, it is found that, asG→ ∞: the effect of temperature coupling vanishes more rapidly than that of viscosity; the upper branch of the neutral curve is oscillatory but does approach a finite non-zero inviscid asymptote. For moderate and large values of σ, a loop appears in the neutral stability curve as a result of the merging of two unstable modes. As σ → ∞, the mode associated with the uncoupled (i.e. Orr–Sommerfeld) problem rapidly becomes less unstable than that arising from the temperature coupling, with the stability characteristics being independent of the thermal capacity of the plate. For small values of σ, only one unstable mode is found to exist with the coupling effect being negligible in the case of large thermal capacity plates but markedly destabilizing when the thermal capacity is small.

By obtaining numerical results out toG≈ 1010for the cases σ = 0·733 and 6·7, it becomes possible to attempt to directly relate the theory to the actual observance of turbulent transition. Based upon comparison with available experimental data, empirical correlations are obtained between the linear stability theory and the régimes in which: (i) the boundary layer is first noticeably oscillatory; (ii) the mean (temporal) flow quantities first deviate significantly from those of laminar flow.
The Rayleigh problem for a slightly diffusive density-stratified fluid
Authors: Standing R. G.
Published: March 2006

A doubly-infinite sloping flat plate, initially at rest in a slightly diffusive viscous density-stratified fluid, starts to move impulsively with a constant velocity along the line of greatest slope. The resulting flow is found to be an unsteady motion superimposed on a steady diffusion-induced flow, which is present throughout. Laplace transform methods give solutions which are valid either in an essentially non-diffusive outer layer or in a diffusive inner layer. The impulsive start sets up oscillations in the outer layer. These gradually die out, and a steady diffusive flow develops.

A glass plate was towed vertically through stratified brine, into which aluminium particles were introduced. The flow velocities deduced from the particle motions confirmed the theoretical predictions.
Convection experiments with electrolytically heated fluid layers
Authors: Schwiderski E. W. , Schwab H. J. A.
Published: March 2006

Convection experiments described by Tritton & Zarraga (1967) with electrolytically heated fluid layers were renewed in order to investigate the reported phenomena, which were hitherto unknown and which contradicted a corresponding theory of Roberts. While the apparatus was essentially unchanged, provisions were incorporated to study the possible influence of several flow and equipment parameters on the convection pattern. With the exception of the temperature dependence of the electric conductivity, the new experiments displayed no essential effects of the convection parameters. Experiments with shallow fluid layers revealed a clear co-orientation of the convection flows with the electric current and a strong time dependence of the hexagonal patterns. Experiments with deeper fluid layers exhibited a considerably diminished time and direction dependence of the convection flow, and a significant reduction of the dilation of the cells. Based on these observations, it is concluded that no drastic differences between theory and experiments, and between internal and external heating, exist, provided the heating is sufficiently uniform.
The response of a turbulent boundary layer to a step change in surface roughness Part 1. Smooth to rough
Authors: Antonia R. A. , Luxton R. E.
Published: March 2006

The structure and growth of the internal boundary layer which forms downstream of a sudden change from a smooth to a rough surface under zero pressure gradient conditions has been studied experimentally. To keep pressure disturbances due to the roughness change small, the level of the rough surface was depressed, so that the crest of the roughness was aligned with the level of the smooth surface. It has been found that, in the region near the change, the structure of the internal layer is largely independent of that in the almost undisturbed outer layer, whilst both the zero time delay and the moving axis integral length scales in the internal layer are significantly reduced below those on the smooth wall. The growth-rate of the internal layer is similar to that of the zero pressure gradient boundary layer, whilst the level of turbulence inside the internal layer is high because of the large turbulent energy production near the rough wall. From the mixing length results, and an analysis of the turbulent energy equation, it is deduced that the internal layer flow near the wall is not in energy equilibrium, and hence the concept of inner layer similarity breaks down. From an initially self-preserving state on the smooth wall, the turbulent boundary layer approaches a second self-preserving state on the rough wall well downstream of the roughness step.
The effect of velocity sensitivity on temperature derivative statistics in isotropic turbulence
Authors: Wyngaard J. C.
Published: March 2006

The velocity sensitivity of a resistance-wire temperature sensor is expressed in terms of sensor parameters, and the resulting errors in temperature derivative moments in isotropic turbulence are evaluated. It is shown that velocity sensitivity of a degree completely negligible for most purposes causes severe contamination of the measured third moment. The contamination terms are shown to be production rates of the mean square temperature gradient and vorticity, respectively, and therefore create positive values of measured derivative skewness. The dominant contamination term is related to the temperature spectrum through the balance equation for the mean-square temperature gradient, and calculations based on an assumed spectral form show that under typical conditions the measured skewness is large. This mechanism could provide an alternative to anisotropy as an explanation of the positive skewnesses recently measured in the atmosphere.
Thermally-driven linear vortex
Authors: Blumsack S. , Barcilon A.
Published: March 2006

We investigate steady axially symmetric small Rossby number flows in which the driving consists of prescribed axial heat sources. By letting the velocity be proportional to the shear at the bottom surface we study the effects of that boundary condition on the resulting flows.

A multi-boundary-layer structure is found in the core, surrounding the heat sources. That structure depends on the relative magnitudes of the aspect ratio, stratification parameter and Ekman number.
Hydromagnetic instability of a free shear layer at small magnetic Reynolds numbers
Authors: Gotoh Kanefusa
Published: March 2006

The effect of a uniform and parallel magnetic field upon the stability of a free shear layer of an electrically conducting fluid is investigated. The equations of the velocity and the magnetic disturbances are solved numerically and it is shown that the flow is stabilized with increasing magnetic field. When the magnetic field is expressed in terms of the parameter N (= M2/R2), where M is the Hartmann number and R is the Reynolds number, the lowest critical Reynolds number is caused by the two-dimensional disturbances. So long as 0 [les ] N [les ] 0·0092 the flow is unstable at all R. For 0·0092 < N [les ] 0·0233 the flow is unstable at 0 < R < Ruc where Ruc decreases as N increases. For 0·0233 < N < 0·0295 the flow is unstable at Rlc < R < Ruc where Rlc increases with N. Lastly for N > 0·0295 the flow is stable at all R. When the magnetic field is measured by M, the lowest critical Reynolds number is still due to the two-dimensional disturbances provided 0 [les ] M [les ] 0·52, and Rc is given by the corresponding Rlc. For M > 0·52, Rc is expressed as Rc = 5·8M, and the responsible disturbance is the three-dimensional one which propagates at angle cos−1(0·52/M) to the direction of the basic flow.
Numerical simulation of incompressible flows within simple boundaries: accuracy
Authors: Orszag Steven A.
Published: March 2006

Galerkin (spectral) methods for numerical simulation of incompressible flows within simple boundaries are shown to possess many advantages over existing finite-difference methods. In this paper, the accuracy of Galerkin approximations obtained from truncated Fourier expansions is explored. Accuracy of simulation is tested empirically using a simple scalar-convection test problem and the Taylor–Green vortex-decay problem. It is demonstrated empirically that the Galerkin (Fourier) equations involving Np degrees of freedom, where p is the number of space dimensions, give simulations at least as accurate as finite-difference simulations involving (2N)p degrees of freedom. The theoretical basis for the improved accuracy of the Galerkin (Fourier) method is explained. In particular, the nature of aliasing errors is examined in detail. It is shown that ‘aliasing’ errors need not be errors at all, but that aliasing should be avoided in flow simulations. An eigenvalue analysis of schemes for simulation of passive scalar convection supplies the mathematical basis for the improved accuracy of the Galerkin (Fourier) method. A comparison is made of the computational efficiency of Galerkin and finite-difference simulations, and a survey is given of those problems where Galerkin methods are likely to be applied most usefully. We conclude that numerical simulation of many of the flows of current interest is done most efficiently and accurately using the spectral methods advocated here.
The reflexion of internal/inertial waves from bumpy surfaces. Part 2. Split reflexion and diffraction
Authors: Baines P. G.
Published: March 2006

This paper considers the linear inviscid reflexion of internal/inertial waves from smooth bumpy surfaces where a characteristic (or ray) is tangent to the surface at some point. There are two principal cases. When a characteristic associated with the incident wave is tangent to the surface we have diffraction; when the tangential characteristic is associated with a reflected wave we have split reflexion, a phenomenon which has no counterpart in classical non-dispersive wave theory. In both these cases the problem of determining the wave field may be reduced to a set of coupled integral equations with two unknown functions. These equations are solved for the simplest topography for each case, and the properties of the wave fields for more general topographies are discussed. For both split reflexion and diffraction, the fluid velocity has an inverse-square-root singularity on the tangential characteristic, and the energy density has a corresponding logarithmic singularity. The diffracted wave field penetrates into the shadow region a distance which is of the order of the incident wavelength. Possibilities for instability and mixing are discussed.
Swirling flow boundary layers
Authors: Carrier G. F.
Published: March 2006

The modified Oseen method is extended to provide a description of the boundary layers which accompany certain swirling flows over a rigid boundary in a rotating container. By comparison with known results it is shown that a refined procedure has errors of the order of 1% when the inviscid flow is a rigid body rotation; it is anticipated that, for the more interesting flows, the error is of the order of 30%.
The intensification of hurricanes
Authors: Carrier G. F.
Published: March 2006

An account is given of the dynamic balance and the thermodynamic considerations which underlie the intensification of a tropical disturbance into a mature hurricane. In particular, it is deduced that the e-folding time for the later stages of the intensification process is of the order of 16 h but that the eye formation itself can occur on a much shorter time scale.
A theory for the laminar wake of a two-dimensional body in a boundary layer
Authors: Hunt J. C. R.
Published: March 2006

A new theory is developed for the wake far downstream of a cylindrical body of heighth, placed with its generators perpendicular to the flow on a surface above which there is a boundary layer of thickness δ. If the streamwise (x) velocity in the wakeis (U+u), then assuming (h/δ) is small enough that the velocity profile in the boundary layer may be regarded asU= αy, and assuming |u| [Lt ]U, linear differential equations governinguare derived. It is found that a constant along the wake is\[ I=\frac{3}{2}\int_0^{\infty} yUu\,dy. \]This result can be used to find an order of magnitude estimate foru, becauseIis related to the forces on the body producing the wake by the approximate formula\[ I \simeq - C_1/\rho, \]whereC1is that component of the couple on the body produced by pressure and viscous stresses in thexdirection. For the particular case of a small hump on the boundary of heighthand lengthb, such thath[Lt ]b, the above relation is shown to be exact. The perturbation velocity in the wake is found to have a similarity solution\[ u = [I/(xv)]f(y^3/[xv/\alpha]), \]the physical implications of which are discussed in detail. The relevance of the theory to the problem of transition behind a trip wire is also mentioned.