bluuebunny/crossref_metadata_2025 huggingface dataset:
Static menisci in a vertical right circular cylinder
Authors: Concus Paul
Published: March 2006

The solution of the differential equation describing the equilibrium meniscus in a vertical right circular cylinder is obtained over the entire range of contact angles and Bond numbers (dimensionless ratios of gravitational to capillary forces) for which a stable meniscus exists. The first few terms of the asymptotic series valid for Bond numbers of small and large magnitude are given, and the numerical solution for intermediate values is computed. The behaviour of the solution as a function of contact angle and Bond number is depicted graphically.
Correlation measurements in grid turbulence using digital harmonic analysis
Authors: Atta C. W. Van , Chen W. Y.
Published: March 2006

Two-point time correlations up to eighth order of longitudinal velocity fluctuations in grid-generated turbulence have been measured using linearized hot-wire anemometry, digital sampling, and a high-speed digital computer. A novel feature of the present measurements is the adoption of digital Fourier analysis, using the recently developed fast-Fourier transform method. The joint probability density function for the velocity fluctuations at two points separated in time is found to be significantly non-Gaussian. All measured even-order correlations are nearly identical with those reported by Frenkiel & Klebanoff (1967 a, b), and higher-order correlations may be accurately predicted from the second-order correlation by assuming a Gaussian joint probability density. All individual odd-order correlations are substantially different from those reported by Frenkiel & Klebanoff. In particular, all mean values of odd powers of the fluctuating velocity are nearly zero, and the correlations are nearly antisymmetrical functions of the time delay as would be the case for purely isotropic homogeneous turbulence. In spite of the large difference between the individual measured odd-order correlations and previous measurements, quantities such as the skewness and skewness factor derived from certain combinations of the correlations are found to be quite insensitive to observed differences in the form of the correlations and are very similar to previous measurements.
Resonant gravity-wave interactions in a shear flow
Authors: Craik Alex. D. D.
Published: March 2006

Among a triad of gravity waves in a uniform shear flow, a remarkably powerful second-order resonant interaction may take place. This interaction is characterized by large growth rates of waves which propagate in directions oblique to that of the primary flow, and by a systematic transfer of energy from the primary flow to such waves. Most of the energy transfer takes place in the vicinity of a ‘critical layer’, where viscous forces are dominant.

Provided the resonance condition may be satisfied, a uniform shear flow which is perturbed by a two-dimensional wave of small but finite amplitude may be unstable, owing to the growth of two initially infinitesimal oblique waves which complete the resonant triad.
A theoretical investigation of disturbance amplification in external laminar natural convection
Authors: Dring R. P. , Gebhart B.
Published: March 2006

The nature of instability and disturbance amplification in the laminar natural convection boundary layer over a vertical flat surface with uniform heat flux has been theoretically investigated. The coupled Orr-Sommerfeld equation has been numerically integrated for a Prandtl number of 6·7, with the boundary condition that the disturbance heat flux be zero at the surface. The spatial amplification characteristics of disturbances convected downstream were analyzed, and constant amplification rate contours were determined. The relative amplification has been calculated from these contours and is presented in the form of amplitude ratio contours. An important feature of these results is that the low frequency disturbances, which become unstable first, amplify very slowly and also have wavelengths which are much longer than the distance to the leading edge. The higher frequency, shorter wavelength, disturbances amplify much faster and are, therefore, presumed to be the dominant ones in stability considerations. The nature of the velocity and temperature amplitudes and phase profiles across the boundary layer has also been examined.
Equilibrium-range spectra of sand waves formed by flowing water
Authors: Hino Mikio
Published: March 2006

Based on a dimensional consideration, the ‘−3 power law’ on the spatial spectrum of sand waves formed by flowing water Sηη(k) is derived for a large wave-number equilibrium subrange,
\[
S_{\eta\eta}(k)\sim \alpha k^{-3},
\]
where α is a constant depending on the angle of repose of sand particles and k denotes the wave-number.

Likewise, the frequency spectrum is shown to have the ‘−3 power law’ range for higher frequencies as well as the ‘−2 power law’ range for frequencies near a spectral peak.

These spectra are shown to agree with experimental data from various sources.
Swirling flow through a convergent funnel
Authors: Wilks Graham
Published: March 2006

The work that follows considers the velocity profiles within the boundary layer at the wall of an arbitrarily converging funnel. The occurrence of super-velocities, i.e. components of velocity within the boundary layer exceeding their corresponding free stream component, is investigated and the relevance of such a phenomenon to the efficiency of discharge discussed.
On the effect of a sharp bend in a fully developed turbulent pipe-flow
Authors: Tunstall M. J. , Harvey J. K.
Published: March 2006

It has been found experimentally that the turbulent pipe flow through a mitred, right-angle bend produces a downstream secondary circulation which does not conform to the twin-circulatory flow usually to be found in pipe bends. The secondary flow is dominated by a single circulation about the axis in either a clockwise or an anticlockwise sense, between which it switches abruptly at a low, random frequency. The phenomenon is explained in terms of the asymmetry of the inner wall separation and the turbulent axial circulation generated in the upstream flow.
Reflexion and stability of waves in stably stratified fluids with shear flow: a numerical study
Authors: Jones Walter L.
Published: March 2006

A numerical examination has been made of the reflectivity of critical levels with low Richardson number to internal gravity waves propagating in stratified fluids with shear. At sufficiently low positive Richardson numbers the reflected wave may actually be stronger than the incident.

The normal mode instabilities of three simple models have also been computed. The results are presented in three dimensions: Richardson number, horizontal wave scale and real wave frequency.
Distribution of local pressure and skin friction around a circular cylinder in cross-flow up to Re = 5 × 106
Authors: Achenbach E.
Published: March 2006

In a large range of Reynolds numbers, 6 × 104 < Re < 5 × 106, the flow around single cylinders with smooth surfaces has been investigated. The high values of the Reynolds numbers were obtained in a test channel which could be pressurized up to 40 bar of static pressure. New experiments were performed to measure the local pressure and skin friction distribution around the cylinder. From these results the total drag, the pressure drag and the friction drag were calculated. By means of the skin friction distribution the position of the separation points, separation bubbles or transition points can be localized. These data allow one to define three states of the flow: the subcritical flow, where the boundary layer separates laminarly; the critical flow, in which a separation bubble, followed by a turbulent reattachment, occurs; and the supercritical flow, where an immediate transition from the laminar to the turbulent boundary layer is observed at a critical distance from the stagnation point. According to the total drag coefficient the values found in this paper connect the subcritical region represented by the measurements of Wieselsberger (1923) and Fage & Warsap (1930) with the supercritical range in which Roshko (1961) carried out his experiments.
Entry-length flow in a vertical cooled pipe
Authors: Takhar H. S.
Published: March 2006

A numerical solution is presented for predicting the flow and heat transfer due to free convection in the entry region of a cooled vertical pipe, open at both ends. Following Lighthill (1953) the Kármán-Pohlhausen method is used in this analysis. Velocity and temperature profiles are assumed satisfying the physical boundary conditions, and the integrated forms of the equations of motion and the equations themselves at the axis and the walls of the pipe are used to calculate the various parameters involved in the profiles assumed. Two cases of constant wall temperature and linearly decreasing temperature with height were considered. Cooling decelerates the fluid in the boundary layer that forms at the wall and the fluid in the core is accelerated by virtue of continuity. As cooling progresses, at Rayleigh number O(103) the fluid in the boundary layer starts reversing at first and then assumes progressively increasing velocities. Graphs are presented for the development of the predicted velocity and temperature profiles and the other parameters involved, for a situation when the boundary layer fills the whole pipe.
Speed of a surge in a bathtub vortex
Authors: Granger Robert A.
Published: March 2006

The surge studied in this paper is due to the sudden closure of the sink of a bathtub vortex. Experimental evidence established that the surge is not initially a wave but is in fact a slug of fluid which has, for a very short period of time, a distinctive motion of its own. The purpose of this paper is to present the salient features of an experimental investigation of the effect of circulation, geometry, and viscosity on the speed of the surge and to report some rather unexpected observations.
The stability of the laminar natural convection boundary layer
Authors: Knowles C. P. , Gebhart B.
Published: March 2006

This paper concerns the stability characteristics of laminar natural convection in external flows. Until recently, very little was known about such stability because of the inherent complexity of temperature-coupled flows and because of the complicated mechanisms of disturbance propagation. In this work the stability of the laminar natural convection boundary layer is examined more closely in an attempt to predict the experimental results recently obtained. In particular, it is shown that an important thermal capacity coupling exists between the fluid and the wall which generates the flow. This thermal capacity coupling is shown to have a first-order effect for particular Grashof-number wave-number products. Solutions are obtained for a Prandtl number of 0·733 and several values of relative wall thermal capacity. These solutions indicate the important role of this wall coupling. In particular, the results predict the experimental data previously obtained.

In addition, solutions with ‘zero wall storage’ are obtained for a range of Prandtl numbers from 0·733 to 6·9. The relative disturbance u-velocity and temperature amplitudes and their phases are shown for Pr = 0·733 and several wall-storage parameters, and for Pr = 6·9 with zero wall storage. A comparison between the disturbance temperature distribution and the data obtained from a recent experimental investigation shows close agreement when the thermal capacity of the wall is taken into account.

In the appendix, it is shown that for temperature-coupled flows and wall-coupled boundary conditions the flow is unstable at a lower Grashof number for two-dimensional disturbances than it is for three-dimensional disturbances. This result has been supported by the recent experimental observations.
Axisymmetric hypersonic flow with strong viscous interaction
Authors: Ellinwood John Webster , Mirels Harold
Published: March 2006

Stewartson's theory for axisymmetric hypersonic flow of a model gas over slender bodies with strong viscous interaction and strong shock wave is extended to power-law viscosity variation and Prandtl numbers other than one. Flow properties at the body surface and shock are obtained without recourse to numerical integration. Numerical computations are presented for axisymmetric flow over a three-quarter power-law body with strong shock wave and viscous interactions that range from weak to strong.
On the interaction between internal gravity waves and a shear flow
Authors: Garrett C. J. R.
Published: March 2006

The theory of wave action conservation is summarized, and its interpretation in terms of the working, against the rate of strain of the basic flow, of an interaction stress associated with the waves is discussed. Usually this interaction stress is identical with the radiation stress of a uniform plane wave. The problem of internal gravity wave propagation in an incompressible, stratified Boussinesq liquid is considered in detail for a more general basic flow than has hitherto been treated, and the interaction stress is derived. One component of the interaction stress tensor is only equal to the corresponding component of the radiation stress tensor if we include in the latter, in addition to the Reynolds stress, a term associated with the redistribution of matter, on the average, by the wave. Two other components of the radiation stress tensor are modified in a similar manner, but the corresponding components of the interaction stress tensor are undefined, and so no comparison is possible.
A three-dimensional model of the wind-driven ocean circulation
Authors: Johnson J. A.
Published: March 2006

A linear three-dimensional model of the wind-driven ocean circulation is treated by boundary-layer methods. The interior flow, below the Ekman layer, differs from the classical gyres of Munk (1950). There is a north-eastwards transport of fluid from the western boundary current of the southern gyre across the latitude of zero wind stress curl into the northern gyre. A return flow in the Ekman layer preserves continuity.
High-frequency sound waves in ideal gases with internal dissipation
Authors: Dunwoody J.
Published: March 2006

High-frequency plane sound waves in ideal gases with internal dissipation are discussed. Particular applications to dissociating diatomic gases and gases displaying vibrational relaxation are considered. A criterion in the form of an inequality is derived for the validity of the high-frequency approximation and an asymptotic analysis is developed.
Scattering of gravity waves by a circular dock
Authors: Miles John , Gilbert Freeman
Published: March 2006

The scattering of a gravity wave of wave number k by a circular dock of radius a and draft d – h in water of depth d is calculated through a variational approximation. The total and differential scattering cross-sections, the peripheral displacement, and the lateral force on the dock are presented as functions of ka with d/a and h/d as parameters and compared with the classical results for a circular cylinder (h = 0). A pronounced resonance is found near ka = 2 for certain values of d/a and h/d.
Viscoelastic properties of fine-grained incompressible turbulence
Authors: Crow S. C.
Published: March 2006

A number of shear-flow phenomena can be explained qualitatively if turbulence is regarded as a continuous viscoelastic medium with respect to its action on a mean field. Conditions are sought under which the analogy is quantitative, and it is found that the turbulence must be fine-grained and the mean field weak. For geometrical convenience the turbulence is assumed to be nearly homogeneous and isotropic so that body forces are required to maintain it. The turbulence is found to respond initially to an arbitrary deformation as an elastic medium, in which Reynolds stress is linearly proportional to strain. Three processes that cause the resulting Reynolds stress to relax are distinguished: viscous diffusion, body-force agitation and non-linear scrambling. It is argued that, regardless of which process dominates, Reynolds stress evolves in a continuously changing mean field according to a viscoelastic constitutive law, relating stress to deformation history by means of a scalar memory function. The argument is carried through analytically for weak turbulence, in which non-linear scrambling is negligible, and the memory function is computed in terms of the wave-number-frequency spectrum of the background turbulence. In the course of the analysis, a new type of Reynolds stress arises related to the passage of the turbulence through its sustaining environment of body forces. It is found that the mean field must be surprisingly weak for this ‘translation stress’ to be negligible. Applications of the viscoelasticity theory of turbulent shear flow are discussed in which body forces and therefore translation stress are absent.
The stability of thermally stratified plane Poiseuille flow
Authors: Gage K. S. , Reid W. H.
Published: March 2006

In studying the stability of a thermally stratified fluid in the presence of a viscous shear flow, we have a situation in which there is an important interaction between the mechanism of instability due to the stratification and the Tollmien-Schlichting mechanism due to the shear. A complete analysis has been carried out for the Bénard problem in the presence of a plane Poiseuille flow and it is shown that, although Squire's transformation can be used to reduce the three-dimensional problem to an equivalent two-dimensional one, a theorem of Squire's type does not follow unless the Richardson number exceeds a certain small negative value. This conclusion follows from the fact that, when the stratification is unstable and the Prandtl number is unity, the equivalent two-dimensional problem becomes identical mathematically to the stability problem for spiral flow between rotating cylinders and, from the known results for the spiral flow problem, Squire's transformation can then be used to obtain the complete three-dimensional stability boundary. For the case of stable stratification, however, Squire's theorem is valid and the instability is of the usual Tollmien—Schlichting type. Additional calculations have been made for this case which show that the flow is completely stabilized when the Richardson number exceeds a certain positive value.
A note on the static stability of an elastico-viscous fluid
Authors: Craik Alex. D. D.
Published: March 2006

A recent analysis by Gupta (1967) suggests that a layer of elastico-viscous fluid at rest between parallel plane boundaries may be in unstable equilibrium. This surprising result is attributable to the inadequacy of the constitutive equation adopted by Gupta as the basis for his analysis. An alternative constitutive relation, which takes account of the entire strain-history of the motion, leads to the more reasonable result that the equilibrium is stable whenever the fluid has a ‘fading memory’.
On the singular points in the laminar two-dimensional near wake flow field
Authors: Weinbaum Sheldon
Published: March 2006

It is shown that useful information concerning the flow in the neighbourhood of the various separation and stagnation points in the laminar near wake of a blunt-based two-dimensional wedge can be learned from the locally valid Stokes type series solutions to the incompressible Navier-Stokes vorticity equation derived previously by Dean & Montagnon (1949) and Moffatt (1964). This theory, which is in qualitative agreement with the experiments of Hama (1967) and Donaldson (1967), shows that the flow separates from the base of a blunt-based body and not from its trailing edge. The series solution for the two-dimensional stagnation point is treated in detail and compared with Howarth's (1934) numerical solution in order to study the convergence and conditions for completeness of the Stokes type series solution. Finally, the wake rear stagnation point is examined to provide insight into the problem of wake closure.
On the potential distribution resulting from flow across a magnetic field projecting from a plane wall
Authors: Baker Roger C.
Published: March 2006

When a fluid of low conductivity flows parallel to a plane wall from behind which projects a magnetic field, an electric potential field is established throughout the fluid. In this paper the potential field is obtained explicitly in terms of the velocity field when the latter is unidirectional and depends only on the coordinate normal to the wall. Experiments with a variety of velocity profiles are described, and the agreement with the theory is satisfactory. The effect of slow variation of the profiles in the direction of the flow is considered, and is shown to be unimportant under the conditions of the experiments.
A note on the spin-up of a stratified fluid
Authors: Holton James R. , Stone Peter H.
Published: March 2006

It is pointed out that recent theoretical results for the spin-up of a continuously stratified fluid with insulating boundary conditions are at variance with experiment. However, it is then shown that the theoretical analysis contains an inconsistent scaling assumption, so that the apparent contradiction is not a real one. The nature of the spin-up as shown by the experiments is briefly described.
An analytical and experimental investigation of the velocities of particles entrained by the gas flow in nozzles
Authors: Neilson John H. , Gilchrist Alastair
Published: March 2006

Among the parameters which determine the erosion damage sustained by the walls of a nozzle, in which a mixture of gas and particles is flowing is the speed attained by the particle before collision with the wall surface. This work is concerned with the determination of the particle velocity, and a number of relationships are given from which the variation in particle velocity can be obtained for a variety of gas conditions. The changes of state and velocity of the gas, occasioned by the interchange of heat and work between the gas and the particles are dependent on the ratio of the mass flow rate of particles to the mass flow rate of gas. It is shown that if this ratio is small the particle velocity may be obtained without serious error by assuming that the gas conditions are not affected by the presence of particles. Figures for the limiting value of this ratio for certain flows are given. The effects of particle size, density and initial relative velocity are investigated analytically and experimentally.
Non-linear capillary instability of a liquid jet
Authors: Yuen Man-Chuen
Published: March 2006

A third-order theory has been developed to study capillary instability of a liquid jet. The result shows that the asymmetrical development of an initially sinusoidal wave is a non-linear effect with generation of higher harmonics as well as feedback into the fundamental. The growth of the surface wave is found to depend explicitly on the dimensionless initial amplitude of the disturbance and the dimensionless wave-number k of the wave. For the same initial disturbance, the wave is found to have a maximum growth rate at k = 0·7 in agreement with the linearized theory. For the same wave-number, the growth is proportional to the initial amplitude of the disturbance. The cut-off wave-number and the fundamental frequency (or growth rate for the unstable case) of the wave for a given k are found to be different from the linearized theory. Furthermore, at the cut-off wave-number, the present theory shows the disturbance experiences a growth which is proportional to t2. The excellent agreement between Donnelly & Glaberson's experiment and Rayleigh's linearized theory is found to be due to their method of measurement.
On the stability against shear waves of steady flows of non-linear viscoelastic fluids
Authors: Coleman Bernard D. , Gurtin Morton E.
Published: March 2006

A shear-acceleration wave is a propagating singular surface across which the velocity vector and the normal component of the acceleration are continuous, while the tangential component$\dot{v}$of the acceleration suffers a jump discontinuity [$\dot{v}$]. We here discuss plane-rectilinear shearing flows of general, non-linear, incompressible simple fluids with fading memory. Working within the framework of such planar motions, we derive a general and exact formula for the time-dependence of the amplitudea= [$\dot{v}$] of a shear-acceleration wave propagating into a region undergoing a steady but not necessarily homogeneous shearing flow. When this expression is specialized to the case in which the velocity gradient is constant in space ahead of the wave, it assumes a form familiar in the theory of longitudinal acceleration waves in compressible materials with fading memory (cf., e.g., Coleman & Gurtin 1965, equation (4.12)).

In earlier work (1965) we observed that a planar shear-acceleration wave cannot grow in amplitude if it is propagating into a fluid in a state of equilibrium. It is clear from our present results that if the fluid ahead of the wave is being sheared, |a(t)| not only increases, but can approach infinity in a finite time, provideda(0) is of proper sign and |a(0)| exceeds a certain critical amplitude. We expect this critical amplitude to decrease as the rate of shear ahead of the wave is increased.
The behaviour of a stable salinity gradient heated from below
Authors: Turner J. S.
Published: March 2006

The motions resulting when a linear, stable salt gradient is heated uniformly and at a steady rate from below are investigated theoretically and by laboratory experiment. A convecting, growing layer is first formed whose depth, temperature and salinity differences from the fluid above, are all increasing as t½. The way in which these quantities depend on the salinity gradient and heating rate is also predicted, and verified experimentally. A stability criterion is then developed which describes the breakdown of the diffusive boundary layer ahead of the advancing front, and leads to an expression for the thickness of the bottom layer when a second layer forms above it. The predicted form of dependence of layer thickness on the given parameters is again borne out by the experiments.
The Galerkin method applied to convective instability problems
Authors: Finlayson Bruce A.
Published: March 2006

The Galerkin method is applied in a new way to problems of stationary and oscillatory convective instability. By retaining the time derivatives in the equations rather than assuming an exponential time-dependence, the exact solution is approximated by the solution to a set of ordinary differential equations in time. Computations are simplified because the stability of this set of equations can be determined without finding the detailed solution. Furthermore, both stationary and oscillatory instability can be studied by means of the same trial functions. Previous studies which have treated only stationary instability by the Galerkin method can now be extended easily to include oscillatory instability. The method is illustrated for convective instability of a rotating fluid layer transferring heat.
Solitary waves in trapezoidal channels
Authors: Peregrine D. H.
Published: March 2006

Experimental measurements were made of the variation of water-surface height across the crests of solitary waves travelling along trapezoidal channels. The channels had one vertical side and the other side sloped at either 30°, 45° or 60° to the vertical. Reliable results were not obtained with the last channel, but for the other channels there was reasonable agreement with recent theoretical results.
Laboratory investigation of non-steady penetrative convection
Authors: Deardorff J. W. , Willis G. E. , Lilly D. K.
Published: March 2006

Laboratory experiments of non-steady penetrative convection in water are performed that closely simulate the lifting of an atmospheric inversion above heated ground. Vertical profiles of horizontally averaged temperature and heat flux are measured and interpreted. The rate at which kinetic energy is destroyed by the downward heat flux in the vicinity of the inversion base is found to be a very small fraction of the rate at which it is generated in the lower convective region. The interface separating the convective region from the stable region is examined and its rate of rise explained.
Centrifugally driven thermal convection in a rotating cylinder
Authors: Homsy G. M. , Hudson J. L.
Published: March 2006

Thermally induced convection in a rotating cylinder of fluid heated from above and strongly influenced by centrifugal accelerations is treated using boundary-layer methods. As in the theory of homogeneous rotating fluids, the horizontal Ekman layers control the inviscid axial flow. The solution also largely depends upon the thermal conditions assumed at the side wall, and if these be insulated, consideration of the side-wall boundary layers is necessary for complete specification of the problem. For perfectly conducting side walls, the side layers do not influence the zeroth-order flow, but contribute a second-order correction, which would be absent if the lateral boundaries were ignored. The critical parameters governing the solutions in both cases are found to be γ and the group σβε−½, where γ is the aspect ratio, σ the Prandtl number, ε the Ekman number, and β the thermal Rossby number for the flow. Boundary-layer solutions are given for a wide range of parameters, and gravity is seen to have at most only a local effect on the flow near the side walls.
A point explosion in a cold exponential atmosphere
Authors: Laumbach Dallas D. , Probstein Ronald F.
Published: March 2006

The problem considered is that of a strong shock propagating from a point energy source into a cold atmosphere whose density varies exponentially with altitude. An explicit analytic solution is obtained by taking the flow field as ‘locally radial’ and using an integral method with an energy constraint. A scaling law is given which eliminates the parametric dependence of the solution on the explosion energy, scale height, and atmospheric density at the point of the explosion. The scaling law also transforms the infinity of solutions for various polar angles into two distinct solutions which show that all motions of the ascending portion of the shock may be scaled from the vertically upward behaviour and all motions of the descending portion of the shock may be scaled from the vertically downward behaviour. The limit in the lateral direction of both of the fundamental solutions corresponds to the case of the uniform density atmosphere. The results for the uniform density atmosphere show remarkable agreement with the exact Taylor—Sedov results. Comparison with finite difference calculations of Troutman & Davis for the vertically upward and downward directions shows excellent agreement with respect to the prediction of shock propagation velocity, position, and the flow variables behind the shock. A scaling law for the time, shock velocity, and pressure for different values of the adiabatic exponent γ is proposed which correlates the results of the present analysis for different values of γ over the entire range of shock positions where the analysis applies. The solution shows that, contrary to the result obtained by Kompaneets, there is no theoretical limit as to how far downward a strong shock may propagate. The far field behaviour of the shock wave in the upward and downward directions is found to be of the same form as the self-similar asymptotic solutions obtained by Raizer for a plane shock. It is shown by relaxing the energy constraint in the vertically downward direction that the asymptotic result obtained agrees closely with that obtained by Raizer. The energy constraint, however, is the appropriate one for all but the far field behaviour. The far field limit of the present solution in the upward direction is found to compare favourably with the approximate asymptotic calculations of Hayes for an ascending curved shock. The empirical concept of ‘modified Sachs scaling’ for calculating the overpressure is considered and shown within this model to have a justification in the downward direction but a limited range of applicability in the upward direction.
Large-amplitude motions of a liquid—vapour interface in an accelerating container
Authors: Perko L. M.
Published: March 2006

This paper considers the large-amplitude symmetric and asymmetric irrota-tional motion of an inviscid incompressible fluid with a liquid—vapour interface in an accelerating container of revolution. A combined analytical—numerical method which involves no linearizations in the hydrodynamical equations and applies to all but surface-tension dominated motions is used to compute a variety of such motions. One important aspect of this non-linear method is that it accurately determines the initial development of surface instabilities such as breakers near the wall of the container.
An analysis of second-order effects on laminar boundary-layer flow
Authors: Honda M. , Kiyokawa Y.
Published: March 2006

Treated in the present paper are the second-order effects, i.e. the effect of displacement thickness, longitudinal curvature, external shear and slip, on the two-dimensional laminar boundary-layer flow of incompressible fluid. The analysis is developed in terms of the stream-function co-ordinates proposed for the analysis of the rotational flow by the senior author previously. An inverse problem is set in the co-ordinates plane, and, within the framework of the second-order approximation, the problem is reduced to solving a parabolic partial differential equation for the total head. An implicit finite-difference scheme is then devised to solve the equation, and the practical computations are carried out for the flow along a flat plate or the one around a parabolic body, by making use of an electronic computer.
Linear theory of the circulation of a stratified ocean
Authors: Pedlosky Joseph
Published: March 2006

A linear model of the circulation of a stratified ocean, in a closed basin, driven by both wind stress and heating is presented. Particular attention is given to the interdependence of the primary features of the oceanic circulation. The upwelling process is studied in detail and it is shown that the complete determination of the mid-ocean thermocline solution depends on the upwelling in the boundary layers on the ocean basin's side walls. The morphology of the side wall boundary layers as a function of the stratification is also discussed.
Axisymmetric internal waves generated by a travelling oscillating body
Authors: Stevenson T. N.
Published: March 2006

Experiments are presented in which axisymmetric internal waves are generated by an oscillating sphere moving vertically in a stably stratified salt solution. The Reynolds numbers for the sphere based on the diameter and the mean velocity are between 10 and 200. Lighthill's theory for dispersive waves is used to calculate the phase configuration of the internal waves. The agreement between experiment and theory is reasonably good.
Effect of modulation on the onset of thermal convection
Authors: Venezian Giulio
Published: March 2006

The stability of a horizontal layer of fluid heated from below is examined when, in addition to a steady temperature difference between the walls of the layer, a time-dependent sinusoidal perturbation is applied to the wall temperatures. Only infinitesimal disturbances are considered. The effects of the oscillating temperature field are treated by a perturbation expansion in powers of the amplitude of the applied field. The shift in the critical Rayleigh number is calculated as a function of frequency, and it is found that it is possible to advance or delay the onset of convection by time modulation of the wall temperatures.
Wave-number selection at finite amplitude in rotating Couette flow
Authors: Snyder H. A.
Published: March 2006

Measurements have been made of the wavelength of Taylor vortices between rotating cylinders. It is shown that the relaxation time of such a vortex system is approximatelyL2/6v, whereLis the length of the vortex column andvis the kinematic viscosity. Previous measurements reported in the literature have not been steady-state measurements because of the long relaxation time. The present data are accurate to 1% and extend to 40 times the critical Taylor number. The variation of wavelength with Taylor number is linear and the slope is exceedingly small and negative. The non-uniqueness of wave-number observed by Coles (1965) in doubly periodic flows is here shown to occur in the rotationally symmetric case. It is argued that variational methods are inapplicable in determining the wave-number of finite-amplitude secondary flows. The experimental results show that the wave-number is determined uniquely by the initial conditions of the system. It is suggested that any method which neglects the time-dependent behaviour of the system cannot select the final state from the manifold of solutions which occur in non-linear problems.
Acoustic energy flux from shock-turbulence interaction
Authors: Ribner H. S.
Published: March 2006

The analysis of the sound field generated by the passage of isotropic turbulence through a shock of finite strength (Ribner 1953, 1954) has been extended to provide the flux of acoustic energy emanating from unit area on the downstream side of the shock. This is motivated by the problem of estimating the sound power emerging from a supersonic jet containing shock waves. The energy flux is found to vary almost linearly with shock density ratio, reaching a maximum at infinite Mach number of 0[sdot ]062 of the flux of turbulence kinetic energy convected into unit area of the shock.

Direct comparison with a result obtained by Lighthill (1953) is misleading. His energy relations, reckoned relative to a frame moving with the fluid, must be converted to the shock-fixed frame used herein. The converted results of his theory (weak shocks) and the results of our theory (arbitrary shocks) appear to show a similar asymptotic behaviour for vanishing shock strength; they diverge with increasing shock strength.
The effect of pressure gradient on the law of the wall in turbulent flow
Authors: Mcdonald Henry
Published: March 2006

The effect of a streamwise pressure gradient on the velocity profile in the viscous sublayer of a turbulent flow along a smooth wall in two-dimensional flow is estimated. In the analysis, a similarity argument is used and the necessary empirical information obtained from a constant pressure flow. An allowance is made for the departure from the wall value of the gradient of total shear stress normal to the wall. The results of analysis were used to generate new additive constants for use with Townsend's modified law of the wall velocity profile and subsequently Townsend's profile is found to be in good agreement with the measured velocity profiles in an adverse pressure gradient.
Change in wave-form and mean flow associated with wavelength variations in rotating Couette flow. Part 1
Authors: Snyder H. A.
Published: March 2006

When rotating Couette flow becomes unstable a periodic vortex structure is formed. For the wide-gap case, this flow is steady for a rather large range of the Taylor number above onset. In the region of finite amplitude instability the wave-numbers of the periodic structure are not unique. It is shown empirically that the non-uniqueness is not an end effect but a bonafide property of the flow and that the wave-form is a unique function of the wavelength. Data is presented to demonstrate the interval over which the wave-numbers can be varied when the parameters of the system are fixed. The large effect on the wave-form of small changes in the wavelength is also illustrated. These conclusions are based on extensive measurements of the azimuthal drift velocity for a particular mode of secondary flow.
Experimental studies in magneto-fluid dynamics: flow over a sphere with a cylindrical afterbody
Authors: Maxworthy T.
Published: March 2006

The measured pressure distributions over the front hemisphere of a hemispherecylinder combination placed in an aligned fields magneto-fluid dynamic flow are presented. Integration of the pressure profiles show that the form or pressure drag of the composite body first increases as the magnetic field strength increases, at a fixed flow velocity, but then decreases as the magnetic field becomes still stronger.
The temporal development of a model of high Rayleigh number convection
Authors: Elder J. W.
Published: March 2006

The evolution of a model of the flow in a layer of fluid suddenly heated from below at a Rayleigh number sufficient for a laboratory flow to ultimately become turbulent is investigated with numerical experiments. The numerical study simulates the flow by means of the mean field equations along the lines of Herring's (1963, 1964) pioneering study but uses a different finite difference technique and concentrates attention on the flow development rather than on the final statistically steady state. These solutions are compared with previous and some new simulations in two dimensions. The solutions confirm Herring's work and in addition show that the mean field equations, and in particular the weak-coupling approximations, describe the gross features of the model sufficiently well for the mean field equations to be used with reasonable confidence in evolutionary studies.
The effect of buoyancy forces on the boundary-layer flow over a semi-infinite vertical flat plate in a uniform free stream
Authors: Merkin J. H.
Published: March 2006

The boundary-layer flow over a semi-infinite vertical flat plate, heated to a constant temperature in a uniform free stream, is discussed in the two cases when the buoyancy forces aid and oppose the development of the boundary layer. In the former case, two series solutions are obtained, one of which is valid near the leading edge and the other is valid asymptotically. An accurate numerical method is used to describe the flow in the region where the series are not valid. In the latter case, a series, valid near the leading edge is obtained and it is extended by a numerical method to the point where the boundary layer is shown to separate.
Mixed region collapse with internal wave generation in a density-stratified medium
Authors: Wu Jin
Published: March 2006

An experiment has been conducted modelling a two-dimensional mixed region collapsing in a continuously density-stratified medium. The process of collapse can be divided into three stages. Empirical formulae have been derived to describe the process of the first two stages, during which gravitational effects determine the modelling criterion. The collapse in the final stage is complicated by viscous effects; a ratio between the Froude number and the Reynolds number seems to provide a probable modification of the time scale.

The pattern of internal waves generated by the initial impulsive collapse of this mixed region can be represented by moving rays connecting either wave crests or troughs. These rays move away from the collapse centre and at the same time decrease their slopes from the horizontal. A simpler steady-state wave pattern generated by an oscillating plunger has also been studied. Taken together, these experimental results are interpreted to show that the energy density of the collapse is skewed toward high frequencies and is peaked at 8/10 of the Brunt-Väisälä frequency of the medium.
An analytical and experimental investigation of the trajectories of particles entrained by the gas flow in nozzles
Authors: Neilson John H. , Gilchrist Alastair
Published: March 2006

Among the parameters which determine the erosion damage sustained by the walls of a nozzle in which a mixture of gas and particles is flowing, is the angle between the direction of the particle flow and the wall surface at the moment of impact. In this work an approximate analytical solution is made for a number of gas particle flows to determine broadly the features on which particle trajectory depends and some experimental results are given which confirm the theoretical computations. It is shown that the divergent region of a conical nozzle is unlikely to suffer a severe particle attack but that for parallel flow convergent-divergent nozzles the convex region near the exit may be affected. The choke, on the other hand, is most susceptible to particle attack even by fairly small particles. It may be said, in general, that any particle which enters the choke section with a velocity which, in the absence of effects from the gas would allow the particle to strike the choke wall, will in fact hit the wall at some point along the length of the choke.
On fluctuating flow of an elastico-viscous fluid past an infinite plate with variable suction
Authors: Soundalgekar V. M. , Puri Pratap
Published: March 2006

An exact solution is obtained for the two-dimensional flow of an elastico-viscous (Walters fluid B’) incompressible fluid past an infinite porous wall under the following conditions: (i) the suction velocity normal to the plate oscillates in magnitude but not in direction about a non-zero mean; (ii) the free-stream velocity oscillates in time about a constant mean.

The response of the skin-friction to the fluctuating stream and suction velocity is studied for variations in the suction parameter A, the elasticity parameter k and the frequency parameter μ. It is found that the back-flow at the wall is enhanced by k. For the same value of A, the amplitude of the skin-friction decreases with increasing k. Also an increase in k and μ leads to a decrease in the phase of the skin-friction. For moderately large A and k, the phase of the skin-friction may be completely negative.
The structure of shock-waves in gas mixtures
Authors: Goldman Edward , Sirovich Lawrence
Published: March 2006

The structure of shock-waves in gas mixtures is studied. The separation of component velocities and temperatures is described. Velocity overshoot is never found to exist. Other effects, namely, temperature overshoot and undershoot and velocity undershoot are shown to exist in a manner which is self-consistent with the derivation of the governing equations.
Mass flow rate for nearly-free molecular slit flow
Authors: Stewart J. Daniel
Published: March 2006

The local and average mass flow rates for nearly free molecular flow through a two-dimensional slit are determined for several tank pressure ratios. The equilibrium gas in the two tanks and the container walls are assumed to be at the same temperature and the Willis iterative method with the Bhatnager-Gross-Krook model is used for the analysis. The results for an infinite pressure ratio are also presented in order to illustrate the effects of a finite pressure ratio.
An experimental investigation of thermosolutal convection at marginal stability
Authors: Shirtcliffe T. G. L.
Published: March 2006

Experiments are described in which the stability of a liquid stabilized by a gradient of concentration of a solute has been investigated. In all the cases observed, convection began at marginal stability with an oscillatory motion. The boundary of stability in the (R, Rs)-plane departs somewhat from that predicted by the simplest theories; the boundary is a curve, concave to the origin, and the critical Rayleigh number is high. The total rate of transport of solute increases much more rapidly than that of heat when the oscillations begin. The motions begin in cells which are separate from one another.